id	sid	tid	token	lemma	pos
bracis-28360	1	1	d	d	X
bracis-28360	1	2	-	-	PUNCT
bracis-28360	1	3	cc	cc	NOUN
bracis-28360	1	4	integrals	integral	NOUN
bracis-28360	1	5	:	:	PUNCT
bracis-28360	1	6	generalizing	generalize	VERB
bracis-28360	1	7	cc	cc	NOUN
bracis-28360	1	8	-	-	NOUN
bracis-28360	1	9	integrals	integral	NOUN
bracis-28360	1	10	by	by	ADP
bracis-28360	1	11	 	 	SPACE
bracis-28360	1	12	restricted	restrict	VERB
bracis-28360	1	13	dissimilarity	dissimilarity	NOUN
bracis-28360	1	14	functions	function	NOUN
bracis-28360	1	15	with	with	ADP
bracis-28360	1	16	 	 	SPACE
bracis-28360	1	17	applications	application	NOUN
bracis-28360	1	18	to	to	PART
bracis-28360	1	19	 	 	SPACE
bracis-28360	1	20	fuzzy	fuzzy	ADJ
bracis-28360	1	21	-	-	PUNCT
bracis-28360	1	22	rule	rule	NOUN
bracis-28360	1	23	based	base	VERB
bracis-28360	1	24	systems	system	NOUN
bracis-28360	1	25	|	|	ADP
bracis-28360	1	26	springer	springer	NOUN
bracis-28360	1	27	nature	nature	PROPN
bracis-28360	1	28	link	link	PROPN
bracis-28360	1	29	(	(	PUNCT
bracis-28360	1	30	formerly	formerly	ADV
bracis-28360	1	31	springerlink	springerlink	NOUN
bracis-28360	1	32	)	)	PUNCT
bracis-28360	1	33	skip	skip	VERB
bracis-28360	1	34	to	to	ADP
bracis-28360	1	35	main	main	ADJ
bracis-28360	1	36	content	content	NOUN
bracis-28360	1	37	advertisement	advertisement	NOUN
bracis-28360	1	38	log	log	NOUN
bracis-28360	1	39	in	in	ADP
bracis-28360	1	40	menu	menu	NOUN
bracis-28360	1	41	find	find	VERB
bracis-28360	1	42	a	a	DET
bracis-28360	1	43	journal	journal	NOUN
bracis-28360	1	44	publish	publish	VERB
bracis-28360	1	45	with	with	ADP
bracis-28360	1	46	us	we	PRON
bracis-28360	1	47	track	track	VERB
bracis-28360	1	48	your	your	PRON
bracis-28360	1	49	research	research	NOUN
bracis-28360	1	50	search	search	NOUN
bracis-28360	1	51	cart	cart	NOUN
bracis-28360	1	52	home	home	NOUN
bracis-28360	1	53	intelligent	intelligent	ADJ
bracis-28360	1	54	systems	system	NOUN
bracis-28360	1	55	conference	conference	NOUN
bracis-28360	1	56	paper	paper	NOUN
bracis-28360	2	1	d	d	NOUN
bracis-28360	2	2	-	-	PUNCT
bracis-28360	2	3	cc	cc	NOUN
bracis-28360	2	4	integrals	integral	NOUN
bracis-28360	2	5	:	:	PUNCT
bracis-28360	2	6	generalizing	generalize	VERB
bracis-28360	2	7	cc	cc	NOUN
bracis-28360	2	8	-	-	NOUN
bracis-28360	2	9	integrals	integral	NOUN
bracis-28360	2	10	by	by	ADP
bracis-28360	2	11	 	 	SPACE
bracis-28360	2	12	restricted	restrict	VERB
bracis-28360	2	13	dissimilarity	dissimilarity	NOUN
bracis-28360	2	14	functions	function	NOUN
bracis-28360	2	15	with	with	ADP
bracis-28360	2	16	 	 	SPACE
bracis-28360	2	17	applications	application	NOUN
bracis-28360	2	18	to	to	PART
bracis-28360	2	19	 	 	SPACE
bracis-28360	2	20	fuzzy	fuzzy	ADJ
bracis-28360	2	21	-	-	PUNCT
bracis-28360	2	22	rule	rule	NOUN
bracis-28360	2	23	based	base	VERB
bracis-28360	2	24	systems	system	NOUN
bracis-28360	2	25	conference	conference	NOUN
bracis-28360	2	26	paper	paper	NOUN
bracis-28360	2	27	first	first	ADV
bracis-28360	2	28	online	online	ADV
bracis-28360	2	29	:	:	PUNCT
bracis-28360	2	30	12	12	NUM
bracis-28360	2	31	october	october	NOUN
bracis-28360	2	32	2023	2023	NUM
bracis-28360	2	33	pp	pp	ADP
bracis-28360	2	34	243–258	243–258	NUM
bracis-28360	2	35	cite	cite	VERB
bracis-28360	2	36	this	this	DET
bracis-28360	2	37	conference	conference	NOUN
bracis-28360	2	38	paper	paper	NOUN
bracis-28360	2	39	access	access	NOUN
bracis-28360	2	40	provided	provide	VERB
bracis-28360	2	41	by	by	ADP
bracis-28360	2	42	university	university	PROPN
bracis-28360	2	43	of	of	ADP
bracis-28360	2	44	notre	notre	PROPN
bracis-28360	2	45	dame	dame	PROPN
bracis-28360	2	46	hesburgh	hesburgh	PROPN
bracis-28360	2	47	library	library	PROPN
bracis-28360	2	48	download	download	PROPN
bracis-28360	2	49	book	book	NOUN
bracis-28360	2	50	pdf	pdf	PROPN
bracis-28360	2	51	download	download	NOUN
bracis-28360	2	52	book	book	NOUN
bracis-28360	2	53	epub	epub	PROPN
bracis-28360	2	54	intelligent	intelligent	ADJ
bracis-28360	2	55	systems	system	NOUN
bracis-28360	2	56	(	(	PUNCT
bracis-28360	2	57	bracis	bracis	NOUN
bracis-28360	2	58	2023	2023	NUM
bracis-28360	2	59	)	)	PUNCT
bracis-28360	3	1	d	d	X
bracis-28360	3	2	-	-	PUNCT
bracis-28360	3	3	cc	cc	NOUN
bracis-28360	3	4	integrals	integral	NOUN
bracis-28360	3	5	:	:	PUNCT
bracis-28360	3	6	generalizing	generalize	VERB
bracis-28360	3	7	cc	cc	NOUN
bracis-28360	3	8	-	-	NOUN
bracis-28360	3	9	integrals	integral	NOUN
bracis-28360	3	10	by	by	ADP
bracis-28360	3	11	 	 	SPACE
bracis-28360	3	12	restricted	restrict	VERB
bracis-28360	3	13	dissimilarity	dissimilarity	NOUN
bracis-28360	3	14	functions	function	NOUN
bracis-28360	3	15	with	with	ADP
bracis-28360	3	16	 	 	SPACE
bracis-28360	3	17	applications	application	NOUN
bracis-28360	3	18	to	to	PART
bracis-28360	3	19	 	 	SPACE
bracis-28360	3	20	fuzzy	fuzzy	ADJ
bracis-28360	3	21	-	-	PUNCT
bracis-28360	3	22	rule	rule	NOUN
bracis-28360	3	23	based	base	VERB
bracis-28360	3	24	systems	system	NOUN
bracis-28360	3	25	download	download	NOUN
bracis-28360	3	26	book	book	NOUN
bracis-28360	3	27	pdf	pdf	PROPN
bracis-28360	3	28	download	download	NOUN
bracis-28360	3	29	book	book	PROPN
bracis-28360	3	30	epub	epub	PROPN
bracis-28360	3	31	joelson	joelson	PROPN
bracis-28360	3	32	sartori	sartori	PROPN
bracis-28360	3	33	  	  	SPACE
bracis-28360	3	34	orcid	orcid	PROPN
bracis-28360	3	35	:	:	PUNCT
bracis-28360	3	36	orcid.org/0000-0001-5379-82539	orcid.org/0000-0001-5379-82539	NOUN
bracis-28360	3	37	,	,	PUNCT
bracis-28360	3	38	giancarlo	giancarlo	PROPN
bracis-28360	3	39	lucca	lucca	PROPN
bracis-28360	3	40	  	  	SPACE
bracis-28360	3	41	orcid	orcid	NOUN
bracis-28360	3	42	:	:	PUNCT
bracis-28360	3	43	orcid.org/0000-0002-3776-02609	orcid.org/0000-0002-3776-02609	NOUN
bracis-28360	3	44	,	,	PUNCT
bracis-28360	3	45	tiago	tiago	PROPN
bracis-28360	3	46	asmus	asmus	PROPN
bracis-28360	3	47	  	  	SPACE
bracis-28360	3	48	orcid	orcid	NOUN
bracis-28360	3	49	:	:	PUNCT
bracis-28360	3	50	orcid.org/0000-0002-7066-715610	orcid.org/0000-0002-7066-715610	PROPN
bracis-28360	3	51	,	,	PUNCT
bracis-28360	3	52	helida	helida	PROPN
bracis-28360	3	53	santos	santos	PROPN
bracis-28360	3	54	  	  	SPACE
bracis-28360	3	55	orcid	orcid	NOUN
bracis-28360	3	56	:	:	PUNCT
bracis-28360	3	57	orcid.org/0000-0003-2994-28629	orcid.org/0000-0003-2994-28629	PROPN
bracis-28360	3	58	,	,	PUNCT
bracis-28360	3	59	eduardo	eduardo	PROPN
bracis-28360	3	60	borges	borges	PROPN
bracis-28360	3	61	  	  	SPACE
bracis-28360	3	62	orcid	orcid	NOUN
bracis-28360	3	63	:	:	PUNCT
bracis-28360	3	64	orcid.org/0000-0003-1595-76769	orcid.org/0000-0003-1595-76769	NOUN
bracis-28360	3	65	,	,	PUNCT
bracis-28360	3	66	benjamin	benjamin	PROPN
bracis-28360	3	67	bedregal	bedregal	PROPN
bracis-28360	3	68	  	  	SPACE
bracis-28360	3	69	orcid	orcid	NOUN
bracis-28360	3	70	:	:	PUNCT
bracis-28360	3	71	orcid.org/0000-0002-6757-793411	orcid.org/0000-0002-6757-793411	ADJ
bracis-28360	3	72	,	,	PUNCT
bracis-28360	3	73	humberto	humberto	PROPN
bracis-28360	3	74	bustince	bustince	NOUN
bracis-28360	3	75	  	  	SPACE
bracis-28360	3	76	orcid	orcid	NOUN
bracis-28360	3	77	:	:	PUNCT
bracis-28360	3	78	orcid.org/0000-0002-1279-619512	orcid.org/0000-0002-1279-619512	NOUN
bracis-28360	3	79	&	&	CCONJ
bracis-28360	3	80	…	…	PUNCT
bracis-28360	3	81	graçaliz	graçaliz	PROPN
bracis-28360	3	82	pereira	pereira	PROPN
bracis-28360	3	83	dimuro	dimuro	PROPN
bracis-28360	3	84	  	  	SPACE
bracis-28360	3	85	orcid	orcid	NOUN
bracis-28360	3	86	:	:	PUNCT
bracis-28360	3	87	orcid.org/0000-0001-6986-98889	orcid.org/0000-0001-6986-98889	NOUN
bracis-28360	3	88	  	  	SPACE
bracis-28360	3	89	show	show	VERB
bracis-28360	3	90	authors	author	NOUN
bracis-28360	3	91	part	part	NOUN
bracis-28360	3	92	of	of	ADP
bracis-28360	3	93	the	the	DET
bracis-28360	3	94	book	book	NOUN
bracis-28360	3	95	series	series	NOUN
bracis-28360	3	96	:	:	PUNCT
bracis-28360	3	97	lecture	lecture	NOUN
bracis-28360	3	98	notes	note	NOUN
bracis-28360	3	99	in	in	ADP
bracis-28360	3	100	computer	computer	NOUN
bracis-28360	3	101	science	science	NOUN
bracis-28360	3	102	(	(	PUNCT
bracis-28360	3	103	(	(	PUNCT
bracis-28360	3	104	lnai	lnai	ADJ
bracis-28360	3	105	,	,	PUNCT
bracis-28360	3	106	volume	volume	NOUN
bracis-28360	3	107	14195	14195	NUM
bracis-28360	3	108	)	)	PUNCT
bracis-28360	3	109	)	)	PUNCT
bracis-28360	3	110	included	include	VERB
bracis-28360	3	111	in	in	ADP
bracis-28360	3	112	the	the	DET
bracis-28360	3	113	following	follow	VERB
bracis-28360	3	114	conference	conference	NOUN
bracis-28360	3	115	series	series	NOUN
bracis-28360	3	116	:	:	PUNCT
bracis-28360	3	117	brazilian	brazilian	ADJ
bracis-28360	3	118	conference	conference	NOUN
bracis-28360	3	119	on	on	ADP
bracis-28360	3	120	intelligent	intelligent	ADJ
bracis-28360	3	121	systems	system	NOUN
bracis-28360	3	122	573	573	NUM
bracis-28360	3	123	accesses	access	NOUN
bracis-28360	3	124	6	6	NUM
bracis-28360	3	125	citations	citation	NOUN
bracis-28360	3	126	abstract	abstract	ADJ
bracis-28360	3	127	the	the	DET
bracis-28360	3	128	discrete	discrete	ADJ
bracis-28360	3	129	choquet	choquet	NOUN
bracis-28360	3	130	integral	integral	ADJ
bracis-28360	3	131	(	(	PUNCT
bracis-28360	3	132	ci	ci	NOUN
bracis-28360	3	133	)	)	PUNCT
bracis-28360	3	134	and	and	CCONJ
bracis-28360	3	135	its	its	PRON
bracis-28360	3	136	generalizations	generalization	NOUN
bracis-28360	3	137	have	have	AUX
bracis-28360	3	138	been	be	AUX
bracis-28360	3	139	successfully	successfully	ADV
bracis-28360	3	140	applied	apply	VERB
bracis-28360	3	141	in	in	ADP
bracis-28360	3	142	many	many	ADJ
bracis-28360	3	143	different	different	ADJ
bracis-28360	3	144	fields	field	NOUN
bracis-28360	3	145	,	,	PUNCT
bracis-28360	3	146	with	with	ADP
bracis-28360	3	147	particularly	particularly	ADV
bracis-28360	3	148	good	good	ADJ
bracis-28360	3	149	results	result	NOUN
bracis-28360	3	150	when	when	SCONJ
bracis-28360	3	151	considered	consider	VERB
bracis-28360	3	152	in	in	ADP
bracis-28360	3	153	fuzzy	fuzzy	ADJ
bracis-28360	3	154	rule	rule	NOUN
bracis-28360	3	155	-	-	PUNCT
bracis-28360	3	156	based	base	VERB
bracis-28360	3	157	classification	classification	NOUN
bracis-28360	3	158	systems	system	NOUN
bracis-28360	3	159	(	(	PUNCT
bracis-28360	3	160	frbcss	frbcss	ADJ
bracis-28360	3	161	)	)	PUNCT
bracis-28360	3	162	.	.	PUNCT
bracis-28360	4	1	one	one	NUM
bracis-28360	4	2	of	of	ADP
bracis-28360	4	3	those	those	DET
bracis-28360	4	4	functions	function	NOUN
bracis-28360	4	5	is	be	AUX
bracis-28360	4	6	the	the	DET
bracis-28360	4	7	cc	cc	NOUN
bracis-28360	4	8	-	-	NOUN
bracis-28360	4	9	integral	integral	ADJ
bracis-28360	4	10	,	,	PUNCT
bracis-28360	4	11	where	where	SCONJ
bracis-28360	4	12	the	the	DET
bracis-28360	4	13	product	product	NOUN
bracis-28360	4	14	operations	operation	NOUN
bracis-28360	4	15	in	in	ADP
bracis-28360	4	16	the	the	DET
bracis-28360	4	17	expanded	expand	VERB
bracis-28360	4	18	form	form	NOUN
bracis-28360	4	19	of	of	ADP
bracis-28360	4	20	the	the	DET
bracis-28360	4	21	ci	ci	NOUN
bracis-28360	4	22	are	be	AUX
bracis-28360	4	23	generalized	generalize	VERB
bracis-28360	4	24	by	by	ADP
bracis-28360	4	25	copulas	copula	NOUN
bracis-28360	4	26	.	.	PUNCT
bracis-28360	5	1	recently	recently	ADV
bracis-28360	5	2	,	,	PUNCT
bracis-28360	5	3	some	some	DET
bracis-28360	5	4	new	new	ADJ
bracis-28360	5	5	choquet	choquet	NOUN
bracis-28360	5	6	-	-	PUNCT
bracis-28360	5	7	like	like	ADJ
bracis-28360	5	8	operators	operator	NOUN
bracis-28360	5	9	were	be	AUX
bracis-28360	5	10	developed	develop	VERB
bracis-28360	5	11	by	by	ADP
bracis-28360	5	12	generalizing	generalize	VERB
bracis-28360	5	13	the	the	DET
bracis-28360	5	14	difference	difference	NOUN
bracis-28360	5	15	operation	operation	NOUN
bracis-28360	5	16	by	by	ADP
bracis-28360	5	17	a	a	DET
bracis-28360	5	18	restricted	restricted	ADJ
bracis-28360	5	19	dissimilarity	dissimilarity	NOUN
bracis-28360	5	20	function	function	NOUN
bracis-28360	5	21	(	(	PUNCT
bracis-28360	5	22	rdf	rdf	NOUN
bracis-28360	5	23	)	)	PUNCT
bracis-28360	5	24	in	in	ADP
bracis-28360	5	25	either	either	CCONJ
bracis-28360	5	26	the	the	DET
bracis-28360	5	27	usual	usual	ADJ
bracis-28360	5	28	or	or	CCONJ
bracis-28360	5	29	the	the	DET
bracis-28360	5	30	expanded	expand	VERB
bracis-28360	5	31	form	form	NOUN
bracis-28360	5	32	of	of	ADP
bracis-28360	5	33	the	the	DET
bracis-28360	5	34	original	original	ADJ
bracis-28360	5	35	ci	ci	NOUN
bracis-28360	5	36	,	,	PUNCT
bracis-28360	5	37	also	also	ADV
bracis-28360	5	38	providing	provide	VERB
bracis-28360	5	39	good	good	ADJ
bracis-28360	5	40	results	result	NOUN
bracis-28360	5	41	in	in	ADP
bracis-28360	5	42	practical	practical	ADJ
bracis-28360	5	43	applications	application	NOUN
bracis-28360	5	44	.	.	PUNCT
bracis-28360	6	1	so	so	ADV
bracis-28360	6	2	,	,	PUNCT
bracis-28360	6	3	motivated	motivate	VERB
bracis-28360	6	4	by	by	ADP
bracis-28360	6	5	such	such	ADJ
bracis-28360	6	6	developments	development	NOUN
bracis-28360	6	7	,	,	PUNCT
bracis-28360	6	8	in	in	ADP
bracis-28360	6	9	this	this	DET
bracis-28360	6	10	paper	paper	NOUN
bracis-28360	6	11	we	we	PRON
bracis-28360	6	12	propose	propose	VERB
bracis-28360	6	13	the	the	DET
bracis-28360	6	14	generalization	generalization	NOUN
bracis-28360	6	15	of	of	ADP
bracis-28360	6	16	the	the	DET
bracis-28360	6	17	cc	cc	NOUN
bracis-28360	6	18	-	-	NOUN
bracis-28360	6	19	integral	integral	ADJ
bracis-28360	6	20	by	by	ADP
bracis-28360	6	21	means	mean	NOUN
bracis-28360	6	22	of	of	ADP
bracis-28360	6	23	rdfs	rdfs	NOUN
bracis-28360	6	24	,	,	PUNCT
bracis-28360	6	25	resulting	result	VERB
bracis-28360	6	26	in	in	ADP
bracis-28360	6	27	a	a	DET
bracis-28360	6	28	function	function	NOUN
bracis-28360	6	29	that	that	PRON
bracis-28360	6	30	we	we	PRON
bracis-28360	6	31	call	call	VERB
bracis-28360	6	32	d	d	PROPN
bracis-28360	6	33	-	-	PUNCT
bracis-28360	6	34	cc	cc	NOUN
bracis-28360	6	35	-	-	NOUN
bracis-28360	6	36	integral	integral	ADJ
bracis-28360	6	37	.	.	PUNCT
bracis-28360	7	1	we	we	PRON
bracis-28360	7	2	study	study	VERB
bracis-28360	7	3	some	some	DET
bracis-28360	7	4	relevant	relevant	ADJ
bracis-28360	7	5	properties	property	NOUN
bracis-28360	7	6	of	of	ADP
bracis-28360	7	7	this	this	DET
bracis-28360	7	8	new	new	ADJ
bracis-28360	7	9	definition	definition	NOUN
bracis-28360	7	10	,	,	PUNCT
bracis-28360	7	11	focusing	focus	VERB
bracis-28360	7	12	on	on	ADP
bracis-28360	7	13	its	its	PRON
bracis-28360	7	14	monotonicity	monotonicity	NOUN
bracis-28360	7	15	-	-	PUNCT
bracis-28360	7	16	like	like	ADJ
bracis-28360	7	17	behavior	behavior	NOUN
bracis-28360	7	18	.	.	PUNCT
bracis-28360	8	1	then	then	ADV
bracis-28360	8	2	,	,	PUNCT
bracis-28360	8	3	we	we	PRON
bracis-28360	8	4	proceed	proceed	VERB
bracis-28360	8	5	to	to	PART
bracis-28360	8	6	apply	apply	VERB
bracis-28360	8	7	d	d	PROPN
bracis-28360	8	8	-	-	PUNCT
bracis-28360	8	9	cc	cc	NOUN
bracis-28360	8	10	-	-	PUNCT
bracis-28360	8	11	integrals	integral	NOUN
bracis-28360	8	12	in	in	ADP
bracis-28360	8	13	a	a	DET
bracis-28360	8	14	classification	classification	NOUN
bracis-28360	8	15	problem	problem	NOUN
bracis-28360	8	16	,	,	PUNCT
bracis-28360	8	17	comparing	compare	VERB
bracis-28360	8	18	different	different	ADJ
bracis-28360	8	19	d	d	PROPN
bracis-28360	8	20	-	-	PUNCT
bracis-28360	8	21	cc	cc	NOUN
bracis-28360	8	22	-	-	PUNCT
bracis-28360	8	23	integrals	integral	NOUN
bracis-28360	8	24	between	between	ADP
bracis-28360	8	25	them	they	PRON
bracis-28360	8	26	.	.	PUNCT
bracis-28360	9	1	the	the	DET
bracis-28360	9	2	classification	classification	NOUN
bracis-28360	9	3	acuity	acuity	NOUN
bracis-28360	9	4	of	of	ADP
bracis-28360	9	5	the	the	DET
bracis-28360	9	6	best	good	ADJ
bracis-28360	9	7	d	d	ADJ
bracis-28360	9	8	-	-	PUNCT
bracis-28360	9	9	cc	cc	ADJ
bracis-28360	9	10	-	-	ADJ
bracis-28360	9	11	integral	integral	ADJ
bracis-28360	9	12	surpasses	surpasse	NOUN
bracis-28360	9	13	the	the	DET
bracis-28360	9	14	one	one	NOUN
bracis-28360	9	15	achieved	achieve	VERB
bracis-28360	9	16	by	by	ADP
bracis-28360	9	17	the	the	DET
bracis-28360	9	18	best	good	ADJ
bracis-28360	9	19	cc	cc	NOUN
bracis-28360	9	20	-	-	ADJ
bracis-28360	9	21	integral	integral	ADJ
bracis-28360	9	22	and	and	CCONJ
bracis-28360	9	23	is	be	AUX
bracis-28360	9	24	statistically	statistically	ADV
bracis-28360	9	25	equivalent	equivalent	ADJ
bracis-28360	9	26	to	to	ADP
bracis-28360	9	27	the	the	DET
bracis-28360	9	28	state	state	NOUN
bracis-28360	9	29	-	-	PUNCT
bracis-28360	9	30	of	of	ADP
bracis-28360	9	31	-	-	PUNCT
bracis-28360	9	32	the	the	DET
bracis-28360	9	33	-	-	PUNCT
bracis-28360	9	34	art	art	NOUN
bracis-28360	9	35	in	in	ADP
bracis-28360	9	36	frbcss	frbcss	ADJ
bracis-28360	9	37	.	.	PUNCT
bracis-28360	10	1	this	this	DET
bracis-28360	10	2	research	research	NOUN
bracis-28360	10	3	was	be	AUX
bracis-28360	10	4	funded	fund	VERB
bracis-28360	10	5	by	by	ADP
bracis-28360	10	6	fapergs	fapergs	PROPN
bracis-28360	10	7	/	/	SYM
bracis-28360	10	8	brazil	brazil	PROPN
bracis-28360	10	9	(	(	PUNCT
bracis-28360	10	10	proc	proc	NOUN
bracis-28360	10	11	.	.	PUNCT
bracis-28360	11	1	19/2551	19/2551	PROPN
bracis-28360	11	2	-	-	SYM
bracis-28360	11	3	0001660	0001660	NUM
bracis-28360	11	4	-	-	SYM
bracis-28360	11	5	3	3	NUM
bracis-28360	11	6	,	,	PUNCT
bracis-28360	11	7	23/2551	23/2551	NUM
bracis-28360	11	8	-	-	SYM
bracis-28360	11	9	0000126	0000126	NUM
bracis-28360	11	10	-	-	SYM
bracis-28360	11	11	8)	8)	NUM
bracis-28360	11	12	,	,	PUNCT
bracis-28360	11	13	cnpq	cnpq	PROPN
bracis-28360	11	14	/	/	SYM
bracis-28360	11	15	brazil	brazil	PROPN
bracis-28360	11	16	(	(	PUNCT
bracis-28360	11	17	301618/2019	301618/2019	NUM
bracis-28360	11	18	-	-	SYM
bracis-28360	11	19	4	4	NUM
bracis-28360	11	20	,	,	PUNCT
bracis-28360	11	21	305805/2021	305805/2021	NUM
bracis-28360	11	22	-	-	SYM
bracis-28360	11	23	5	5	NUM
bracis-28360	11	24	,	,	PUNCT
bracis-28360	11	25	150160/	150160/	NUM
bracis-28360	11	26	2023	2023	NUM
bracis-28360	11	27	-	-	SYM
bracis-28360	11	28	2	2	NUM
bracis-28360	11	29	)	)	PUNCT
bracis-28360	11	30	.	.	PUNCT
bracis-28360	12	1	access	access	NOUN
bracis-28360	12	2	provided	provide	VERB
bracis-28360	12	3	by	by	ADP
bracis-28360	12	4	university	university	PROPN
bracis-28360	12	5	of	of	ADP
bracis-28360	12	6	notre	notre	PROPN
bracis-28360	12	7	dame	dame	PROPN
bracis-28360	12	8	hesburgh	hesburgh	PROPN
bracis-28360	12	9	library	library	PROPN
bracis-28360	12	10	.	.	PUNCT
bracis-28360	13	1	download	download	PROPN
bracis-28360	13	2	conference	conference	NOUN
bracis-28360	13	3	paper	paper	NOUN
bracis-28360	13	4	pdf	pdf	NOUN
bracis-28360	13	5	similar	similar	ADJ
bracis-28360	13	6	content	content	NOUN
bracis-28360	13	7	being	be	AUX
bracis-28360	13	8	viewed	view	VERB
bracis-28360	13	9	by	by	ADP
bracis-28360	13	10	others	other	NOUN
bracis-28360	13	11	cmin	cmin	NOUN
bracis-28360	13	12	-	-	PUNCT
bracis-28360	13	13	integral	integral	ADJ
bracis-28360	13	14	:	:	PUNCT
bracis-28360	13	15	a	a	DET
bracis-28360	13	16	choquet	choquet	ADJ
bracis-28360	13	17	-	-	PUNCT
bracis-28360	13	18	like	like	ADJ
bracis-28360	13	19	aggregation	aggregation	NOUN
bracis-28360	13	20	function	function	NOUN
bracis-28360	13	21	based	base	VERB
bracis-28360	13	22	on	on	ADP
bracis-28360	13	23	the	the	DET
bracis-28360	13	24	minimum	minimum	ADJ
bracis-28360	13	25	t	t	NOUN
bracis-28360	13	26	-	-	PUNCT
bracis-28360	13	27	norm	norm	NOUN
bracis-28360	13	28	for	for	ADP
bracis-28360	13	29	applications	application	NOUN
bracis-28360	13	30	to	to	PART
bracis-28360	13	31	fuzzy	fuzzy	ADJ
bracis-28360	13	32	rule	rule	NOUN
bracis-28360	13	33	-	-	PUNCT
bracis-28360	13	34	based	base	VERB
bracis-28360	13	35	classification	classification	NOUN
bracis-28360	13	36	systems	system	NOUN
bracis-28360	13	37	chapter	chapter	NOUN
bracis-28360	13	38	©	©	PROPN
bracis-28360	13	39	2018	2018	NUM
bracis-28360	13	40	dissimilarity	dissimilarity	NOUN
bracis-28360	13	41	based	base	VERB
bracis-28360	13	42	choquet	choquet	NOUN
bracis-28360	13	43	integrals	integral	NOUN
bracis-28360	13	44	chapter	chapter	NOUN
bracis-28360	13	45	©	©	PROPN
bracis-28360	13	46	2020	2020	NUM
bracis-28360	13	47	a	a	DET
bracis-28360	13	48	way	way	NOUN
bracis-28360	13	49	to	to	ADP
bracis-28360	13	50	proper	proper	ADJ
bracis-28360	13	51	generalization	generalization	NOUN
bracis-28360	13	52	of	of	ADP
bracis-28360	13	53	\(\phi	\(\phi	NOUN
bracis-28360	13	54	\)-divergence	\)-divergence	NUM
bracis-28360	13	55	based	base	VERB
bracis-28360	13	56	on	on	ADP
bracis-28360	13	57	choquet	choquet	NOUN
bracis-28360	13	58	derivatives	derivative	NOUN
bracis-28360	13	59	article	article	NOUN
bracis-28360	13	60	12	12	NUM
bracis-28360	13	61	september	september	PROPN
bracis-28360	13	62	2022	2022	NUM
bracis-28360	13	63	explore	explore	VERB
bracis-28360	13	64	related	relate	VERB
bracis-28360	13	65	subjects	subject	NOUN
bracis-28360	13	66	discover	discover	VERB
bracis-28360	13	67	the	the	DET
bracis-28360	13	68	latest	late	ADJ
bracis-28360	13	69	articles	article	NOUN
bracis-28360	13	70	,	,	PUNCT
bracis-28360	13	71	books	book	NOUN
bracis-28360	13	72	and	and	CCONJ
bracis-28360	13	73	news	news	NOUN
bracis-28360	13	74	in	in	ADP
bracis-28360	13	75	related	related	ADJ
bracis-28360	13	76	subjects	subject	NOUN
bracis-28360	13	77	,	,	PUNCT
bracis-28360	13	78	suggested	suggest	VERB
bracis-28360	13	79	using	use	VERB
bracis-28360	13	80	machine	machine	NOUN
bracis-28360	13	81	learning	learning	NOUN
bracis-28360	13	82	.	.	PUNCT
bracis-28360	14	1	functions	function	NOUN
bracis-28360	14	2	of	of	ADP
bracis-28360	14	3	a	a	DET
bracis-28360	14	4	complex	complex	ADJ
bracis-28360	14	5	variable	variable	ADJ
bracis-28360	14	6	measure	measure	NOUN
bracis-28360	14	7	and	and	CCONJ
bracis-28360	14	8	integration	integration	NOUN
bracis-28360	14	9	real	real	ADJ
bracis-28360	14	10	functions	function	NOUN
bracis-28360	14	11	special	special	ADJ
bracis-28360	14	12	functions	function	NOUN
bracis-28360	14	13	stochastic	stochastic	NOUN
bracis-28360	14	14	integrals	integral	NOUN
bracis-28360	14	15	integral	integral	ADJ
bracis-28360	14	16	transforms	transform	NOUN
bracis-28360	14	17	and	and	CCONJ
bracis-28360	14	18	operational	operational	ADJ
bracis-28360	14	19	calculus	calculus	NOUN
bracis-28360	14	20	1	1	NUM
bracis-28360	14	21	introduction	introduction	NOUN
bracis-28360	14	22	the	the	DET
bracis-28360	14	23	discrete	discrete	ADJ
bracis-28360	14	24	choquet	choquet	NOUN
bracis-28360	14	25	integral	integral	ADJ
bracis-28360	14	26	(	(	PUNCT
bracis-28360	14	27	ci	ci	NOUN
bracis-28360	14	28	)	)	PUNCT
bracis-28360	14	29	is	be	AUX
bracis-28360	14	30	an	an	DET
bracis-28360	14	31	interesting	interesting	ADJ
bracis-28360	14	32	aggregation	aggregation	NOUN
bracis-28360	14	33	operator	operator	NOUN
bracis-28360	14	34	that	that	PRON
bracis-28360	14	35	can	can	AUX
bracis-28360	14	36	capture	capture	VERB
bracis-28360	14	37	the	the	DET
bracis-28360	14	38	relationship	relationship	NOUN
bracis-28360	14	39	between	between	ADP
bracis-28360	14	40	the	the	DET
bracis-28360	14	41	aggregated	aggregate	VERB
bracis-28360	14	42	data	datum	NOUN
bracis-28360	14	43	by	by	ADP
bracis-28360	14	44	means	mean	NOUN
bracis-28360	14	45	of	of	ADP
bracis-28360	14	46	a	a	DET
bracis-28360	14	47	fuzzy	fuzzy	ADJ
bracis-28360	14	48	measure	measure	NOUN
bracis-28360	14	49	(	(	PUNCT
bracis-28360	14	50	fm	fm	NOUN
bracis-28360	14	51	)	)	PUNCT
bracis-28360	15	1	[	[	X
bracis-28360	15	2	10	10	NUM
bracis-28360	15	3	]	]	PUNCT
bracis-28360	15	4	.	.	PUNCT
bracis-28360	16	1	it	it	PRON
bracis-28360	16	2	has	have	AUX
bracis-28360	16	3	been	be	AUX
bracis-28360	16	4	successfully	successfully	ADV
bracis-28360	16	5	applied	apply	VERB
bracis-28360	16	6	in	in	ADP
bracis-28360	16	7	many	many	ADJ
bracis-28360	16	8	different	different	ADJ
bracis-28360	16	9	fields	field	NOUN
bracis-28360	16	10	,	,	PUNCT
bracis-28360	16	11	such	such	ADJ
bracis-28360	16	12	as	as	ADP
bracis-28360	16	13	decision	decision	NOUN
bracis-28360	16	14	-	-	PUNCT
bracis-28360	16	15	making	making	NOUN
bracis-28360	16	16	[	[	X
bracis-28360	16	17	13	13	NUM
bracis-28360	16	18	,	,	PUNCT
bracis-28360	16	19	29	29	NUM
bracis-28360	16	20	]	]	PUNCT
bracis-28360	16	21	,	,	PUNCT
bracis-28360	16	22	classification	classification	NOUN
bracis-28360	16	23	[	[	X
bracis-28360	16	24	13	13	NUM
bracis-28360	16	25	,	,	PUNCT
bracis-28360	16	26	28	28	NUM
bracis-28360	16	27	]	]	PUNCT
bracis-28360	16	28	and	and	CCONJ
bracis-28360	16	29	image	image	NOUN
bracis-28360	16	30	processing	processing	NOUN
bracis-28360	16	31	[	[	X
bracis-28360	16	32	24	24	NUM
bracis-28360	16	33	]	]	PUNCT
bracis-28360	16	34	.	.	PUNCT
bracis-28360	17	1	this	this	PRON
bracis-28360	17	2	yielded	yield	VERB
bracis-28360	17	3	the	the	DET
bracis-28360	17	4	theoretical	theoretical	ADJ
bracis-28360	17	5	development	development	NOUN
bracis-28360	17	6	of	of	ADP
bracis-28360	17	7	several	several	ADJ
bracis-28360	17	8	generalizations	generalization	NOUN
bracis-28360	17	9	[	[	X
bracis-28360	17	10	13	13	NUM
bracis-28360	17	11	]	]	PUNCT
bracis-28360	17	12	of	of	ADP
bracis-28360	17	13	the	the	DET
bracis-28360	17	14	ci	ci	NOUN
bracis-28360	17	15	,	,	PUNCT
bracis-28360	17	16	such	such	ADJ
bracis-28360	17	17	as	as	ADP
bracis-28360	17	18	the	the	DET
bracis-28360	17	19	cc	cc	NOUN
bracis-28360	17	20	-	-	ADJ
bracis-28360	17	21	integral	integral	ADJ
bracis-28360	17	22	[	[	X
bracis-28360	17	23	22	22	NUM
bracis-28360	17	24	]	]	PUNCT
bracis-28360	17	25	(	(	PUNCT
bracis-28360	17	26	a	a	DET
bracis-28360	17	27	generalization	generalization	NOUN
bracis-28360	17	28	by	by	ADP
bracis-28360	17	29	copulas	copula	NOUN
bracis-28360	17	30	[	[	X
bracis-28360	17	31	3	3	NUM
bracis-28360	17	32	]	]	PUNCT
bracis-28360	17	33	)	)	PUNCT
bracis-28360	17	34	and	and	CCONJ
bracis-28360	17	35	\(c_{f_1f_2}\)-integral	\(c_{f_1f_2}\)-integral	ADJ
bracis-28360	17	36	[	[	X
bracis-28360	17	37	19	19	NUM
bracis-28360	17	38	]	]	PUNCT
bracis-28360	17	39	(	(	PUNCT
bracis-28360	17	40	a	a	DET
bracis-28360	17	41	generalization	generalization	NOUN
bracis-28360	17	42	by	by	ADP
bracis-28360	17	43	fusion	fusion	NOUN
bracis-28360	17	44	functions	function	NOUN
bracis-28360	17	45	\(f_1\	\(f_1\	PROPN
bracis-28360	17	46	)	)	PUNCT
bracis-28360	17	47	and	and	CCONJ
bracis-28360	17	48	\(f_2\	\(f_2\	PROPN
bracis-28360	17	49	)	)	PUNCT
bracis-28360	17	50	under	under	ADP
bracis-28360	17	51	some	some	DET
bracis-28360	17	52	constraints	constraint	NOUN
bracis-28360	17	53	)	)	PUNCT
bracis-28360	17	54	,	,	PUNCT
bracis-28360	17	55	all	all	PRON
bracis-28360	17	56	of	of	ADP
bracis-28360	17	57	them	they	PRON
bracis-28360	17	58	providing	provide	VERB
bracis-28360	17	59	at	at	ADP
bracis-28360	17	60	least	least	ADJ
bracis-28360	17	61	competitive	competitive	ADJ
bracis-28360	17	62	results	result	NOUN
bracis-28360	17	63	when	when	SCONJ
bracis-28360	17	64	applied	apply	VERB
bracis-28360	17	65	in	in	ADP
bracis-28360	17	66	practical	practical	ADJ
bracis-28360	17	67	problems	problem	NOUN
bracis-28360	17	68	.	.	PUNCT
bracis-28360	18	1	in	in	ADP
bracis-28360	18	2	particular	particular	ADJ
bracis-28360	18	3	,	,	PUNCT
bracis-28360	18	4	fuzzy	fuzzy	ADJ
bracis-28360	18	5	rule	rule	NOUN
bracis-28360	18	6	-	-	PUNCT
bracis-28360	18	7	based	base	VERB
bracis-28360	18	8	classification	classification	NOUN
bracis-28360	18	9	systems	system	NOUN
bracis-28360	18	10	(	(	PUNCT
bracis-28360	18	11	frbcss	frbcss	ADJ
bracis-28360	18	12	)	)	PUNCT
bracis-28360	18	13	 	 	SPACE
bracis-28360	19	1	[	[	X
bracis-28360	19	2	17	17	NUM
bracis-28360	19	3	]	]	PUNCT
bracis-28360	19	4	,	,	PUNCT
bracis-28360	19	5	which	which	PRON
bracis-28360	19	6	are	be	AUX
bracis-28360	19	7	notable	notable	ADJ
bracis-28360	19	8	for	for	ADP
bracis-28360	19	9	their	their	PRON
bracis-28360	19	10	high	high	ADJ
bracis-28360	19	11	interpretability	interpretability	NOUN
bracis-28360	19	12	while	while	SCONJ
bracis-28360	19	13	still	still	ADV
bracis-28360	19	14	achieving	achieve	VERB
bracis-28360	19	15	good	good	ADJ
bracis-28360	19	16	classification	classification	NOUN
bracis-28360	19	17	results	result	NOUN
bracis-28360	19	18	,	,	PUNCT
bracis-28360	19	19	seem	seem	VERB
bracis-28360	19	20	to	to	PART
bracis-28360	19	21	benefit	benefit	VERB
bracis-28360	19	22	from	from	ADP
bracis-28360	19	23	the	the	DET
bracis-28360	19	24	application	application	NOUN
bracis-28360	19	25	of	of	ADP
bracis-28360	19	26	the	the	DET
bracis-28360	19	27	ci	ci	NOUN
bracis-28360	19	28	and	and	CCONJ
bracis-28360	19	29	their	their	PRON
bracis-28360	19	30	generalizations	generalization	NOUN
bracis-28360	19	31	in	in	ADP
bracis-28360	19	32	the	the	DET
bracis-28360	19	33	aggregation	aggregation	NOUN
bracis-28360	19	34	process	process	NOUN
bracis-28360	19	35	that	that	PRON
bracis-28360	19	36	occur	occur	VERB
bracis-28360	19	37	in	in	ADP
bracis-28360	19	38	the	the	DET
bracis-28360	19	39	reasoning	reasoning	NOUN
bracis-28360	19	40	method	method	NOUN
bracis-28360	19	41	.	.	PUNCT
bracis-28360	20	1	this	this	PRON
bracis-28360	20	2	can	can	AUX
bracis-28360	20	3	be	be	AUX
bracis-28360	20	4	seen	see	VERB
bracis-28360	20	5	in	in	ADP
bracis-28360	20	6	the	the	DET
bracis-28360	20	7	works	work	NOUN
bracis-28360	20	8	of	of	ADP
bracis-28360	20	9	lucca	lucca	PROPN
bracis-28360	20	10	et	et	PROPN
bracis-28360	20	11	al	al	PROPN
bracis-28360	20	12	.	.	PUNCT
bracis-28360	21	1	[	[	X
bracis-28360	21	2	19	19	NUM
bracis-28360	21	3	]	]	PUNCT
bracis-28360	21	4	,	,	PUNCT
bracis-28360	21	5	where	where	SCONJ
bracis-28360	21	6	the	the	DET
bracis-28360	21	7	application	application	NOUN
bracis-28360	21	8	of	of	ADP
bracis-28360	21	9	such	such	ADJ
bracis-28360	21	10	integrals	integral	NOUN
bracis-28360	21	11	produced	produce	VERB
bracis-28360	21	12	results	result	NOUN
bracis-28360	21	13	that	that	PRON
bracis-28360	21	14	rival	rival	VERB
bracis-28360	21	15	the	the	DET
bracis-28360	21	16	state	state	NOUN
bracis-28360	21	17	of	of	ADP
bracis-28360	21	18	the	the	DET
bracis-28360	21	19	art	art	NOUN
bracis-28360	21	20	in	in	ADP
bracis-28360	21	21	frbcss	frbcss	ADJ
bracis-28360	21	22	.	.	PUNCT
bracis-28360	22	1	bustince	bustince	NOUN
bracis-28360	22	2	et	et	PROPN
bracis-28360	22	3	al	al	PROPN
bracis-28360	22	4	.	.	PUNCT
bracis-28360	23	1	[	[	X
bracis-28360	23	2	8	8	NUM
bracis-28360	23	3	]	]	PUNCT
bracis-28360	23	4	generalized	generalize	VERB
bracis-28360	23	5	the	the	DET
bracis-28360	23	6	ci	ci	NOUN
bracis-28360	23	7	using	use	VERB
bracis-28360	23	8	restricted	restrict	VERB
bracis-28360	23	9	dissimilarity	dissimilarity	NOUN
bracis-28360	23	10	functions	function	NOUN
bracis-28360	23	11	(	(	PUNCT
bracis-28360	23	12	rdf	rdf	NOUN
bracis-28360	23	13	)	)	PUNCT
bracis-28360	23	14	,	,	PUNCT
bracis-28360	23	15	in	in	ADP
bracis-28360	23	16	the	the	DET
bracis-28360	23	17	form	form	NOUN
bracis-28360	23	18	of	of	ADP
bracis-28360	23	19	d	d	NOUN
bracis-28360	23	20	-	-	PUNCT
bracis-28360	23	21	integrals	integral	NOUN
bracis-28360	23	22	.	.	PUNCT
bracis-28360	24	1	following	follow	VERB
bracis-28360	24	2	that	that	PRON
bracis-28360	24	3	,	,	PUNCT
bracis-28360	24	4	wieczynski	wieczynski	PROPN
bracis-28360	24	5	et	et	PROPN
bracis-28360	24	6	al	al	PROPN
bracis-28360	24	7	.	.	PROPN
bracis-28360	24	8	studied	study	VERB
bracis-28360	24	9	\(dc_{f}\)-integrals	\(dc_{f}\)-integral	NOUN
bracis-28360	24	10	[	[	X
bracis-28360	24	11	28	28	NUM
bracis-28360	24	12	]	]	PUNCT
bracis-28360	24	13	and	and	CCONJ
bracis-28360	24	14	d	d	X
bracis-28360	24	15	-	-	PUNCT
bracis-28360	24	16	xc	xc	NOUN
bracis-28360	24	17	-	-	PUNCT
bracis-28360	24	18	integrals	integral	NOUN
bracis-28360	24	19	[	[	X
bracis-28360	24	20	29	29	NUM
bracis-28360	24	21	]	]	PUNCT
bracis-28360	24	22	,	,	PUNCT
bracis-28360	24	23	obtaining	obtain	VERB
bracis-28360	24	24	promising	promising	ADJ
bracis-28360	24	25	results	result	NOUN
bracis-28360	24	26	not	not	PART
bracis-28360	24	27	only	only	ADV
bracis-28360	24	28	in	in	ADP
bracis-28360	24	29	decision	decision	NOUN
bracis-28360	24	30	making	making	NOUN
bracis-28360	24	31	and	and	CCONJ
bracis-28360	24	32	classification	classification	NOUN
bracis-28360	24	33	but	but	CCONJ
bracis-28360	24	34	also	also	ADV
bracis-28360	24	35	in	in	ADP
bracis-28360	24	36	signal	signal	ADJ
bracis-28360	24	37	processing	processing	NOUN
bracis-28360	24	38	,	,	PUNCT
bracis-28360	24	39	based	base	VERB
bracis-28360	24	40	on	on	ADP
bracis-28360	24	41	motor	motor	NOUN
bracis-28360	24	42	-	-	PUNCT
bracis-28360	24	43	imagery	imagery	NOUN
bracis-28360	24	44	brain	brain	NOUN
bracis-28360	24	45	-	-	PUNCT
bracis-28360	24	46	computer	computer	NOUN
bracis-28360	24	47	interface	interface	NOUN
bracis-28360	24	48	.	.	PUNCT
bracis-28360	25	1	recently	recently	ADV
bracis-28360	25	2	,	,	PUNCT
bracis-28360	25	3	boczek	boczek	NOUN
bracis-28360	25	4	and	and	CCONJ
bracis-28360	25	5	kaluszka	kaluszka	VERB
bracis-28360	25	6	[	[	X
bracis-28360	25	7	4	4	X
bracis-28360	25	8	]	]	PUNCT
bracis-28360	25	9	introduced	introduce	VERB
bracis-28360	25	10	the	the	DET
bracis-28360	25	11	preliminary	preliminary	ADJ
bracis-28360	25	12	notion	notion	NOUN
bracis-28360	25	13	of	of	ADP
bracis-28360	25	14	the	the	DET
bracis-28360	25	15	extended	extend	VERB
bracis-28360	25	16	choquet	choquet	NOUN
bracis-28360	25	17	-	-	PUNCT
bracis-28360	25	18	sugeno	sugeno	NOUN
bracis-28360	25	19	-	-	PUNCT
bracis-28360	25	20	like	like	ADJ
bracis-28360	25	21	(	(	PUNCT
bracis-28360	25	22	ecs	ecs	NOUN
bracis-28360	25	23	)	)	PUNCT
bracis-28360	25	24	operator	operator	NOUN
bracis-28360	25	25	,	,	PUNCT
bracis-28360	25	26	which	which	PRON
bracis-28360	25	27	generalizes	generalize	VERB
bracis-28360	25	28	most	most	ADJ
bracis-28360	25	29	of	of	ADP
bracis-28360	25	30	the	the	DET
bracis-28360	25	31	modifications	modification	NOUN
bracis-28360	25	32	of	of	ADP
bracis-28360	25	33	the	the	DET
bracis-28360	25	34	ci	ci	NOUN
bracis-28360	25	35	known	know	VERB
bracis-28360	25	36	in	in	ADP
bracis-28360	25	37	the	the	DET
bracis-28360	25	38	literature	literature	NOUN
bracis-28360	25	39	(	(	PUNCT
bracis-28360	25	40	briefly	briefly	ADV
bracis-28360	25	41	discussed	discuss	VERB
bracis-28360	25	42	above	above	ADV
bracis-28360	25	43	)	)	PUNCT
bracis-28360	25	44	,	,	PUNCT
bracis-28360	25	45	and	and	CCONJ
bracis-28360	25	46	also	also	ADV
bracis-28360	25	47	generates	generate	VERB
bracis-28360	25	48	some	some	DET
bracis-28360	25	49	new	new	ADJ
bracis-28360	25	50	ci	ci	NOUN
bracis-28360	25	51	-	-	PUNCT
bracis-28360	25	52	type	type	NOUN
bracis-28360	25	53	operators	operator	NOUN
bracis-28360	25	54	.	.	PUNCT
bracis-28360	26	1	this	this	PRON
bracis-28360	26	2	inspired	inspire	VERB
bracis-28360	26	3	us	we	PRON
bracis-28360	26	4	to	to	PART
bracis-28360	26	5	further	far	ADV
bracis-28360	26	6	research	research	VERB
bracis-28360	26	7	their	their	PRON
bracis-28360	26	8	properties	property	NOUN
bracis-28360	26	9	and	and	CCONJ
bracis-28360	26	10	applications	application	NOUN
bracis-28360	26	11	.	.	PUNCT
bracis-28360	27	1	then	then	ADV
bracis-28360	27	2	,	,	PUNCT
bracis-28360	27	3	the	the	DET
bracis-28360	27	4	objectives	objective	NOUN
bracis-28360	27	5	of	of	ADP
bracis-28360	27	6	this	this	DET
bracis-28360	27	7	paper	paper	NOUN
bracis-28360	27	8	are	be	AUX
bracis-28360	27	9	:	:	PUNCT
bracis-28360	27	10	(	(	PUNCT
bracis-28360	27	11	1	1	X
bracis-28360	27	12	)	)	PUNCT
bracis-28360	27	13	to	to	PART
bracis-28360	27	14	study	study	VERB
bracis-28360	27	15	some	some	DET
bracis-28360	27	16	important	important	ADJ
bracis-28360	27	17	theoretical	theoretical	ADJ
bracis-28360	27	18	properties	property	NOUN
bracis-28360	27	19	of	of	ADP
bracis-28360	27	20	an	an	DET
bracis-28360	27	21	instance	instance	NOUN
bracis-28360	27	22	of	of	ADP
bracis-28360	27	23	the	the	DET
bracis-28360	27	24	ecs	ecs	NOUN
bracis-28360	27	25	-	-	PUNCT
bracis-28360	27	26	operator	operator	NOUN
bracis-28360	27	27	,	,	PUNCT
bracis-28360	27	28	introducing	introduce	VERB
bracis-28360	27	29	a	a	DET
bracis-28360	27	30	generalization	generalization	NOUN
bracis-28360	27	31	of	of	ADP
bracis-28360	27	32	cc	cc	NOUN
bracis-28360	27	33	-	-	NOUN
bracis-28360	27	34	integrals	integral	NOUN
bracis-28360	27	35	by	by	ADP
bracis-28360	27	36	rdfs	rdfs	PROPN
bracis-28360	27	37	,	,	PUNCT
bracis-28360	27	38	called	call	VERB
bracis-28360	27	39	d	d	PROPN
bracis-28360	27	40	-	-	PUNCT
bracis-28360	27	41	cc	cc	NOUN
bracis-28360	27	42	-	-	PUNCT
bracis-28360	27	43	integrals	integral	NOUN
bracis-28360	27	44	(	(	PUNCT
bracis-28360	27	45	sect	sect	NOUN
bracis-28360	27	46	.	.	PUNCT
bracis-28360	27	47	 	 	SPACE
bracis-28360	27	48	3	3	NUM
bracis-28360	27	49	)	)	PUNCT
bracis-28360	27	50	;	;	PUNCT
bracis-28360	27	51	(	(	PUNCT
bracis-28360	27	52	2	2	X
bracis-28360	27	53	)	)	PUNCT
bracis-28360	27	54	to	to	PART
bracis-28360	27	55	apply	apply	VERB
bracis-28360	27	56	d	d	PROPN
bracis-28360	27	57	-	-	PUNCT
bracis-28360	27	58	cc	cc	NOUN
bracis-28360	27	59	-	-	PUNCT
bracis-28360	27	60	integrals	integral	NOUN
bracis-28360	27	61	in	in	ADP
bracis-28360	27	62	frbcss	frbcss	ADJ
bracis-28360	27	63	in	in	ADP
bracis-28360	27	64	an	an	DET
bracis-28360	27	65	experimental	experimental	ADJ
bracis-28360	27	66	study	study	NOUN
bracis-28360	27	67	,	,	PUNCT
bracis-28360	27	68	where	where	SCONJ
bracis-28360	27	69	we	we	PRON
bracis-28360	27	70	compare	compare	VERB
bracis-28360	27	71	the	the	DET
bracis-28360	27	72	classification	classification	NOUN
bracis-28360	27	73	accuracy	accuracy	NOUN
bracis-28360	27	74	of	of	ADP
bracis-28360	27	75	different	different	ADJ
bracis-28360	27	76	d	d	PROPN
bracis-28360	27	77	-	-	PUNCT
bracis-28360	27	78	cc	cc	NOUN
bracis-28360	27	79	-	-	PUNCT
bracis-28360	27	80	integrals	integral	NOUN
bracis-28360	27	81	based	base	VERB
bracis-28360	27	82	on	on	ADP
bracis-28360	27	83	combinations	combination	NOUN
bracis-28360	27	84	of	of	ADP
bracis-28360	27	85	rdfs	rdfs	NOUN
bracis-28360	27	86	and	and	CCONJ
bracis-28360	27	87	copulas	copula	NOUN
bracis-28360	27	88	with	with	ADP
bracis-28360	27	89	the	the	DET
bracis-28360	27	90	best	good	ADJ
bracis-28360	27	91	results	result	NOUN
bracis-28360	27	92	obtained	obtain	VERB
bracis-28360	27	93	by	by	ADP
bracis-28360	27	94	other	other	ADJ
bracis-28360	27	95	approaches	approach	NOUN
bracis-28360	27	96	in	in	ADP
bracis-28360	27	97	the	the	DET
bracis-28360	27	98	literature	literature	NOUN
bracis-28360	27	99	(	(	PUNCT
bracis-28360	27	100	sect	sect	NOUN
bracis-28360	27	101	.	.	PUNCT
bracis-28360	27	102	 	 	SPACE
bracis-28360	27	103	4	4	NUM
bracis-28360	27	104	and	and	CCONJ
bracis-28360	27	105	5	5	NUM
bracis-28360	27	106	)	)	PUNCT
bracis-28360	27	107	.	.	PUNCT
bracis-28360	28	1	additionally	additionally	ADV
bracis-28360	28	2	,	,	PUNCT
bracis-28360	28	3	sect	sect	NOUN
bracis-28360	28	4	.	.	PUNCT
bracis-28360	28	5	 	 	SPACE
bracis-28360	28	6	2	2	NUM
bracis-28360	28	7	recalls	recall	VERB
bracis-28360	28	8	preliminary	preliminary	ADJ
bracis-28360	28	9	concepts	concept	NOUN
bracis-28360	28	10	and	and	CCONJ
bracis-28360	28	11	sect	sect	NOUN
bracis-28360	28	12	.	.	PUNCT
bracis-28360	28	13	 	 	SPACE
bracis-28360	29	1	6	6	NUM
bracis-28360	29	2	is	be	AUX
bracis-28360	29	3	the	the	DET
bracis-28360	29	4	conclusion	conclusion	NOUN
bracis-28360	29	5	.	.	PUNCT
bracis-28360	30	1	2	2	NUM
bracis-28360	30	2	preliminaries	preliminary	NOUN
bracis-28360	30	3	consider	consider	VERB
bracis-28360	30	4	\(n	\(n	NOUN
bracis-28360	30	5	=	=	SYM
bracis-28360	30	6	\{1	\{1	NUM
bracis-28360	30	7	,	,	PUNCT
bracis-28360	30	8	\dots	\dot	NOUN
bracis-28360	30	9	,	,	PUNCT
bracis-28360	30	10	n\}\	n\}\	NOUN
bracis-28360	30	11	)	)	PUNCT
bracis-28360	30	12	,	,	PUNCT
bracis-28360	30	13	with	with	ADP
bracis-28360	30	14	\(n	\(n	NOUN
bracis-28360	30	15	>	>	X
bracis-28360	30	16	0\	0\	PROPN
bracis-28360	30	17	)	)	PUNCT
bracis-28360	30	18	,	,	PUNCT
bracis-28360	30	19	and	and	CCONJ
bracis-28360	30	20	\(\textbf{x}=(x_1,\ldots	\(\textbf{x}=(x_1,\ldot	NOUN
bracis-28360	30	21	,	,	PUNCT
bracis-28360	30	22	x_n)\	x_n)\	PROPN
bracis-28360	30	23	)	)	PUNCT
bracis-28360	30	24	.	.	PUNCT
bracis-28360	31	1	a	a	DET
bracis-28360	31	2	function	function	NOUN
bracis-28360	31	3	\(a	\(a	NOUN
bracis-28360	31	4	:	:	PUNCT
bracis-28360	31	5	[	[	X
bracis-28360	31	6	0,1]^n\rightarrow	0,1]^n\rightarrow	NOUN
bracis-28360	31	7	[	[	X
bracis-28360	31	8	0,1]\	0,1]\	X
bracis-28360	31	9	)	)	PUNCT
bracis-28360	31	10	is	be	AUX
bracis-28360	31	11	an	an	DET
bracis-28360	31	12	aggregation	aggregation	NOUN
bracis-28360	31	13	function	function	NOUN
bracis-28360	31	14	if	if	SCONJ
bracis-28360	31	15	(	(	PUNCT
bracis-28360	31	16	a1	a1	NOUN
bracis-28360	31	17	)	)	PUNCT
bracis-28360	31	18	it	it	PRON
bracis-28360	31	19	is	be	AUX
bracis-28360	31	20	increasing	increase	VERB
bracis-28360	31	21	,	,	PUNCT
bracis-28360	31	22	and	and	CCONJ
bracis-28360	31	23	(	(	PUNCT
bracis-28360	31	24	a2	a2	NOUN
bracis-28360	31	25	)	)	PUNCT
bracis-28360	31	26	\(a(0,\ldots	\(a(0,\ldot	NOUN
bracis-28360	31	27	,	,	PUNCT
bracis-28360	31	28	0)=0\	0)=0\	NUM
bracis-28360	31	29	)	)	PUNCT
bracis-28360	31	30	and	and	CCONJ
bracis-28360	31	31	\(a(1,\ldots	\(a(1,\ldot	NOUN
bracis-28360	31	32	,	,	PUNCT
bracis-28360	31	33	1)=1\	1)=1\	NUM
bracis-28360	31	34	)	)	PUNCT
bracis-28360	31	35	.	.	PUNCT
bracis-28360	32	1	copulas	copula	NOUN
bracis-28360	32	2	are	be	AUX
bracis-28360	32	3	a	a	DET
bracis-28360	32	4	special	special	ADJ
bracis-28360	32	5	type	type	NOUN
bracis-28360	32	6	of	of	ADP
bracis-28360	32	7	aggregation	aggregation	NOUN
bracis-28360	32	8	function	function	NOUN
bracis-28360	32	9	that	that	SCONJ
bracis-28360	32	10	,	,	PUNCT
bracis-28360	32	11	in	in	ADP
bracis-28360	32	12	the	the	DET
bracis-28360	32	13	context	context	NOUN
bracis-28360	32	14	of	of	ADP
bracis-28360	32	15	the	the	DET
bracis-28360	32	16	theory	theory	NOUN
bracis-28360	32	17	of	of	ADP
bracis-28360	32	18	metric	metric	ADJ
bracis-28360	32	19	spaces	space	NOUN
bracis-28360	32	20	,	,	PUNCT
bracis-28360	32	21	link	link	NOUN
bracis-28360	32	22	(	(	PUNCT
bracis-28360	32	23	2	2	NUM
bracis-28360	32	24	-	-	PUNCT
bracis-28360	32	25	dimensional	dimensional	ADJ
bracis-28360	32	26	)	)	PUNCT
bracis-28360	32	27	probability	probability	NOUN
bracis-28360	32	28	distribution	distribution	NOUN
bracis-28360	32	29	functions	function	NOUN
bracis-28360	32	30	to	to	ADP
bracis-28360	32	31	their	their	PRON
bracis-28360	32	32	1	1	NUM
bracis-28360	32	33	-	-	PUNCT
bracis-28360	32	34	dimensional	dimensional	ADJ
bracis-28360	32	35	margins	margin	NOUN
bracis-28360	32	36	.	.	PUNCT
bracis-28360	33	1	a	a	DET
bracis-28360	33	2	bivariate	bivariate	ADJ
bracis-28360	33	3	function	function	NOUN
bracis-28360	33	4	\(c	\(c	NOUN
bracis-28360	33	5	:	:	PUNCT
bracis-28360	34	1	[	[	X
bracis-28360	34	2	0,1]^2	0,1]^2	NUM
bracis-28360	34	3	\rightarrow	\rightarrow	PROPN
bracis-28360	34	4	[	[	X
bracis-28360	34	5	0,1]\	0,1]\	NOUN
bracis-28360	34	6	)	)	PUNCT
bracis-28360	34	7	is	be	AUX
bracis-28360	34	8	a	a	DET
bracis-28360	34	9	copula	copula	NOUN
bracis-28360	34	10	if	if	SCONJ
bracis-28360	34	11	,	,	PUNCT
bracis-28360	34	12	for	for	ADP
bracis-28360	34	13	all	all	DET
bracis-28360	34	14	\(x	\(x	NOUN
bracis-28360	34	15	,	,	PUNCT
bracis-28360	34	16	x',y	x',y	PROPN
bracis-28360	34	17	,	,	PUNCT
bracis-28360	34	18	y	y	PROPN
bracis-28360	34	19	'	'	PUNCT
bracis-28360	34	20	\in	\in	PROPN
bracis-28360	34	21	[	[	X
bracis-28360	34	22	0,1]\	0,1]\	NOUN
bracis-28360	34	23	)	)	PUNCT
bracis-28360	34	24	with	with	ADP
bracis-28360	34	25	\	\	PROPN
bracis-28360	34	26	(	(	PUNCT
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bracis-28360	34	29	x'\	x'\	PROPN
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bracis-28360	34	33	\le	\le	PROPN
bracis-28360	34	34	y'\	y'\	PROPN
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bracis-28360	34	36	(	(	PUNCT
bracis-28360	34	37	c1	c1	NOUN
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bracis-28360	34	39	\(c(x	\(c(x	PROPN
bracis-28360	34	40	,	,	PUNCT
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bracis-28360	34	42	)	)	PUNCT
bracis-28360	34	43	+	+	CCONJ
bracis-28360	34	44	c(x',y	c(x',y	NOUN
bracis-28360	34	45	'	'	PUNCT
bracis-28360	34	46	)	)	PUNCT
bracis-28360	34	47	\ge	\ge	PROPN
bracis-28360	34	48	c(x	c(x	NOUN
bracis-28360	34	49	,	,	PUNCT
bracis-28360	34	50	y	y	NOUN
bracis-28360	34	51	'	'	PUNCT
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bracis-28360	35	1	+	+	CCONJ
bracis-28360	35	2	c(x	c(x	NOUN
bracis-28360	35	3	'	'	PUNCT
bracis-28360	35	4	,	,	PUNCT
bracis-28360	35	5	y)\	y)\	NUM
bracis-28360	35	6	)	)	PUNCT
bracis-28360	35	7	;	;	PUNCT
bracis-28360	35	8	(	(	PUNCT
bracis-28360	35	9	c2	c2	PROPN
bracis-28360	35	10	)	)	PUNCT
bracis-28360	35	11	\(c(x,0	\(c(x,0	PROPN
bracis-28360	35	12	)	)	PUNCT
bracis-28360	35	13	=	=	SYM
bracis-28360	35	14	c(0,x	c(0,x	PROPN
bracis-28360	35	15	)	)	PUNCT
bracis-28360	35	16	=	=	SYM
bracis-28360	35	17	0\	0\	PROPN
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bracis-28360	35	19	;	;	PUNCT
bracis-28360	35	20	(	(	PUNCT
bracis-28360	35	21	c3	c3	PROPN
bracis-28360	35	22	)	)	PUNCT
bracis-28360	35	23	\(c(x,1	\(c(x,1	NOUN
bracis-28360	35	24	)	)	PUNCT
bracis-28360	35	25	=	=	SYM
bracis-28360	35	26	c(1,x	c(1,x	X
bracis-28360	35	27	)	)	PUNCT
bracis-28360	35	28	=	=	SYM
bracis-28360	35	29	x\	x\	NOUN
bracis-28360	35	30	)	)	PUNCT
bracis-28360	36	1	[	[	X
bracis-28360	36	2	3	3	NUM
bracis-28360	36	3	]	]	PUNCT
bracis-28360	36	4	.	.	PUNCT
bracis-28360	37	1	proposition	proposition	NOUN
bracis-28360	37	2	1	1	NUM
bracis-28360	38	1	[	[	X
bracis-28360	38	2	3	3	NUM
bracis-28360	38	3	]	]	PUNCT
bracis-28360	38	4	.	.	PUNCT
bracis-28360	39	1	for	for	ADP
bracis-28360	39	2	each	each	DET
bracis-28360	39	3	copula	copula	NOUN
bracis-28360	39	4	c	c	VERB
bracis-28360	39	5	it	it	PRON
bracis-28360	39	6	holds	hold	VERB
bracis-28360	39	7	that	that	SCONJ
bracis-28360	39	8	:	:	PUNCT
bracis-28360	39	9	(	(	PUNCT
bracis-28360	39	10	i	i	NOUN
bracis-28360	39	11	)	)	PUNCT
bracis-28360	39	12	c	c	PROPN
bracis-28360	39	13	is	be	AUX
bracis-28360	39	14	increasing	increase	VERB
bracis-28360	39	15	;	;	PUNCT
bracis-28360	39	16	(	(	PUNCT
bracis-28360	39	17	ii	ii	NOUN
bracis-28360	39	18	)	)	PUNCT
bracis-28360	39	19	c	c	NOUN
bracis-28360	39	20	satisfies	satisfy	VERB
bracis-28360	39	21	the	the	DET
bracis-28360	39	22	lipschitz	lipschitz	NOUN
bracis-28360	39	23	property	property	NOUN
bracis-28360	39	24	with	with	ADP
bracis-28360	39	25	constant	constant	ADJ
bracis-28360	39	26	1	1	NUM
bracis-28360	39	27	,	,	PUNCT
bracis-28360	39	28	that	that	ADV
bracis-28360	39	29	is	is	ADV
bracis-28360	39	30	,	,	PUNCT
bracis-28360	39	31	for	for	ADP
bracis-28360	39	32	all	all	DET
bracis-28360	39	33	\(x_1,x_2,y_1,y_2	\(x_1,x_2,y_1,y_2	NOUN
bracis-28360	39	34	\in	\in	PROPN
bracis-28360	39	35	[	[	NOUN
bracis-28360	39	36	0,1]\	0,1]\	NOUN
bracis-28360	39	37	)	)	PUNCT
bracis-28360	39	38	,	,	PUNCT
bracis-28360	39	39	one	one	PRON
bracis-28360	39	40	has	have	VERB
bracis-28360	39	41	that	that	PRON
bracis-28360	39	42	\(\mid	\(\mid	ADP
bracis-28360	39	43	c(x_1,y_1	c(x_1,y_1	PROPN
bracis-28360	39	44	)	)	PUNCT
bracis-28360	39	45	c(x_2,y_2	c(x_2,y_2	NOUN
bracis-28360	39	46	)	)	PUNCT
bracis-28360	40	1	\mid	\mid	ADP
bracis-28360	40	2	\le	\le	PROPN
bracis-28360	40	3	\mid	\mid	ADP
bracis-28360	40	4	x_1	x_1	X
bracis-28360	40	5	x_2	x_2	PROPN
bracis-28360	40	6	\mid	\mid	PUNCT
bracis-28360	40	7	+	+	PUNCT
bracis-28360	40	8	\mid	\mid	ADP
bracis-28360	40	9	y_1	y_1	NOUN
bracis-28360	40	10	y_2\mid	y_2\mid	ADP
bracis-28360	40	11	\	\	PROPN
bracis-28360	40	12	)	)	PUNCT
bracis-28360	40	13	.	.	PUNCT
bracis-28360	41	1	table	table	NOUN
bracis-28360	41	2	 	 	SPACE
bracis-28360	41	3	1	1	NUM
bracis-28360	41	4	shows	show	VERB
bracis-28360	41	5	examples	example	NOUN
bracis-28360	41	6	of	of	ADP
bracis-28360	41	7	copulas	copula	NOUN
bracis-28360	41	8	,	,	PUNCT
bracis-28360	41	9	which	which	PRON
bracis-28360	41	10	are	be	AUX
bracis-28360	41	11	used	use	VERB
bracis-28360	41	12	in	in	ADP
bracis-28360	41	13	the	the	DET
bracis-28360	41	14	rest	rest	NOUN
bracis-28360	41	15	of	of	ADP
bracis-28360	41	16	the	the	DET
bracis-28360	41	17	paper	paper	NOUN
bracis-28360	41	18	.	.	PUNCT
bracis-28360	42	1	we	we	PRON
bracis-28360	42	2	divided	divide	VERB
bracis-28360	42	3	them	they	PRON
bracis-28360	42	4	into	into	ADP
bracis-28360	42	5	three	three	NUM
bracis-28360	42	6	groups	group	NOUN
bracis-28360	42	7	:	:	PUNCT
bracis-28360	42	8	t	t	NOUN
bracis-28360	42	9	-	-	PUNCT
bracis-28360	42	10	norms	norm	NOUN
bracis-28360	42	11	[	[	X
bracis-28360	42	12	3	3	NUM
bracis-28360	42	13	]	]	PUNCT
bracis-28360	42	14	,	,	PUNCT
bracis-28360	42	15	overlap	overlap	NOUN
bracis-28360	42	16	functions	function	NOUN
bracis-28360	42	17	[	[	X
bracis-28360	42	18	6	6	NUM
bracis-28360	42	19	]	]	PUNCT
bracis-28360	42	20	,	,	PUNCT
bracis-28360	42	21	and	and	CCONJ
bracis-28360	42	22	copulas	copula	NOUN
bracis-28360	42	23	that	that	PRON
bracis-28360	42	24	are	be	AUX
bracis-28360	42	25	neither	neither	PRON
bracis-28360	42	26	t	t	NOUN
bracis-28360	42	27	-	-	PUNCT
bracis-28360	42	28	norms	norm	NOUN
bracis-28360	42	29	nor	nor	CCONJ
bracis-28360	42	30	overlap	overlap	NOUN
bracis-28360	42	31	functions	function	NOUN
bracis-28360	42	32	.	.	PUNCT
bracis-28360	43	1	table	table	NOUN
bracis-28360	43	2	1	1	NUM
bracis-28360	43	3	.	.	PUNCT
bracis-28360	43	4	example	example	NOUN
bracis-28360	43	5	of	of	ADP
bracis-28360	43	6	copulas	copula	NOUN
bracis-28360	43	7	used	use	VERB
bracis-28360	43	8	as	as	ADP
bracis-28360	43	9	the	the	DET
bracis-28360	43	10	basis	basis	NOUN
bracis-28360	43	11	for	for	ADP
bracis-28360	43	12	the	the	DET
bracis-28360	43	13	d	d	PROPN
bracis-28360	43	14	-	-	PUNCT
bracis-28360	43	15	cc	cc	VERB
bracis-28360	43	16	integralsfull	integralsfull	ADJ
bracis-28360	43	17	size	size	NOUN
bracis-28360	43	18	table	table	NOUN
bracis-28360	43	19	a	a	DET
bracis-28360	43	20	restricted	restricted	ADJ
bracis-28360	43	21	dissimilarity	dissimilarity	NOUN
bracis-28360	43	22	function	function	NOUN
bracis-28360	43	23	(	(	PUNCT
bracis-28360	43	24	rdf	rdf	NOUN
bracis-28360	43	25	)	)	PUNCT
bracis-28360	44	1	[	[	X
bracis-28360	44	2	7	7	X
bracis-28360	44	3	]	]	SYM
bracis-28360	44	4	\(\delta	\(\delta	NOUN
bracis-28360	44	5	:	:	PUNCT
bracis-28360	45	1	[	[	X
bracis-28360	45	2	0,1]^2	0,1]^2	NUM
bracis-28360	45	3	\rightarrow	\rightarrow	PROPN
bracis-28360	45	4	[	[	X
bracis-28360	45	5	0,1]\	0,1]\	NOUN
bracis-28360	45	6	)	)	PUNCT
bracis-28360	45	7	is	be	AUX
bracis-28360	45	8	a	a	DET
bracis-28360	45	9	function	function	NOUN
bracis-28360	45	10	such	such	ADJ
bracis-28360	45	11	that	that	SCONJ
bracis-28360	45	12	,	,	PUNCT
bracis-28360	45	13	for	for	ADP
bracis-28360	45	14	all	all	DET
bracis-28360	45	15	\(x	\(x	NOUN
bracis-28360	45	16	,	,	PUNCT
bracis-28360	45	17	y	y	PROPN
bracis-28360	45	18	,	,	PUNCT
bracis-28360	45	19	z	z	NOUN
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bracis-28360	46	1	[	[	X
bracis-28360	46	2	0,1]\	0,1]\	NUM
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bracis-28360	46	4	(	(	PUNCT
bracis-28360	46	5	d1	d1	NOUN
bracis-28360	46	6	)	)	PUNCT
bracis-28360	46	7	\(\delta	\(\delta	NOUN
bracis-28360	46	8	(	(	PUNCT
bracis-28360	46	9	x	x	NOUN
bracis-28360	46	10	,	,	PUNCT
bracis-28360	46	11	y	y	NOUN
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bracis-28360	46	13	=	=	SYM
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bracis-28360	46	17	,	,	PUNCT
bracis-28360	46	18	x)\	x)\	PROPN
bracis-28360	46	19	)	)	PUNCT
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bracis-28360	46	21	(	(	PUNCT
bracis-28360	46	22	d2	d2	NOUN
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bracis-28360	46	24	\(\delta	\(\delta	NOUN
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bracis-28360	46	31	1\	1\	X
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bracis-28360	46	34	and	and	CCONJ
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bracis-28360	46	39	y\	y\	NOUN
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bracis-28360	46	45	(	(	PUNCT
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bracis-28360	46	48	\(\delta	\(\delta	NOUN
bracis-28360	46	49	(	(	PUNCT
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bracis-28360	46	51	,	,	PUNCT
bracis-28360	46	52	y	y	NOUN
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bracis-28360	46	54	=	=	SYM
bracis-28360	46	55	0\	0\	PROPN
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bracis-28360	46	57	if	if	SCONJ
bracis-28360	47	1	and	and	CCONJ
bracis-28360	47	2	only	only	ADV
bracis-28360	47	3	if	if	SCONJ
bracis-28360	47	4	\(x	\(x	NOUN
bracis-28360	47	5	=	=	SYM
bracis-28360	47	6	y\	y\	NOUN
bracis-28360	47	7	)	)	PUNCT
bracis-28360	47	8	;	;	PUNCT
bracis-28360	47	9	(	(	PUNCT
bracis-28360	47	10	d4	d4	PROPN
bracis-28360	47	11	)	)	PUNCT
bracis-28360	48	1	if	if	SCONJ
bracis-28360	48	2	\(x	\(x	ADJ
bracis-28360	48	3	\le	\le	PROPN
bracis-28360	48	4	y	y	PROPN
bracis-28360	48	5	\le	\le	PROPN
bracis-28360	48	6	z\	z\	NUM
bracis-28360	48	7	)	)	PUNCT
bracis-28360	48	8	,	,	PUNCT
bracis-28360	48	9	then	then	ADV
bracis-28360	48	10	\(\delta	\(\delta	NOUN
bracis-28360	48	11	(	(	PUNCT
bracis-28360	48	12	x	x	NOUN
bracis-28360	48	13	,	,	PUNCT
bracis-28360	48	14	y	y	NOUN
bracis-28360	48	15	)	)	PUNCT
bracis-28360	48	16	\le	\le	PROPN
bracis-28360	48	17	\delta	\delta	PROPN
bracis-28360	48	18	(	(	PUNCT
bracis-28360	48	19	x	x	NOUN
bracis-28360	48	20	,	,	PUNCT
bracis-28360	48	21	z)\	z)\	NUM
bracis-28360	48	22	)	)	PUNCT
bracis-28360	48	23	and	and	CCONJ
bracis-28360	48	24	\(\delta	\(\delta	NOUN
bracis-28360	48	25	(	(	PUNCT
bracis-28360	48	26	y	y	NOUN
bracis-28360	48	27	,	,	PUNCT
bracis-28360	48	28	z	z	NOUN
bracis-28360	48	29	)	)	PUNCT
bracis-28360	48	30	\le	\le	PROPN
bracis-28360	48	31	\delta	\delta	PROPN
bracis-28360	48	32	(	(	PUNCT
bracis-28360	48	33	x	x	NOUN
bracis-28360	48	34	,	,	PUNCT
bracis-28360	48	35	z)\	z)\	NUM
bracis-28360	48	36	)	)	PUNCT
bracis-28360	48	37	.	.	PUNCT
bracis-28360	49	1	one	one	NUM
bracis-28360	49	2	convenient	convenient	ADJ
bracis-28360	49	3	way	way	NOUN
bracis-28360	49	4	of	of	ADP
bracis-28360	49	5	constructing	construct	VERB
bracis-28360	49	6	rdfs	rdfs	NOUN
bracis-28360	49	7	is	be	AUX
bracis-28360	49	8	through	through	ADP
bracis-28360	49	9	automorphisms	automorphisms	PROPN
bracis-28360	49	10	(	(	PUNCT
bracis-28360	49	11	strictly	strictly	ADV
bracis-28360	49	12	increasing	increase	VERB
bracis-28360	49	13	bijections	bijection	NOUN
bracis-28360	49	14	)	)	PUNCT
bracis-28360	49	15	of	of	ADP
bracis-28360	49	16	the	the	DET
bracis-28360	49	17	unit	unit	NOUN
bracis-28360	49	18	interval	interval	NOUN
bracis-28360	49	19	:	:	PUNCT
bracis-28360	49	20	proposition	proposition	NOUN
bracis-28360	49	21	2	2	NUM
bracis-28360	50	1	[	[	X
bracis-28360	50	2	7	7	NUM
bracis-28360	50	3	]	]	PUNCT
bracis-28360	50	4	.	.	PUNCT
bracis-28360	51	1	let	let	VERB
bracis-28360	51	2	\(\varphi	\(\varphi	PUNCT
bracis-28360	51	3	_	_	NOUN
bracis-28360	51	4	1	1	NUM
bracis-28360	51	5	,	,	PUNCT
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bracis-28360	51	7	_	_	NOUN
bracis-28360	51	8	2	2	NUM
bracis-28360	51	9	:	:	PUNCT
bracis-28360	52	1	[	[	X
bracis-28360	52	2	0,1	0,1	NUM
bracis-28360	52	3	]	]	X
bracis-28360	52	4	\rightarrow	\rightarrow	PROPN
bracis-28360	52	5	[	[	X
bracis-28360	52	6	0,1]\	0,1]\	X
bracis-28360	52	7	)	)	PUNCT
bracis-28360	52	8	be	be	VERB
bracis-28360	52	9	two	two	NUM
bracis-28360	52	10	automorphisms	automorphism	NOUN
bracis-28360	52	11	.	.	PUNCT
bracis-28360	53	1	then	then	ADV
bracis-28360	53	2	,	,	PUNCT
bracis-28360	53	3	the	the	DET
bracis-28360	53	4	function	function	NOUN
bracis-28360	53	5	\(\delta	\(\delta	NOUN
bracis-28360	53	6	^{\varphi	^{\varphi	NUM
bracis-28360	53	7	_	_	NOUN
bracis-28360	53	8	1	1	NUM
bracis-28360	53	9	,	,	PUNCT
bracis-28360	53	10	\varphi	\varphi	PROPN
bracis-28360	53	11	_	_	NOUN
bracis-28360	53	12	2	2	NUM
bracis-28360	53	13	}	}	PUNCT
bracis-28360	53	14	:	:	PUNCT
bracis-28360	54	1	[	[	X
bracis-28360	54	2	0,1]^2	0,1]^2	NUM
bracis-28360	54	3	\rightarrow	\rightarrow	PROPN
bracis-28360	54	4	[	[	X
bracis-28360	54	5	0,1]\	0,1]\	NOUN
bracis-28360	54	6	)	)	PUNCT
bracis-28360	54	7	,	,	PUNCT
bracis-28360	54	8	given	give	VERB
bracis-28360	54	9	,	,	PUNCT
bracis-28360	54	10	for	for	ADP
bracis-28360	54	11	all	all	DET
bracis-28360	54	12	\(x	\(x	NOUN
bracis-28360	54	13	,	,	PUNCT
bracis-28360	54	14	y	y	PROPN
bracis-28360	54	15	\in	\in	PROPN
bracis-28360	54	16	[	[	X
bracis-28360	54	17	0,1]\	0,1]\	NOUN
bracis-28360	54	18	)	)	PUNCT
bracis-28360	54	19	,	,	PUNCT
bracis-28360	54	20	by	by	ADP
bracis-28360	54	21	\(\delta	\(\delta	NOUN
bracis-28360	54	22	^{\varphi	^{\varphi	NUM
bracis-28360	54	23	_	_	NOUN
bracis-28360	54	24	1	1	NUM
bracis-28360	54	25	,	,	PUNCT
bracis-28360	54	26	\varphi	\varphi	PROPN
bracis-28360	54	27	_	_	PROPN
bracis-28360	54	28	2}(x	2}(x	NUM
bracis-28360	54	29	,	,	PUNCT
bracis-28360	54	30	y)=\varphi	y)=\varphi	PROPN
bracis-28360	54	31	_	_	PRON
bracis-28360	54	32	1(|\varphi	1(|\varphi	NUM
bracis-28360	54	33	_	_	NOUN
bracis-28360	54	34	2(x)-\varphi	2(x)-\varphi	NUM
bracis-28360	54	35	_	_	NOUN
bracis-28360	54	36	2(y)|)\	2(y)|)\	NUM
bracis-28360	54	37	)	)	PUNCT
bracis-28360	54	38	,	,	PUNCT
bracis-28360	54	39	is	be	AUX
bracis-28360	54	40	a	a	DET
bracis-28360	54	41	restricted	restricted	ADJ
bracis-28360	54	42	dissimilarity	dissimilarity	NOUN
bracis-28360	54	43	function	function	NOUN
bracis-28360	54	44	.	.	PUNCT
bracis-28360	55	1	all	all	DET
bracis-28360	55	2	functions	function	NOUN
bracis-28360	55	3	from	from	ADP
bracis-28360	55	4	table	table	NOUN
bracis-28360	55	5	 	 	SPACE
bracis-28360	55	6	2	2	NUM
bracis-28360	55	7	are	be	AUX
bracis-28360	55	8	examples	example	NOUN
bracis-28360	55	9	of	of	ADP
bracis-28360	55	10	rdfs	rdfs	NOUN
bracis-28360	55	11	,	,	PUNCT
bracis-28360	55	12	constructed	construct	VERB
bracis-28360	55	13	via	via	ADP
bracis-28360	55	14	proposition	proposition	NOUN
bracis-28360	55	15	2	2	NUM
bracis-28360	55	16	,	,	PUNCT
bracis-28360	55	17	which	which	PRON
bracis-28360	55	18	are	be	AUX
bracis-28360	55	19	considered	consider	VERB
bracis-28360	55	20	in	in	ADP
bracis-28360	55	21	our	our	PRON
bracis-28360	55	22	experiments	experiment	NOUN
bracis-28360	55	23	presented	present	VERB
bracis-28360	55	24	in	in	ADP
bracis-28360	55	25	sect	sect	NOUN
bracis-28360	55	26	.	.	PUNCT
bracis-28360	55	27	 	 	SPACE
bracis-28360	56	1	5	5	NUM
bracis-28360	56	2	.	.	PUNCT
bracis-28360	56	3	table	table	NOUN
bracis-28360	56	4	2	2	NUM
bracis-28360	56	5	.	.	PUNCT
bracis-28360	57	1	examples	example	NOUN
bracis-28360	57	2	of	of	ADP
bracis-28360	57	3	rdfs	rdfs	NOUN
bracis-28360	57	4	based	base	VERB
bracis-28360	57	5	on	on	ADP
bracis-28360	57	6	proposition	proposition	NOUN
bracis-28360	57	7	2full	2full	NUM
bracis-28360	57	8	size	size	NOUN
bracis-28360	57	9	table	table	NOUN
bracis-28360	57	10	a	a	DET
bracis-28360	57	11	function	function	NOUN
bracis-28360	57	12	\(m	\(m	NOUN
bracis-28360	57	13	:	:	PUNCT
bracis-28360	57	14	2^{n	2^{n	NUM
bracis-28360	57	15	}	}	PUNCT
bracis-28360	57	16	\rightarrow	\rightarrow	PROPN
bracis-28360	58	1	[	[	X
bracis-28360	58	2	0,1]\	0,1]\	NOUN
bracis-28360	58	3	)	)	PUNCT
bracis-28360	58	4	is	be	AUX
bracis-28360	58	5	a	a	DET
bracis-28360	58	6	fuzzy	fuzzy	ADJ
bracis-28360	58	7	measure	measure	NOUN
bracis-28360	58	8	(	(	PUNCT
bracis-28360	58	9	fm	fm	NOUN
bracis-28360	58	10	)	)	PUNCT
bracis-28360	59	1	[	[	X
bracis-28360	59	2	10	10	NUM
bracis-28360	59	3	]	]	PUNCT
bracis-28360	59	4	if	if	SCONJ
bracis-28360	59	5	,	,	PUNCT
bracis-28360	59	6	for	for	ADP
bracis-28360	59	7	all	all	DET
bracis-28360	59	8	\(x	\(x	NOUN
bracis-28360	59	9	,	,	PUNCT
bracis-28360	59	10	y	y	PROPN
bracis-28360	59	11	\subseteq	\subseteq	PROPN
bracis-28360	59	12	n\	n\	NOUN
bracis-28360	59	13	)	)	PUNCT
bracis-28360	59	14	,	,	PUNCT
bracis-28360	59	15	it	it	PRON
bracis-28360	59	16	satisfies	satisfy	VERB
bracis-28360	59	17	the	the	DET
bracis-28360	59	18	following	follow	VERB
bracis-28360	59	19	properties	property	NOUN
bracis-28360	59	20	:	:	PUNCT
bracis-28360	59	21	(	(	PUNCT
bracis-28360	59	22	m	m	NOUN
bracis-28360	59	23	1	1	NUM
bracis-28360	59	24	)	)	PUNCT
bracis-28360	59	25	increasing	increase	VERB
bracis-28360	59	26	:	:	PUNCT
bracis-28360	59	27	if	if	SCONJ
bracis-28360	59	28	\(x\subseteq	\(x\subseteq	ADJ
bracis-28360	59	29	y\	y\	NOUN
bracis-28360	59	30	)	)	PUNCT
bracis-28360	59	31	,	,	PUNCT
bracis-28360	59	32	then	then	ADV
bracis-28360	59	33	\(m(x)\le	\(m(x)\le	AUX
bracis-28360	59	34	m(y)\	m(y)\	ADV
bracis-28360	59	35	)	)	PUNCT
bracis-28360	59	36	;	;	PUNCT
bracis-28360	59	37	(	(	PUNCT
bracis-28360	59	38	m	m	NOUN
bracis-28360	59	39	2	2	NUM
bracis-28360	59	40	)	)	PUNCT
bracis-28360	59	41	boundary	boundary	ADJ
bracis-28360	59	42	conditions	condition	NOUN
bracis-28360	59	43	:	:	PUNCT
bracis-28360	59	44	\(m(\emptyset	\(m(\emptyset	ADJ
bracis-28360	59	45	)	)	PUNCT
bracis-28360	60	1	=	=	SYM
bracis-28360	60	2	0\	0\	PROPN
bracis-28360	60	3	)	)	PUNCT
bracis-28360	60	4	and	and	CCONJ
bracis-28360	60	5	\(m(n	\(m(n	PROPN
bracis-28360	60	6	)	)	PUNCT
bracis-28360	60	7	=	=	NOUN
bracis-28360	60	8	1\	1\	NUM
bracis-28360	60	9	)	)	PUNCT
bracis-28360	60	10	.	.	PUNCT
bracis-28360	61	1	an	an	DET
bracis-28360	61	2	example	example	NOUN
bracis-28360	61	3	of	of	ADP
bracis-28360	61	4	fm	fm	PROPN
bracis-28360	61	5	is	be	AUX
bracis-28360	61	6	the	the	DET
bracis-28360	61	7	power	power	NOUN
bracis-28360	61	8	measure	measure	NOUN
bracis-28360	61	9	\(m_{pm	\(m_{pm	PROPN
bracis-28360	61	10	}	}	PUNCT
bracis-28360	61	11	:	:	PUNCT
bracis-28360	61	12	2^{n	2^{n	NUM
bracis-28360	61	13	}	}	PUNCT
bracis-28360	61	14	\rightarrow	\rightarrow	PROPN
bracis-28360	62	1	[	[	X
bracis-28360	63	1	0,1]\	0,1]\	NOUN
bracis-28360	63	2	)	)	PUNCT
bracis-28360	63	3	,	,	PUNCT
bracis-28360	63	4	which	which	PRON
bracis-28360	63	5	is	be	AUX
bracis-28360	63	6	defined	define	VERB
bracis-28360	63	7	,	,	PUNCT
bracis-28360	63	8	for	for	ADP
bracis-28360	63	9	all	all	DET
bracis-28360	63	10	\(x	\(x	NOUN
bracis-28360	63	11	\subseteq	\subseteq	PROPN
bracis-28360	63	12	n\	n\	NOUN
bracis-28360	63	13	)	)	PUNCT
bracis-28360	63	14	,	,	PUNCT
bracis-28360	63	15	by	by	ADP
bracis-28360	63	16	\(m_{pm}(x	\(m_{pm}(x	ADV
bracis-28360	63	17	)	)	PUNCT
bracis-28360	63	18	=	=	SYM
bracis-28360	63	19	\left	\left	PROPN
bracis-28360	63	20	(	(	PUNCT
bracis-28360	63	21	\frac{|x|}{n	\frac{|x|}{n	NOUN
bracis-28360	63	22	}	}	PUNCT
bracis-28360	63	23	\right	\right	NOUN
bracis-28360	63	24	)	)	PUNCT
bracis-28360	63	25	^{q}\	^{q}\	NUM
bracis-28360	63	26	)	)	PUNCT
bracis-28360	63	27	,	,	PUNCT
bracis-28360	63	28	where	where	SCONJ
bracis-28360	63	29	the	the	DET
bracis-28360	63	30	exponent	exponent	NOUN
bracis-28360	63	31	\(q	\(q	NOUN
bracis-28360	63	32	>	>	X
bracis-28360	63	33	0\	0\	PROPN
bracis-28360	63	34	)	)	PUNCT
bracis-28360	63	35	can	can	AUX
bracis-28360	63	36	be	be	AUX
bracis-28360	63	37	learned	learn	VERB
bracis-28360	63	38	genetically	genetically	ADV
bracis-28360	63	39	from	from	ADP
bracis-28360	63	40	the	the	DET
bracis-28360	63	41	data	datum	NOUN
bracis-28360	63	42	.	.	PUNCT
bracis-28360	64	1	it	it	PRON
bracis-28360	64	2	is	be	AUX
bracis-28360	64	3	the	the	DET
bracis-28360	64	4	only	only	ADJ
bracis-28360	64	5	fm	fm	NOUN
bracis-28360	64	6	considered	consider	VERB
bracis-28360	64	7	in	in	ADP
bracis-28360	64	8	this	this	DET
bracis-28360	64	9	paper	paper	NOUN
bracis-28360	64	10	,	,	PUNCT
bracis-28360	64	11	since	since	SCONJ
bracis-28360	64	12	it	it	PRON
bracis-28360	64	13	provides	provide	VERB
bracis-28360	64	14	excellent	excellent	ADJ
bracis-28360	64	15	results	result	NOUN
bracis-28360	64	16	in	in	ADP
bracis-28360	64	17	classification	classification	NOUN
bracis-28360	64	18	problems	problem	NOUN
bracis-28360	64	19	,	,	PUNCT
bracis-28360	64	20	as	as	SCONJ
bracis-28360	64	21	discussed	discuss	VERB
bracis-28360	64	22	in	in	ADP
bracis-28360	64	23	[	[	X
bracis-28360	64	24	21	21	NUM
bracis-28360	64	25	]	]	PUNCT
bracis-28360	64	26	.	.	PUNCT
bracis-28360	65	1	the	the	DET
bracis-28360	65	2	discrete	discrete	ADJ
bracis-28360	65	3	ci	ci	NOUN
bracis-28360	65	4	[	[	X
bracis-28360	65	5	10	10	NUM
bracis-28360	65	6	]	]	PUNCT
bracis-28360	65	7	was	be	AUX
bracis-28360	65	8	generalized	generalize	VERB
bracis-28360	65	9	in	in	ADP
bracis-28360	65	10	many	many	ADJ
bracis-28360	65	11	forms	form	NOUN
bracis-28360	65	12	[	[	X
bracis-28360	65	13	4	4	NUM
bracis-28360	65	14	,	,	PUNCT
bracis-28360	65	15	13	13	NUM
bracis-28360	65	16	]	]	PUNCT
bracis-28360	65	17	,	,	PUNCT
bracis-28360	65	18	one	one	NUM
bracis-28360	65	19	of	of	ADP
bracis-28360	65	20	them	they	PRON
bracis-28360	65	21	,	,	PUNCT
bracis-28360	65	22	based	base	VERB
bracis-28360	65	23	on	on	ADP
bracis-28360	65	24	its	its	PRON
bracis-28360	65	25	expanded	expand	VERB
bracis-28360	65	26	form	form	NOUN
bracis-28360	65	27	,	,	PUNCT
bracis-28360	65	28	considers	consider	VERB
bracis-28360	65	29	copulas	copula	NOUN
bracis-28360	65	30	instead	instead	ADV
bracis-28360	65	31	of	of	ADP
bracis-28360	65	32	the	the	DET
bracis-28360	65	33	product	product	NOUN
bracis-28360	65	34	operation	operation	NOUN
bracis-28360	65	35	:	:	PUNCT
bracis-28360	65	36	definition	definition	NOUN
bracis-28360	65	37	1	1	NUM
bracis-28360	65	38	[	[	X
bracis-28360	65	39	22	22	NUM
bracis-28360	65	40	]	]	PUNCT
bracis-28360	65	41	.	.	PUNCT
bracis-28360	66	1	let	let	VERB
bracis-28360	66	2	\(m	\(m	ADV
bracis-28360	66	3	:	:	PUNCT
bracis-28360	66	4	2^{n	2^{n	NUM
bracis-28360	66	5	}	}	PUNCT
bracis-28360	66	6	\rightarrow	\rightarrow	PROPN
bracis-28360	67	1	[	[	X
bracis-28360	67	2	0,1]\	0,1]\	NOUN
bracis-28360	67	3	)	)	PUNCT
bracis-28360	67	4	be	be	VERB
bracis-28360	67	5	a	a	DET
bracis-28360	67	6	fuzzy	fuzzy	ADJ
bracis-28360	67	7	measure	measure	NOUN
bracis-28360	67	8	and	and	CCONJ
bracis-28360	67	9	\(c	\(c	NOUN
bracis-28360	67	10	:	:	PUNCT
bracis-28360	68	1	[	[	X
bracis-28360	68	2	0,1]^2	0,1]^2	NUM
bracis-28360	68	3	\rightarrow	\rightarrow	PROPN
bracis-28360	68	4	[	[	X
bracis-28360	68	5	0,1]\	0,1]\	NOUN
bracis-28360	68	6	)	)	PUNCT
bracis-28360	68	7	be	be	VERB
bracis-28360	68	8	a	a	DET
bracis-28360	68	9	bivariate	bivariate	ADJ
bracis-28360	68	10	copula	copula	NOUN
bracis-28360	68	11	.	.	PUNCT
bracis-28360	69	1	the	the	DET
bracis-28360	69	2	cc	cc	NOUN
bracis-28360	69	3	-	-	ADJ
bracis-28360	69	4	integral	integral	ADJ
bracis-28360	69	5	is	be	AUX
bracis-28360	69	6	defined	define	VERB
bracis-28360	69	7	as	as	ADP
bracis-28360	69	8	a	a	DET
bracis-28360	69	9	function	function	NOUN
bracis-28360	69	10	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	69	11	{	{	PUNCT
bracis-28360	69	12	c}_{m}^c	c}_{m}^c	PROPN
bracis-28360	69	13	:	:	PUNCT
bracis-28360	70	1	[	[	X
bracis-28360	70	2	0,1]^n	0,1]^n	X
bracis-28360	70	3	\rightarrow	\rightarrow	PROPN
bracis-28360	71	1	[	[	X
bracis-28360	71	2	0,1]\	0,1]\	NOUN
bracis-28360	71	3	)	)	PUNCT
bracis-28360	71	4	,	,	PUNCT
bracis-28360	71	5	given	give	VERB
bracis-28360	71	6	,	,	PUNCT
bracis-28360	71	7	for	for	ADP
bracis-28360	71	8	all	all	DET
bracis-28360	71	9	\({\boldsymbol{x	\({\boldsymbol{x	NOUN
bracis-28360	71	10	}	}	PUNCT
bracis-28360	71	11	}	}	PUNCT
bracis-28360	71	12	\in	\in	PROPN
bracis-28360	71	13	[	[	NOUN
bracis-28360	71	14	0,1]^n\	0,1]^n\	NOUN
bracis-28360	71	15	)	)	PUNCT
bracis-28360	71	16	,	,	PUNCT
bracis-28360	71	17	by	by	ADP
bracis-28360	71	18	$	$	SYM
bracis-28360	71	19	$	$	SYM
bracis-28360	71	20	\begin{aligned	\begin{aligne	VERB
bracis-28360	71	21	}	}	PUNCT
bracis-28360	71	22	\mathfrak	\mathfrak	PROPN
bracis-28360	71	23	{	{	PUNCT
bracis-28360	71	24	c}_{m}^c	c}_{m}^c	PROPN
bracis-28360	71	25	(	(	PUNCT
bracis-28360	71	26	{	{	PUNCT
bracis-28360	71	27	\boldsymbol{x	\boldsymbol{x	NOUN
bracis-28360	71	28	}	}	PUNCT
bracis-28360	71	29	}	}	PUNCT
bracis-28360	71	30	)	)	PUNCT
bracis-28360	72	1	=	=	SYM
bracis-28360	72	2	\sum	\sum	NOUN
bracis-28360	72	3	_	_	PUNCT
bracis-28360	72	4	{	{	PUNCT
bracis-28360	72	5	i=1}^{n	i=1}^{n	ADJ
bracis-28360	72	6	}	}	PUNCT
bracis-28360	72	7	c	c	PROPN
bracis-28360	72	8	\left	\left	PROPN
bracis-28360	72	9	(	(	PUNCT
bracis-28360	72	10	x_{(i	x_{(i	PROPN
bracis-28360	72	11	)	)	PUNCT
bracis-28360	72	12	}	}	PUNCT
bracis-28360	72	13	,	,	PUNCT
bracis-28360	72	14	m\left	m\left	X
bracis-28360	72	15	(	(	PUNCT
bracis-28360	72	16	a_{(i	a_{(i	PROPN
bracis-28360	72	17	)	)	PUNCT
bracis-28360	72	18	}	}	PUNCT
bracis-28360	72	19	\right	\right	PROPN
bracis-28360	72	20	)	)	PUNCT
bracis-28360	72	21	\right	\right	NOUN
bracis-28360	72	22	)	)	PUNCT
bracis-28360	72	23	c	c	PROPN
bracis-28360	72	24	\left	\left	PROPN
bracis-28360	72	25	(	(	PUNCT
bracis-28360	72	26	x_{(i-1	x_{(i-1	NOUN
bracis-28360	72	27	)	)	PUNCT
bracis-28360	72	28	}	}	PUNCT
bracis-28360	72	29	,	,	PUNCT
bracis-28360	72	30	m\left	m\left	X
bracis-28360	72	31	(	(	PUNCT
bracis-28360	72	32	a_{(i	a_{(i	PROPN
bracis-28360	72	33	)	)	PUNCT
bracis-28360	72	34	}	}	PUNCT
bracis-28360	72	35	\right	\right	PROPN
bracis-28360	72	36	)	)	PUNCT
bracis-28360	72	37	\right	\right	NOUN
bracis-28360	72	38	)	)	PUNCT
bracis-28360	72	39	,	,	PUNCT
bracis-28360	72	40	\end{aligned}$$	\end{aligned}$$	X
bracis-28360	72	41	(	(	PUNCT
bracis-28360	72	42	1	1	NUM
bracis-28360	72	43	)	)	PUNCT
bracis-28360	72	44	where	where	SCONJ
bracis-28360	72	45	\(\left	\(\left	PROPN
bracis-28360	72	46	(	(	PUNCT
bracis-28360	72	47	x_{(1	x_{(1	PROPN
bracis-28360	72	48	)	)	PUNCT
bracis-28360	72	49	}	}	PUNCT
bracis-28360	72	50	,	,	PUNCT
bracis-28360	72	51	\ldots	\ldots	INTJ
bracis-28360	72	52	,	,	PUNCT
bracis-28360	72	53	x_{(n)}\right	x_{(n)}\right	NOUN
bracis-28360	72	54	)	)	PUNCT
bracis-28360	72	55	\	\	NOUN
bracis-28360	72	56	)	)	PUNCT
bracis-28360	72	57	is	be	AUX
bracis-28360	72	58	an	an	DET
bracis-28360	72	59	increasing	increase	VERB
bracis-28360	72	60	permutation	permutation	NOUN
bracis-28360	72	61	on	on	ADP
bracis-28360	72	62	the	the	DET
bracis-28360	72	63	input	input	NOUN
bracis-28360	72	64	x	x	NOUN
bracis-28360	72	65	,	,	PUNCT
bracis-28360	72	66	that	that	ADV
bracis-28360	72	67	is	is	ADV
bracis-28360	72	68	,	,	PUNCT
bracis-28360	72	69	\(0	\(0	PROPN
bracis-28360	72	70	\le	\le	PROPN
bracis-28360	72	71	x_{(1	x_{(1	PROPN
bracis-28360	72	72	)	)	PUNCT
bracis-28360	72	73	}	}	PUNCT
bracis-28360	72	74	\le	\le	NOUN
bracis-28360	72	75	\ldots	\ldots	ADP
bracis-28360	72	76	\le	\le	PROPN
bracis-28360	72	77	x_{(n)}\	x_{(n)}\	NUM
bracis-28360	72	78	)	)	PUNCT
bracis-28360	72	79	,	,	PUNCT
bracis-28360	72	80	where	where	SCONJ
bracis-28360	72	81	\(x_{(0	\(x_{(0	ADJ
bracis-28360	72	82	)	)	PUNCT
bracis-28360	72	83	}	}	PUNCT
bracis-28360	72	84	=	=	SYM
bracis-28360	72	85	0\	0\	PROPN
bracis-28360	72	86	)	)	PUNCT
bracis-28360	72	87	and	and	CCONJ
bracis-28360	72	88	\(a_{(i	\(a_{(i	PROPN
bracis-28360	72	89	)	)	PUNCT
bracis-28360	72	90	}	}	PUNCT
bracis-28360	72	91	=	=	SYM
bracis-28360	72	92	\{(i	\{(i	NOUN
bracis-28360	72	93	)	)	PUNCT
bracis-28360	72	94	,	,	PUNCT
bracis-28360	72	95	\dots	\dot	NOUN
bracis-28360	72	96	,	,	PUNCT
bracis-28360	72	97	(	(	PUNCT
bracis-28360	72	98	n	n	CCONJ
bracis-28360	72	99	)	)	PUNCT
bracis-28360	72	100	\}\	\}\	NUM
bracis-28360	72	101	)	)	PUNCT
bracis-28360	72	102	is	be	AUX
bracis-28360	72	103	the	the	DET
bracis-28360	72	104	subset	subset	NOUN
bracis-28360	72	105	of	of	ADP
bracis-28360	72	106	indices	index	NOUN
bracis-28360	72	107	corresponding	correspond	VERB
bracis-28360	72	108	to	to	ADP
bracis-28360	72	109	the	the	DET
bracis-28360	72	110	\(n	\(n	PROPN
bracis-28360	72	111	-	-	PUNCT
bracis-28360	72	112	i+1\	i+1\	PROPN
bracis-28360	72	113	)	)	PUNCT
bracis-28360	72	114	largest	large	ADJ
bracis-28360	72	115	components	component	NOUN
bracis-28360	72	116	of	of	ADP
bracis-28360	72	117	\(\boldsymbol{x}\	\(\boldsymbol{x}\	NUM
bracis-28360	72	118	)	)	PUNCT
bracis-28360	72	119	.	.	PUNCT
bracis-28360	73	1	in	in	ADP
bracis-28360	73	2	another	another	DET
bracis-28360	73	3	direction	direction	NOUN
bracis-28360	73	4	,	,	PUNCT
bracis-28360	73	5	the	the	DET
bracis-28360	73	6	ci	ci	NOUN
bracis-28360	73	7	in	in	ADP
bracis-28360	73	8	its	its	PRON
bracis-28360	73	9	expanded	expand	VERB
bracis-28360	73	10	form	form	NOUN
bracis-28360	73	11	was	be	AUX
bracis-28360	73	12	generalized	generalize	VERB
bracis-28360	73	13	considering	consider	VERB
bracis-28360	73	14	rdfs	rdfs	NOUN
bracis-28360	73	15	in	in	ADP
bracis-28360	73	16	the	the	DET
bracis-28360	73	17	place	place	NOUN
bracis-28360	73	18	of	of	ADP
bracis-28360	73	19	the	the	DET
bracis-28360	73	20	subtraction	subtraction	NOUN
bracis-28360	73	21	operation	operation	NOUN
bracis-28360	73	22	:	:	PUNCT
bracis-28360	73	23	definition	definition	NOUN
bracis-28360	73	24	2	2	NUM
bracis-28360	73	25	[	[	X
bracis-28360	73	26	29	29	NUM
bracis-28360	73	27	]	]	PUNCT
bracis-28360	73	28	.	.	PUNCT
bracis-28360	74	1	the	the	DET
bracis-28360	74	2	generalization	generalization	NOUN
bracis-28360	74	3	of	of	ADP
bracis-28360	74	4	the	the	DET
bracis-28360	74	5	ci	ci	NOUN
bracis-28360	74	6	expanded	expand	VERB
bracis-28360	74	7	form	form	NOUN
bracis-28360	74	8	by	by	ADP
bracis-28360	74	9	rdfs	rdfs	NOUN
bracis-28360	74	10	\(\delta	\(\delta	NOUN
bracis-28360	74	11	:	:	PUNCT
bracis-28360	75	1	[	[	X
bracis-28360	75	2	0,1]^2	0,1]^2	NUM
bracis-28360	75	3	\rightarrow	\rightarrow	PROPN
bracis-28360	75	4	[	[	X
bracis-28360	75	5	0,1]\	0,1]\	NOUN
bracis-28360	75	6	)	)	PUNCT
bracis-28360	75	7	with	with	ADP
bracis-28360	75	8	respect	respect	NOUN
bracis-28360	75	9	to	to	ADP
bracis-28360	75	10	an	an	DET
bracis-28360	75	11	fm	fm	NOUN
bracis-28360	75	12	\(m	\(m	NOUN
bracis-28360	75	13	:	:	PUNCT
bracis-28360	75	14	2^n	2^n	NUM
bracis-28360	75	15	\rightarrow	\rightarrow	PROPN
bracis-28360	75	16	[	[	X
bracis-28360	75	17	0,1]\	0,1]\	NOUN
bracis-28360	75	18	)	)	PUNCT
bracis-28360	75	19	,	,	PUNCT
bracis-28360	75	20	named	name	VERB
bracis-28360	75	21	d	d	PROPN
bracis-28360	75	22	-	-	PUNCT
bracis-28360	75	23	xchoquet	xchoquet	ADJ
bracis-28360	75	24	integral	integral	ADJ
bracis-28360	75	25	(	(	PUNCT
bracis-28360	75	26	d	d	PROPN
bracis-28360	75	27	-	-	PUNCT
bracis-28360	75	28	xc	xc	PROPN
bracis-28360	75	29	)	)	PUNCT
bracis-28360	75	30	,	,	PUNCT
bracis-28360	75	31	is	be	AUX
bracis-28360	75	32	a	a	DET
bracis-28360	75	33	mapping	mapping	NOUN
bracis-28360	75	34	\(x\mathfrak	\(x\mathfrak	NOUN
bracis-28360	75	35	{	{	PUNCT
bracis-28360	75	36	c}_{\delta	c}_{\delta	NOUN
bracis-28360	75	37	,	,	PUNCT
bracis-28360	75	38	m	m	NOUN
bracis-28360	75	39	}	}	PUNCT
bracis-28360	75	40	:	:	PUNCT
bracis-28360	76	1	[	[	X
bracis-28360	76	2	0,1]^2	0,1]^2	NUM
bracis-28360	76	3	\rightarrow	\rightarrow	PROPN
bracis-28360	76	4	[	[	X
bracis-28360	76	5	0,n]\	0,n]\	NUM
bracis-28360	76	6	)	)	PUNCT
bracis-28360	76	7	,	,	PUNCT
bracis-28360	76	8	defined	define	VERB
bracis-28360	76	9	,	,	PUNCT
bracis-28360	76	10	for	for	ADP
bracis-28360	76	11	all	all	DET
bracis-28360	76	12	\(\boldsymbol{x	\(\boldsymbol{x	ADJ
bracis-28360	76	13	}	}	PUNCT
bracis-28360	76	14	\in	\in	PROPN
bracis-28360	76	15	[	[	NOUN
bracis-28360	76	16	0,1]^n\	0,1]^n\	NOUN
bracis-28360	76	17	)	)	PUNCT
bracis-28360	76	18	,	,	PUNCT
bracis-28360	76	19	by	by	ADP
bracis-28360	76	20	:	:	PUNCT
bracis-28360	76	21	$	$	SYM
bracis-28360	76	22	$	$	SYM
bracis-28360	76	23	\begin{aligned	\begin{aligne	VERB
bracis-28360	76	24	}	}	PUNCT
bracis-28360	76	25	x\mathfrak	x\mathfrak	PROPN
bracis-28360	76	26	{	{	PUNCT
bracis-28360	76	27	c}_{\delta	c}_{\delta	NOUN
bracis-28360	76	28	,	,	PUNCT
bracis-28360	76	29	m	m	VERB
bracis-28360	76	30	}	}	PUNCT
bracis-28360	76	31	(	(	PUNCT
bracis-28360	76	32	\boldsymbol{x	\boldsymbol{x	ADP
bracis-28360	76	33	}	}	PUNCT
bracis-28360	76	34	)	)	PUNCT
bracis-28360	77	1	=	=	SYM
bracis-28360	77	2	x_{(1	x_{(1	PROPN
bracis-28360	77	3	)	)	PUNCT
bracis-28360	77	4	}	}	PUNCT
bracis-28360	78	1	+	+	CCONJ
bracis-28360	78	2	\sum	\sum	NOUN
bracis-28360	78	3	_	_	PUNCT
bracis-28360	78	4	{	{	PUNCT
bracis-28360	78	5	i=2}^{n	i=2}^{n	ADJ
bracis-28360	78	6	}	}	PUNCT
bracis-28360	78	7	\delta	\delta	PROPN
bracis-28360	78	8	\left	\left	PROPN
bracis-28360	78	9	(	(	PUNCT
bracis-28360	78	10	x_{(i	x_{(i	PROPN
bracis-28360	78	11	)	)	PUNCT
bracis-28360	78	12	}	}	PUNCT
bracis-28360	78	13	\cdot	\cdot	NOUN
bracis-28360	78	14	m(a_{(i)}),\	m(a_{(i)}),\	NOUN
bracis-28360	78	15	x_{(i-1	x_{(i-1	NOUN
bracis-28360	78	16	)	)	PUNCT
bracis-28360	78	17	}	}	PUNCT
bracis-28360	78	18	\cdot	\cdot	NOUN
bracis-28360	78	19	m(a_{(i	m(a_{(i	PROPN
bracis-28360	78	20	)	)	PUNCT
bracis-28360	78	21	}	}	PUNCT
bracis-28360	78	22	)	)	PUNCT
bracis-28360	78	23	\right	\right	NOUN
bracis-28360	78	24	)	)	PUNCT
bracis-28360	78	25	,	,	PUNCT
bracis-28360	78	26	\end{aligned}$$	\end{aligned}$$	X
bracis-28360	78	27	(	(	PUNCT
bracis-28360	78	28	2	2	NUM
bracis-28360	78	29	)	)	PUNCT
bracis-28360	78	30	where	where	SCONJ
bracis-28360	78	31	\	\	PROPN
bracis-28360	78	32	(	(	PUNCT
bracis-28360	78	33	x_{(i	x_{(i	PROPN
bracis-28360	78	34	)	)	PUNCT
bracis-28360	78	35	}	}	PUNCT
bracis-28360	78	36	\	\	NOUN
bracis-28360	78	37	)	)	PUNCT
bracis-28360	78	38	and	and	CCONJ
bracis-28360	78	39	\(a_{(i)}\	\(a_{(i)}\	NUM
bracis-28360	78	40	)	)	PUNCT
bracis-28360	78	41	are	be	AUX
bracis-28360	78	42	defined	define	VERB
bracis-28360	78	43	according	accord	VERB
bracis-28360	78	44	to	to	ADP
bracis-28360	78	45	definition	definition	NOUN
bracis-28360	78	46	1	1	NUM
bracis-28360	78	47	.	.	SYM
bracis-28360	78	48	3	3	NUM
bracis-28360	78	49	d	d	X
bracis-28360	78	50	-	-	PUNCT
bracis-28360	78	51	cc	cc	ADP
bracis-28360	78	52	integrals	integral	NOUN
bracis-28360	78	53	in	in	ADP
bracis-28360	78	54	this	this	DET
bracis-28360	78	55	section	section	NOUN
bracis-28360	78	56	,	,	PUNCT
bracis-28360	78	57	we	we	PRON
bracis-28360	78	58	introduce	introduce	VERB
bracis-28360	78	59	the	the	DET
bracis-28360	78	60	definition	definition	NOUN
bracis-28360	78	61	of	of	ADP
bracis-28360	78	62	d	d	PROPN
bracis-28360	78	63	-	-	PUNCT
bracis-28360	78	64	cc	cc	NOUN
bracis-28360	78	65	-	-	NOUN
bracis-28360	78	66	integrals	integral	NOUN
bracis-28360	78	67	,	,	PUNCT
bracis-28360	78	68	by	by	ADP
bracis-28360	78	69	combining	combine	VERB
bracis-28360	78	70	the	the	DET
bracis-28360	78	71	concepts	concept	NOUN
bracis-28360	78	72	of	of	ADP
bracis-28360	78	73	cc	cc	NOUN
bracis-28360	78	74	-	-	ADJ
bracis-28360	78	75	integral	integral	ADJ
bracis-28360	78	76	(	(	PUNCT
bracis-28360	78	77	definition	definition	NOUN
bracis-28360	78	78	1	1	NUM
bracis-28360	78	79	)	)	PUNCT
bracis-28360	78	80	and	and	CCONJ
bracis-28360	78	81	d	d	X
bracis-28360	78	82	-	-	PUNCT
bracis-28360	78	83	xc	xc	ADJ
bracis-28360	78	84	-	-	ADJ
bracis-28360	78	85	integral	integral	ADJ
bracis-28360	78	86	(	(	PUNCT
bracis-28360	78	87	definition	definition	NOUN
bracis-28360	78	88	2	2	NUM
bracis-28360	78	89	)	)	PUNCT
bracis-28360	78	90	.	.	PUNCT
bracis-28360	79	1	following	follow	VERB
bracis-28360	79	2	that	that	PRON
bracis-28360	79	3	,	,	PUNCT
bracis-28360	79	4	we	we	PRON
bracis-28360	79	5	study	study	VERB
bracis-28360	79	6	some	some	DET
bracis-28360	79	7	aspects	aspect	NOUN
bracis-28360	79	8	of	of	ADP
bracis-28360	79	9	d	d	PROPN
bracis-28360	79	10	-	-	PUNCT
bracis-28360	79	11	cc	cc	NOUN
bracis-28360	79	12	-	-	PUNCT
bracis-28360	79	13	integrals	integral	NOUN
bracis-28360	79	14	that	that	PRON
bracis-28360	79	15	are	be	AUX
bracis-28360	79	16	relevant	relevant	ADJ
bracis-28360	79	17	to	to	ADP
bracis-28360	79	18	our	our	PRON
bracis-28360	79	19	application	application	NOUN
bracis-28360	79	20	in	in	ADP
bracis-28360	79	21	classification	classification	NOUN
bracis-28360	79	22	,	,	PUNCT
bracis-28360	79	23	such	such	ADJ
bracis-28360	79	24	as	as	ADP
bracis-28360	79	25	different	different	ADJ
bracis-28360	79	26	forms	form	NOUN
bracis-28360	79	27	of	of	ADP
bracis-28360	79	28	monotonicity	monotonicity	NOUN
bracis-28360	79	29	.	.	PUNCT
bracis-28360	80	1	definition	definition	NOUN
bracis-28360	80	2	3	3	NUM
bracis-28360	80	3	let	let	VERB
bracis-28360	80	4	\(c	\(c	NOUN
bracis-28360	80	5	:	:	PUNCT
bracis-28360	81	1	[	[	X
bracis-28360	81	2	0,1]^2	0,1]^2	NUM
bracis-28360	81	3	\rightarrow	\rightarrow	PROPN
bracis-28360	81	4	[	[	X
bracis-28360	81	5	0,1]\	0,1]\	NOUN
bracis-28360	81	6	)	)	PUNCT
bracis-28360	81	7	be	be	VERB
bracis-28360	81	8	a	a	DET
bracis-28360	81	9	copula	copula	NOUN
bracis-28360	81	10	.	.	PUNCT
bracis-28360	82	1	the	the	DET
bracis-28360	82	2	generalization	generalization	NOUN
bracis-28360	82	3	of	of	ADP
bracis-28360	82	4	the	the	DET
bracis-28360	82	5	cc	cc	NOUN
bracis-28360	82	6	-	-	NOUN
bracis-28360	82	7	integral	integral	ADJ
bracis-28360	82	8	by	by	ADP
bracis-28360	82	9	rdfs	rdfs	NOUN
bracis-28360	82	10	\(\delta	\(\delta	NOUN
bracis-28360	82	11	:	:	PUNCT
bracis-28360	82	12	[	[	X
bracis-28360	82	13	0,1]^2	0,1]^2	NUM
bracis-28360	82	14	\rightarrow	\rightarrow	PROPN
bracis-28360	82	15	[	[	X
bracis-28360	82	16	0,1]\	0,1]\	NOUN
bracis-28360	82	17	)	)	PUNCT
bracis-28360	82	18	with	with	ADP
bracis-28360	82	19	respect	respect	NOUN
bracis-28360	82	20	to	to	ADP
bracis-28360	82	21	a	a	DET
bracis-28360	82	22	fm	fm	NOUN
bracis-28360	82	23	\(m	\(m	NOUN
bracis-28360	82	24	:	:	PUNCT
bracis-28360	82	25	2^n	2^n	NUM
bracis-28360	82	26	\rightarrow	\rightarrow	PROPN
bracis-28360	82	27	[	[	X
bracis-28360	82	28	0,1]\	0,1]\	NOUN
bracis-28360	82	29	)	)	PUNCT
bracis-28360	82	30	,	,	PUNCT
bracis-28360	82	31	named	name	VERB
bracis-28360	82	32	d	d	PROPN
bracis-28360	82	33	-	-	PUNCT
bracis-28360	82	34	cc	cc	NOUN
bracis-28360	82	35	-	-	ADJ
bracis-28360	82	36	integral	integral	ADJ
bracis-28360	82	37	(	(	PUNCT
bracis-28360	82	38	d	d	NOUN
bracis-28360	82	39	-	-	PUNCT
bracis-28360	82	40	cc	cc	NOUN
bracis-28360	82	41	)	)	PUNCT
bracis-28360	82	42	,	,	PUNCT
bracis-28360	82	43	is	be	AUX
bracis-28360	82	44	a	a	DET
bracis-28360	82	45	mapping	mapping	NOUN
bracis-28360	82	46	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	82	47	{	{	PUNCT
bracis-28360	82	48	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	82	49	,	,	PUNCT
bracis-28360	82	50	m}^c	m}^c	ADJ
bracis-28360	82	51	:	:	PUNCT
bracis-28360	82	52	[	[	X
bracis-28360	82	53	0,1]^2	0,1]^2	NUM
bracis-28360	82	54	\rightarrow	\rightarrow	PROPN
bracis-28360	82	55	[	[	X
bracis-28360	82	56	0,n]\	0,n]\	NUM
bracis-28360	82	57	)	)	PUNCT
bracis-28360	82	58	,	,	PUNCT
bracis-28360	82	59	defined	define	VERB
bracis-28360	82	60	by	by	ADP
bracis-28360	82	61	:	:	PUNCT
bracis-28360	82	62	$	$	SYM
bracis-28360	82	63	$	$	SYM
bracis-28360	82	64	\begin{aligned	\begin{aligne	VERB
bracis-28360	82	65	}	}	PUNCT
bracis-28360	82	66	\mathfrak	\mathfrak	PROPN
bracis-28360	82	67	{	{	PUNCT
bracis-28360	82	68	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	82	69	,	,	PUNCT
bracis-28360	82	70	m}^c	m}^c	PROPN
bracis-28360	82	71	(	(	PUNCT
bracis-28360	82	72	\boldsymbol{x	\boldsymbol{x	NOUN
bracis-28360	82	73	}	}	PUNCT
bracis-28360	82	74	)	)	PUNCT
bracis-28360	82	75	=	=	SYM
bracis-28360	82	76	x_{(1	x_{(1	PROPN
bracis-28360	82	77	)	)	PUNCT
bracis-28360	82	78	}	}	PUNCT
bracis-28360	83	1	+	+	CCONJ
bracis-28360	83	2	\sum	\sum	NOUN
bracis-28360	83	3	_	_	PUNCT
bracis-28360	83	4	{	{	PUNCT
bracis-28360	83	5	i=2}^{n	i=2}^{n	ADJ
bracis-28360	83	6	}	}	PUNCT
bracis-28360	83	7	\delta	\delta	PROPN
bracis-28360	83	8	\left	\left	PROPN
bracis-28360	83	9	(	(	PUNCT
bracis-28360	83	10	c(x_{(i)},m(a_{(i	c(x_{(i)},m(a_{(i	PROPN
bracis-28360	83	11	)	)	PUNCT
bracis-28360	83	12	}	}	PUNCT
bracis-28360	83	13	)	)	PUNCT
bracis-28360	83	14	,	,	PUNCT
bracis-28360	83	15	c(x_{(i-1	c(x_{(i-1	NOUN
bracis-28360	83	16	)	)	PUNCT
bracis-28360	83	17	}	}	PUNCT
bracis-28360	83	18	,	,	PUNCT
bracis-28360	83	19	\	\	PROPN
bracis-28360	83	20	m(a_{(i	m(a_{(i	PROPN
bracis-28360	83	21	)	)	PUNCT
bracis-28360	83	22	}	}	PUNCT
bracis-28360	83	23	)	)	PUNCT
bracis-28360	84	1	\right	\right	NOUN
bracis-28360	84	2	)	)	PUNCT
bracis-28360	84	3	,	,	PUNCT
bracis-28360	84	4	\end{aligned}$$	\end{aligned}$$	X
bracis-28360	84	5	(	(	PUNCT
bracis-28360	84	6	3	3	NUM
bracis-28360	84	7	)	)	PUNCT
bracis-28360	84	8	for	for	ADP
bracis-28360	84	9	all	all	DET
bracis-28360	84	10	\(\boldsymbol{x	\(\boldsymbol{x	ADJ
bracis-28360	84	11	}	}	PUNCT
bracis-28360	84	12	\in	\in	PROPN
bracis-28360	84	13	[	[	NOUN
bracis-28360	84	14	0,1]^n\	0,1]^n\	NOUN
bracis-28360	84	15	)	)	PUNCT
bracis-28360	84	16	,	,	PUNCT
bracis-28360	84	17	where	where	SCONJ
bracis-28360	84	18	the	the	DET
bracis-28360	84	19	ordered	order	VERB
bracis-28360	84	20	\(x_{(i)}\	\(x_{(i)}\	NOUN
bracis-28360	84	21	)	)	PUNCT
bracis-28360	84	22	,	,	PUNCT
bracis-28360	84	23	and	and	CCONJ
bracis-28360	84	24	\(m(a_{(i)})\	\(m(a_{(i)})\	NUM
bracis-28360	84	25	)	)	PUNCT
bracis-28360	84	26	,	,	PUNCT
bracis-28360	84	27	with	with	ADP
bracis-28360	84	28	\(0\le	\(0\le	PRON
bracis-28360	84	29	i\le	i\le	X
bracis-28360	84	30	n\	n\	PROPN
bracis-28360	84	31	)	)	PUNCT
bracis-28360	84	32	,	,	PUNCT
bracis-28360	84	33	were	be	AUX
bracis-28360	84	34	stated	state	VERB
bracis-28360	84	35	in	in	ADP
bracis-28360	84	36	definition	definition	NOUN
bracis-28360	84	37	 	 	SPACE
bracis-28360	84	38	1	1	NUM
bracis-28360	84	39	.	.	PUNCT
bracis-28360	84	40	from	from	ADP
bracis-28360	84	41	now	now	ADV
bracis-28360	84	42	on	on	ADV
bracis-28360	84	43	,	,	PUNCT
bracis-28360	84	44	we	we	PRON
bracis-28360	84	45	denote	denote	VERB
bracis-28360	84	46	\(m(a_{(i)})\	\(m(a_{(i)})\	NOUN
bracis-28360	84	47	)	)	PUNCT
bracis-28360	84	48	simply	simply	ADV
bracis-28360	84	49	by	by	ADP
bracis-28360	84	50	\(m_{(i)}\	\(m_{(i)}\	NOUN
bracis-28360	84	51	)	)	PUNCT
bracis-28360	84	52	.	.	PUNCT
bracis-28360	85	1	observe	observe	VERB
bracis-28360	85	2	that	that	SCONJ
bracis-28360	85	3	d	d	X
bracis-28360	85	4	-	-	PUNCT
bracis-28360	85	5	cc	cc	NOUN
bracis-28360	85	6	-	-	PUNCT
bracis-28360	85	7	integrals	integral	NOUN
bracis-28360	85	8	can	can	AUX
bracis-28360	85	9	also	also	ADV
bracis-28360	85	10	be	be	AUX
bracis-28360	85	11	obtained	obtain	VERB
bracis-28360	85	12	by	by	ADP
bracis-28360	85	13	generalizing	generalize	VERB
bracis-28360	85	14	x	x	PROPN
bracis-28360	85	15	-	-	ADJ
bracis-28360	85	16	dc	dc	NOUN
bracis-28360	85	17	-	-	PUNCT
bracis-28360	85	18	integrals	integral	NOUN
bracis-28360	85	19	(	(	PUNCT
bracis-28360	85	20	definition	definition	NOUN
bracis-28360	85	21	2	2	NUM
bracis-28360	85	22	)	)	PUNCT
bracis-28360	85	23	,	,	PUNCT
bracis-28360	85	24	where	where	SCONJ
bracis-28360	85	25	the	the	DET
bracis-28360	85	26	product	product	NOUN
bracis-28360	85	27	is	be	AUX
bracis-28360	85	28	replaced	replace	VERB
bracis-28360	85	29	by	by	ADP
bracis-28360	85	30	a	a	DET
bracis-28360	85	31	copula	copula	NOUN
bracis-28360	85	32	,	,	PUNCT
bracis-28360	85	33	or	or	CCONJ
bracis-28360	85	34	a	a	DET
bracis-28360	85	35	restriction	restriction	NOUN
bracis-28360	85	36	of	of	ADP
bracis-28360	85	37	\(c_{f_1f_2}\	\(c_{f_1f_2}\	NOUN
bracis-28360	85	38	)	)	PUNCT
bracis-28360	86	1	[	[	X
bracis-28360	86	2	19	19	NUM
bracis-28360	86	3	]	]	PUNCT
bracis-28360	86	4	,	,	PUNCT
bracis-28360	86	5	putting	put	VERB
bracis-28360	86	6	\(f_1	\(f_1	PROPN
bracis-28360	86	7	=	=	NOUN
bracis-28360	86	8	f_2	f_2	NOUN
bracis-28360	86	9	=	=	PUNCT
bracis-28360	86	10	c\	c\	NOUN
bracis-28360	86	11	)	)	PUNCT
bracis-28360	86	12	.	.	PUNCT
bracis-28360	87	1	proposition	proposition	NOUN
bracis-28360	87	2	3	3	NUM
bracis-28360	87	3	under	under	ADP
bracis-28360	87	4	the	the	DET
bracis-28360	87	5	conditions	condition	NOUN
bracis-28360	87	6	given	give	VERB
bracis-28360	87	7	in	in	ADP
bracis-28360	87	8	definition	definition	NOUN
bracis-28360	87	9	3	3	NUM
bracis-28360	87	10	,	,	PUNCT
bracis-28360	87	11	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	87	12	{	{	PUNCT
bracis-28360	87	13	cc}_{\delta	cc}_{\delta	PROPN
bracis-28360	87	14	,	,	PUNCT
bracis-28360	87	15	m}^c\	m}^c\	PROPN
bracis-28360	87	16	)	)	PUNCT
bracis-28360	87	17	is	be	AUX
bracis-28360	87	18	well	well	ADV
bracis-28360	87	19	defined	define	VERB
bracis-28360	87	20	,	,	PUNCT
bracis-28360	87	21	for	for	SCONJ
bracis-28360	87	22	all	all	PRON
bracis-28360	87	23	rdf	rdf	VERB
bracis-28360	87	24	\(\delta	\(\delta	NOUN
bracis-28360	87	25	\	\	NOUN
bracis-28360	87	26	)	)	PUNCT
bracis-28360	87	27	,	,	PUNCT
bracis-28360	87	28	fm	fm	PROPN
bracis-28360	87	29	m	m	PROPN
bracis-28360	87	30	and	and	CCONJ
bracis-28360	87	31	copula	copula	ADJ
bracis-28360	87	32	c.	c.	NOUN
bracis-28360	87	33	proof	proof	NOUN
bracis-28360	87	34	for	for	ADP
bracis-28360	87	35	\(i	\(i	NOUN
bracis-28360	87	36	=	=	SYM
bracis-28360	87	37	1	1	NUM
bracis-28360	87	38	,	,	PUNCT
bracis-28360	87	39	\ldots	\ldots	INTJ
bracis-28360	87	40	,	,	PUNCT
bracis-28360	87	41	n\	n\	PROPN
bracis-28360	87	42	)	)	PUNCT
bracis-28360	87	43	,	,	PUNCT
bracis-28360	87	44	one	one	PRON
bracis-28360	87	45	has	have	VERB
bracis-28360	87	46	that	that	PRON
bracis-28360	87	47	\(0	\(0	PROPN
bracis-28360	87	48	\le	\le	PROPN
bracis-28360	87	49	x_{(i	x_{(i	PROPN
bracis-28360	87	50	)	)	PUNCT
bracis-28360	87	51	}	}	PUNCT
bracis-28360	87	52	\le	\le	PROPN
bracis-28360	87	53	1\	1\	NUM
bracis-28360	87	54	)	)	PUNCT
bracis-28360	87	55	,	,	PUNCT
bracis-28360	87	56	and	and	CCONJ
bracis-28360	87	57	for	for	ADP
bracis-28360	87	58	\(i	\(i	NOUN
bracis-28360	87	59	=	=	SYM
bracis-28360	87	60	2	2	NUM
bracis-28360	87	61	,	,	PUNCT
bracis-28360	87	62	\ldots	\ldots	INTJ
bracis-28360	87	63	,	,	PUNCT
bracis-28360	87	64	n\	n\	PROPN
bracis-28360	87	65	)	)	PUNCT
bracis-28360	87	66	,	,	PUNCT
bracis-28360	87	67	we	we	PRON
bracis-28360	87	68	have	have	VERB
bracis-28360	87	69	that	that	PRON
bracis-28360	87	70	\	\	PROPN
bracis-28360	87	71	(	(	PUNCT
bracis-28360	87	72	0\le	0\le	NUM
bracis-28360	87	73	m_{(i	m_{(i	PROPN
bracis-28360	87	74	)	)	PUNCT
bracis-28360	87	75	}	}	PUNCT
bracis-28360	87	76	\le	\le	PROPN
bracis-28360	87	77	1\	1\	NUM
bracis-28360	87	78	)	)	PUNCT
bracis-28360	87	79	,	,	PUNCT
bracis-28360	88	1	\	\	PROPN
bracis-28360	88	2	(	(	PUNCT
bracis-28360	88	3	0\le	0\le	NUM
bracis-28360	88	4	c(x_{(i)},m_{(i	c(x_{(i)},m_{(i	NOUN
bracis-28360	88	5	)	)	PUNCT
bracis-28360	88	6	}	}	PUNCT
bracis-28360	88	7	)	)	PUNCT
bracis-28360	89	1	\le	\le	PROPN
bracis-28360	89	2	1\	1\	NUM
bracis-28360	89	3	)	)	PUNCT
bracis-28360	89	4	and	and	CCONJ
bracis-28360	89	5	\(0	\(0	PROPN
bracis-28360	89	6	\le	\le	PROPN
bracis-28360	89	7	\delta	\delta	PROPN
bracis-28360	89	8	(	(	PUNCT
bracis-28360	89	9	c(x_{(i)},m_{(i)}),c(x_{(i-1)},m_{(i	c(x_{(i)},m_{(i)}),c(x_{(i-1)},m_{(i	PROPN
bracis-28360	89	10	)	)	PUNCT
bracis-28360	89	11	}	}	PUNCT
bracis-28360	89	12	)	)	PUNCT
bracis-28360	89	13	)	)	PUNCT
bracis-28360	89	14	\le	\le	PROPN
bracis-28360	89	15	1\	1\	NUM
bracis-28360	89	16	)	)	PUNCT
bracis-28360	89	17	.	.	PUNCT
bracis-28360	90	1	it	it	PRON
bracis-28360	90	2	is	be	AUX
bracis-28360	90	3	immediate	immediate	ADJ
bracis-28360	90	4	that	that	SCONJ
bracis-28360	90	5	,	,	PUNCT
bracis-28360	90	6	for	for	ADP
bracis-28360	90	7	\(\boldsymbol{x	\(\boldsymbol{x	ADJ
bracis-28360	90	8	}	}	PUNCT
bracis-28360	90	9	\in	\in	PROPN
bracis-28360	90	10	[	[	NOUN
bracis-28360	90	11	0,1]^n\	0,1]^n\	NOUN
bracis-28360	90	12	)	)	PUNCT
bracis-28360	90	13	,	,	PUNCT
bracis-28360	90	14	\(0	\(0	PROPN
bracis-28360	90	15	\le	\le	PROPN
bracis-28360	90	16	x\mathfrak	x\mathfrak	PROPN
bracis-28360	90	17	{	{	PUNCT
bracis-28360	90	18	c}_{\delta	c}_{\delta	NOUN
bracis-28360	90	19	,	,	PUNCT
bracis-28360	90	20	m	m	VERB
bracis-28360	90	21	}	}	PUNCT
bracis-28360	90	22	(	(	PUNCT
bracis-28360	90	23	\boldsymbol{x	\boldsymbol{x	ADP
bracis-28360	90	24	}	}	PUNCT
bracis-28360	90	25	)	)	PUNCT
bracis-28360	90	26	\le	\le	PROPN
bracis-28360	90	27	n\	n\	PROPN
bracis-28360	90	28	)	)	PUNCT
bracis-28360	90	29	,	,	PUNCT
bracis-28360	90	30	for	for	ADP
bracis-28360	90	31	any	any	DET
bracis-28360	90	32	rdf	rdf	NOUN
bracis-28360	90	33	\(\delta	\(\delta	NOUN
bracis-28360	90	34	\	\	NOUN
bracis-28360	90	35	)	)	PUNCT
bracis-28360	90	36	,	,	PUNCT
bracis-28360	90	37	fm	fm	PROPN
bracis-28360	90	38	m	m	PROPN
bracis-28360	90	39	and	and	CCONJ
bracis-28360	90	40	copula	copula	PROPN
bracis-28360	90	41	c.	c.	PROPN
bracis-28360	90	42	consider	consider	VERB
bracis-28360	90	43	an	an	DET
bracis-28360	90	44	input	input	NOUN
bracis-28360	90	45	vector	vector	NOUN
bracis-28360	90	46	\(\boldsymbol{x	\(\boldsymbol{x	ADJ
bracis-28360	90	47	}	}	PUNCT
bracis-28360	90	48	\in	\in	PROPN
bracis-28360	90	49	[	[	NOUN
bracis-28360	90	50	0,1]^n\	0,1]^n\	NOUN
bracis-28360	90	51	)	)	PUNCT
bracis-28360	90	52	,	,	PUNCT
bracis-28360	90	53	for	for	ADP
bracis-28360	90	54	which	which	PRON
bracis-28360	90	55	there	there	PRON
bracis-28360	90	56	may	may	AUX
bracis-28360	90	57	be	be	AUX
bracis-28360	90	58	different	different	ADJ
bracis-28360	90	59	increasing	increase	VERB
bracis-28360	90	60	permutations	permutation	NOUN
bracis-28360	90	61	,	,	PUNCT
bracis-28360	90	62	meaning	mean	VERB
bracis-28360	90	63	that	that	SCONJ
bracis-28360	90	64	\(\boldsymbol{x	\(\boldsymbol{x	ADJ
bracis-28360	90	65	}	}	PUNCT
bracis-28360	90	66	\	\	NOUN
bracis-28360	90	67	)	)	PUNCT
bracis-28360	90	68	has	have	VERB
bracis-28360	90	69	repeated	repeat	VERB
bracis-28360	90	70	elements	element	NOUN
bracis-28360	90	71	.	.	PUNCT
bracis-28360	91	1	for	for	ADP
bracis-28360	91	2	the	the	DET
bracis-28360	91	3	sake	sake	NOUN
bracis-28360	91	4	of	of	ADP
bracis-28360	91	5	simplicity	simplicity	NOUN
bracis-28360	91	6	,	,	PUNCT
bracis-28360	91	7	but	but	CCONJ
bracis-28360	91	8	without	without	ADP
bracis-28360	91	9	loss	loss	NOUN
bracis-28360	91	10	of	of	ADP
bracis-28360	91	11	generality	generality	NOUN
bracis-28360	91	12	,	,	PUNCT
bracis-28360	91	13	consider	consider	VERB
bracis-28360	91	14	that	that	SCONJ
bracis-28360	91	15	there	there	PRON
bracis-28360	91	16	exists	exist	VERB
bracis-28360	91	17	\(r	\(r	ADJ
bracis-28360	91	18	,	,	PUNCT
bracis-28360	91	19	s	s	NOUN
bracis-28360	91	20	\in	\in	PROPN
bracis-28360	91	21	\{1	\{1	NOUN
bracis-28360	91	22	,	,	PUNCT
bracis-28360	91	23	\ldots	\ldots	INTJ
bracis-28360	91	24	,	,	PUNCT
bracis-28360	91	25	n\}\	n\}\	NOUN
bracis-28360	91	26	)	)	PUNCT
bracis-28360	91	27	such	such	ADJ
bracis-28360	91	28	that	that	DET
bracis-28360	91	29	\(x_r	\(x_r	NOUN
bracis-28360	91	30	=	=	SYM
bracis-28360	91	31	x_s	x_s	PUNCT
bracis-28360	92	1	=	=	PUNCT
bracis-28360	92	2	z	z	X
bracis-28360	92	3	\in	\in	PROPN
bracis-28360	93	1	[	[	X
bracis-28360	93	2	0,1]\	0,1]\	NOUN
bracis-28360	93	3	)	)	PUNCT
bracis-28360	93	4	and	and	CCONJ
bracis-28360	93	5	,	,	PUNCT
bracis-28360	93	6	for	for	ADP
bracis-28360	93	7	all	all	DET
bracis-28360	93	8	\(i	\(i	NOUN
bracis-28360	93	9	\in	\in	PROPN
bracis-28360	93	10	\{1	\{1	PROPN
bracis-28360	93	11	,	,	PUNCT
bracis-28360	93	12	\ldots	\ldots	INTJ
bracis-28360	93	13	,	,	PUNCT
bracis-28360	93	14	n\}\	n\}\	NOUN
bracis-28360	93	15	)	)	PUNCT
bracis-28360	93	16	,	,	PUNCT
bracis-28360	93	17	with	with	ADP
bracis-28360	93	18	\(i	\(i	NOUN
bracis-28360	93	19	\ne	\ne	PROPN
bracis-28360	93	20	r	r	NOUN
bracis-28360	93	21	,	,	PUNCT
bracis-28360	93	22	s\	s\	NOUN
bracis-28360	93	23	)	)	PUNCT
bracis-28360	93	24	,	,	PUNCT
bracis-28360	93	25	it	it	PRON
bracis-28360	93	26	holds	hold	VERB
bracis-28360	93	27	that	that	SCONJ
bracis-28360	93	28	\(x_i	\(x_i	PROPN
bracis-28360	93	29	\ne	\ne	PROPN
bracis-28360	93	30	x_r	x_r	PROPN
bracis-28360	93	31	,	,	PUNCT
bracis-28360	93	32	x_s\	x_s\	PROPN
bracis-28360	93	33	)	)	PUNCT
bracis-28360	93	34	.	.	PUNCT
bracis-28360	94	1	the	the	DET
bracis-28360	94	2	only	only	ADJ
bracis-28360	94	3	two	two	NUM
bracis-28360	94	4	possible	possible	ADJ
bracis-28360	94	5	increasing	increase	VERB
bracis-28360	94	6	permutations	permutation	NOUN
bracis-28360	94	7	are	be	AUX
bracis-28360	94	8	:	:	PUNCT
bracis-28360	94	9	$	$	SYM
bracis-28360	94	10	$	$	SYM
bracis-28360	94	11	\begin{aligned	\begin{aligne	VERB
bracis-28360	94	12	}	}	PUNCT
bracis-28360	94	13	(	(	PUNCT
bracis-28360	94	14	x_{(1	x_{(1	PROPN
bracis-28360	94	15	)	)	PUNCT
bracis-28360	94	16	}	}	PUNCT
bracis-28360	94	17	,	,	PUNCT
bracis-28360	94	18	\ldots	\ldots	PROPN
bracis-28360	94	19	,	,	PUNCT
bracis-28360	94	20	x_{(k-1	x_{(k-1	NUM
bracis-28360	94	21	)	)	PUNCT
bracis-28360	94	22	}	}	PUNCT
bracis-28360	94	23	=	=	SYM
bracis-28360	94	24	x_r	x_r	PROPN
bracis-28360	94	25	,	,	PUNCT
bracis-28360	94	26	&	&	CCONJ
bracis-28360	94	27	x_{(k	x_{(k	PROPN
bracis-28360	94	28	)	)	PUNCT
bracis-28360	94	29	}	}	PUNCT
bracis-28360	94	30	=	=	SYM
bracis-28360	95	1	x_s	x_s	NUM
bracis-28360	95	2	,	,	PUNCT
bracis-28360	95	3	\ldots	\ldots	INTJ
bracis-28360	95	4	,	,	PUNCT
bracis-28360	95	5	x_{(n	x_{(n	PROPN
bracis-28360	95	6	)	)	PUNCT
bracis-28360	95	7	}	}	PUNCT
bracis-28360	95	8	)	)	PUNCT
bracis-28360	95	9	,	,	PUNCT
bracis-28360	95	10	\end{aligned}$$	\end{aligned}$$	X
bracis-28360	95	11	(	(	PUNCT
bracis-28360	95	12	4	4	NUM
bracis-28360	95	13	)	)	PUNCT
bracis-28360	95	14	$	$	SYM
bracis-28360	95	15	$	$	SYM
bracis-28360	95	16	\begin{aligned	\begin{aligne	VERB
bracis-28360	95	17	}	}	PUNCT
bracis-28360	95	18	(	(	PUNCT
bracis-28360	95	19	x_{(1	x_{(1	PROPN
bracis-28360	95	20	)	)	PUNCT
bracis-28360	95	21	}	}	PUNCT
bracis-28360	95	22	,	,	PUNCT
bracis-28360	95	23	\ldots	\ldots	PROPN
bracis-28360	95	24	,	,	PUNCT
bracis-28360	95	25	x_{(k-1	x_{(k-1	NUM
bracis-28360	95	26	)	)	PUNCT
bracis-28360	95	27	}	}	PUNCT
bracis-28360	96	1	=	=	SYM
bracis-28360	96	2	x_s	x_s	PROPN
bracis-28360	96	3	,	,	PUNCT
bracis-28360	96	4	&	&	CCONJ
bracis-28360	96	5	x_{(k	x_{(k	PROPN
bracis-28360	96	6	)	)	PUNCT
bracis-28360	96	7	}	}	PUNCT
bracis-28360	96	8	=	=	SYM
bracis-28360	96	9	x_r	x_r	PROPN
bracis-28360	96	10	,	,	PUNCT
bracis-28360	96	11	\ldots	\ldots	INTJ
bracis-28360	96	12	,	,	PUNCT
bracis-28360	96	13	x_{(n	x_{(n	PROPN
bracis-28360	96	14	)	)	PUNCT
bracis-28360	96	15	}	}	PUNCT
bracis-28360	96	16	)	)	PUNCT
bracis-28360	96	17	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-28360	96	18	(	(	PUNCT
bracis-28360	96	19	5	5	NUM
bracis-28360	96	20	)	)	PUNCT
bracis-28360	96	21	denote	denote	NOUN
bracis-28360	96	22	by	by	ADP
bracis-28360	96	23	\(m_{(i)}^{(1)}=	\(m_{(i)}^{(1)}=	NOUN
bracis-28360	96	24	m^{(1)}(a_{(i)})\	m^{(1)}(a_{(i)})\	NUM
bracis-28360	96	25	)	)	PUNCT
bracis-28360	96	26	and	and	CCONJ
bracis-28360	96	27	\(m_{(i)}^{(2)}=m^{(2)}(a_{(i)})\	\(m_{(i)}^{(2)}=m^{(2)}(a_{(i)})\	PROPN
bracis-28360	96	28	)	)	PUNCT
bracis-28360	96	29	,	,	PUNCT
bracis-28360	96	30	with	with	ADP
bracis-28360	96	31	\(i	\(i	X
bracis-28360	96	32	\in	\in	PROPN
bracis-28360	96	33	\{1	\{1	PROPN
bracis-28360	96	34	,	,	PUNCT
bracis-28360	96	35	\ldots	\ldots	INTJ
bracis-28360	96	36	,	,	PUNCT
bracis-28360	96	37	n\}\	n\}\	NOUN
bracis-28360	96	38	)	)	PUNCT
bracis-28360	96	39	,	,	PUNCT
bracis-28360	96	40	the	the	DET
bracis-28360	96	41	fuzzy	fuzzy	ADJ
bracis-28360	96	42	measures	measure	NOUN
bracis-28360	96	43	of	of	ADP
bracis-28360	96	44	the	the	DET
bracis-28360	96	45	subsets	subset	NOUN
bracis-28360	96	46	of	of	ADP
bracis-28360	96	47	\(a_{(i)}\	\(a_{(i)}\	NOUN
bracis-28360	96	48	)	)	PUNCT
bracis-28360	96	49	of	of	ADP
bracis-28360	96	50	indices	index	NOUN
bracis-28360	96	51	corresponding	correspond	VERB
bracis-28360	96	52	to	to	ADP
bracis-28360	96	53	the	the	DET
bracis-28360	96	54	\(n	\(n	NOUN
bracis-28360	96	55	i	i	PRON
bracis-28360	96	56	+	+	CCONJ
bracis-28360	96	57	1\	1\	X
bracis-28360	96	58	)	)	PUNCT
bracis-28360	96	59	largest	large	ADJ
bracis-28360	96	60	components	component	NOUN
bracis-28360	96	61	of	of	ADP
bracis-28360	96	62	\(\boldsymbol{x}\	\(\boldsymbol{x}\	NUM
bracis-28360	96	63	)	)	PUNCT
bracis-28360	96	64	with	with	ADP
bracis-28360	96	65	respect	respect	NOUN
bracis-28360	96	66	to	to	ADP
bracis-28360	96	67	the	the	DET
bracis-28360	96	68	permutations	permutation	NOUN
bracis-28360	96	69	(	(	PUNCT
bracis-28360	96	70	4	4	NUM
bracis-28360	96	71	)	)	PUNCT
bracis-28360	96	72	and	and	CCONJ
bracis-28360	96	73	(	(	PUNCT
bracis-28360	96	74	5	5	NUM
bracis-28360	96	75	)	)	PUNCT
bracis-28360	96	76	,	,	PUNCT
bracis-28360	96	77	respectively	respectively	ADV
bracis-28360	96	78	.	.	PUNCT
bracis-28360	97	1	observe	observe	VERB
bracis-28360	97	2	that	that	SCONJ
bracis-28360	97	3	$	$	SYM
bracis-28360	97	4	$	$	SYM
bracis-28360	97	5	\begin{aligned	\begin{aligne	VERB
bracis-28360	97	6	}	}	PUNCT
bracis-28360	97	7	m_{(i)}^{(1	m_{(i)}^{(1	NOUN
bracis-28360	97	8	)	)	PUNCT
bracis-28360	97	9	}	}	PUNCT
bracis-28360	97	10	&	&	CCONJ
bracis-28360	97	11	=	=	PROPN
bracis-28360	97	12	&	&	CCONJ
bracis-28360	97	13	m_{(i)}^{(2	m_{(i)}^{(2	PROPN
bracis-28360	97	14	)	)	PUNCT
bracis-28360	97	15	}	}	PUNCT
bracis-28360	97	16	,	,	PUNCT
bracis-28360	97	17	\text	\text	ADP
bracis-28360	97	18	{	{	PUNCT
bracis-28360	97	19	for	for	ADP
bracis-28360	97	20	all	all	PRON
bracis-28360	97	21	}	}	PUNCT
bracis-28360	97	22	i	i	PROPN
bracis-28360	97	23	\ne	\ne	PROPN
bracis-28360	97	24	k	k	NOUN
bracis-28360	97	25	,	,	PUNCT
bracis-28360	97	26	\text	\text	PROPN
bracis-28360	97	27	{	{	PUNCT
bracis-28360	97	28	and	and	CCONJ
bracis-28360	97	29	}	}	PUNCT
bracis-28360	97	30	\end{aligned}$$	\end{aligned}$$	X
bracis-28360	97	31	(	(	PUNCT
bracis-28360	97	32	6	6	NUM
bracis-28360	97	33	)	)	PUNCT
bracis-28360	97	34	$	$	SYM
bracis-28360	97	35	$	$	SYM
bracis-28360	97	36	\begin{aligned	\begin{aligne	VERB
bracis-28360	97	37	}	}	PUNCT
bracis-28360	97	38	m_{(k)}^{(1	m_{(k)}^{(1	NOUN
bracis-28360	97	39	)	)	PUNCT
bracis-28360	97	40	}	}	PUNCT
bracis-28360	97	41	=	=	PUNCT
bracis-28360	97	42	&	&	CCONJ
bracis-28360	97	43	{	{	PUNCT
bracis-28360	97	44	}	}	PUNCT
bracis-28360	97	45	m(\{s	m(\{s	PROPN
bracis-28360	97	46	,	,	PUNCT
bracis-28360	97	47	(	(	PUNCT
bracis-28360	97	48	k+1	k+1	NOUN
bracis-28360	97	49	)	)	PUNCT
bracis-28360	97	50	,	,	PUNCT
bracis-28360	97	51	\ldots	\ldots	PROPN
bracis-28360	97	52	,	,	PUNCT
bracis-28360	97	53	(	(	PUNCT
bracis-28360	97	54	n)\	n)\	NOUN
bracis-28360	97	55	}	}	PUNCT
bracis-28360	97	56	)	)	PUNCT
bracis-28360	97	57	,	,	PUNCT
bracis-28360	97	58	\;\	\;\	NOUN
bracis-28360	97	59	;	;	PUNCT
bracis-28360	97	60	m_{(k)}^{(2	m_{(k)}^{(2	NUM
bracis-28360	97	61	)	)	PUNCT
bracis-28360	97	62	}	}	PUNCT
bracis-28360	97	63	=	=	SYM
bracis-28360	97	64	m(\{r	m(\{r	NOUN
bracis-28360	97	65	,	,	PUNCT
bracis-28360	97	66	(	(	PUNCT
bracis-28360	97	67	k+1	k+1	NOUN
bracis-28360	97	68	)	)	PUNCT
bracis-28360	97	69	,	,	PUNCT
bracis-28360	97	70	\ldots	\ldots	PROPN
bracis-28360	97	71	,	,	PUNCT
bracis-28360	97	72	(	(	PUNCT
bracis-28360	97	73	n)\	n)\	NOUN
bracis-28360	97	74	}	}	PUNCT
bracis-28360	97	75	)	)	PUNCT
bracis-28360	97	76	,	,	PUNCT
bracis-28360	97	77	\end{aligned}$$	\end{aligned}$$	X
bracis-28360	97	78	(	(	PUNCT
bracis-28360	97	79	7	7	X
bracis-28360	97	80	)	)	PUNCT
bracis-28360	97	81	hold	hold	VERB
bracis-28360	97	82	,	,	PUNCT
bracis-28360	97	83	meaning	mean	VERB
bracis-28360	97	84	it	it	PRON
bracis-28360	97	85	may	may	AUX
bracis-28360	97	86	be	be	AUX
bracis-28360	97	87	the	the	DET
bracis-28360	97	88	case	case	NOUN
bracis-28360	97	89	that	that	SCONJ
bracis-28360	97	90	\	\	PROPN
bracis-28360	97	91	(	(	PUNCT
bracis-28360	97	92	m_{(k)}^{(1	m_{(k)}^{(1	NOUN
bracis-28360	97	93	)	)	PUNCT
bracis-28360	97	94	}	}	PUNCT
bracis-28360	97	95	\ne	\ne	PROPN
bracis-28360	97	96	m_{(k)}^{(2)}\	m_{(k)}^{(2)}\	PROPN
bracis-28360	97	97	)	)	PUNCT
bracis-28360	97	98	.	.	PUNCT
bracis-28360	98	1	now	now	ADV
bracis-28360	98	2	,	,	PUNCT
bracis-28360	98	3	denote	denote	VERB
bracis-28360	98	4	by	by	ADP
bracis-28360	98	5	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	98	6	{	{	PUNCT
bracis-28360	98	7	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	98	8	,	,	PUNCT
bracis-28360	98	9	m}^c{(1)}\	m}^c{(1)}\	PROPN
bracis-28360	98	10	)	)	PUNCT
bracis-28360	98	11	and	and	CCONJ
bracis-28360	98	12	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	98	13	{	{	PUNCT
bracis-28360	98	14	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	98	15	,	,	PUNCT
bracis-28360	98	16	m}^c{(2)}\	m}^c{(2)}\	PROPN
bracis-28360	98	17	)	)	PUNCT
bracis-28360	98	18	the	the	DET
bracis-28360	98	19	d	d	PROPN
bracis-28360	98	20	-	-	PUNCT
bracis-28360	98	21	cc	cc	ADP
bracis-28360	98	22	integrals	integral	NOUN
bracis-28360	98	23	with	with	ADP
bracis-28360	98	24	respect	respect	NOUN
bracis-28360	98	25	to	to	ADP
bracis-28360	98	26	the	the	DET
bracis-28360	98	27	permutations	permutation	NOUN
bracis-28360	98	28	(	(	PUNCT
bracis-28360	98	29	4	4	NUM
bracis-28360	98	30	)	)	PUNCT
bracis-28360	98	31	and	and	CCONJ
bracis-28360	98	32	(	(	PUNCT
bracis-28360	98	33	5	5	NUM
bracis-28360	98	34	)	)	PUNCT
bracis-28360	98	35	,	,	PUNCT
bracis-28360	98	36	respectively	respectively	ADV
bracis-28360	98	37	,	,	PUNCT
bracis-28360	98	38	and	and	CCONJ
bracis-28360	98	39	suppose	suppose	VERB
bracis-28360	98	40	that	that	SCONJ
bracis-28360	98	41	$	$	SYM
bracis-28360	98	42	$	$	SYM
bracis-28360	98	43	\begin{aligned	\begin{aligne	VERB
bracis-28360	98	44	}	}	PUNCT
bracis-28360	98	45	\mathfrak	\mathfrak	PROPN
bracis-28360	98	46	{	{	PUNCT
bracis-28360	98	47	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	98	48	,	,	PUNCT
bracis-28360	98	49	m}^c	m}^c	INTJ
bracis-28360	98	50	{	{	PUNCT
bracis-28360	98	51	(	(	PUNCT
bracis-28360	98	52	1)}(\boldsymbol{x	1)}(\boldsymbol{x	NUM
bracis-28360	98	53	}	}	PUNCT
bracis-28360	98	54	)	)	PUNCT
bracis-28360	98	55	\ne	\ne	PROPN
bracis-28360	98	56	\mathfrak	\mathfrak	PROPN
bracis-28360	98	57	{	{	PUNCT
bracis-28360	98	58	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	98	59	,	,	PUNCT
bracis-28360	98	60	m}^c{(2)}(\boldsymbol{x	m}^c{(2)}(\boldsymbol{x	NOUN
bracis-28360	98	61	}	}	PUNCT
bracis-28360	98	62	)	)	PUNCT
bracis-28360	98	63	.	.	PUNCT
bracis-28360	99	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-28360	99	2	(	(	PUNCT
bracis-28360	99	3	8)	8)	NUM
bracis-28360	99	4	from	from	ADP
bracis-28360	99	5	eqs	eqs	PROPN
bracis-28360	99	6	.	.	PUNCT
bracis-28360	100	1	(	(	PUNCT
bracis-28360	100	2	6	6	NUM
bracis-28360	100	3	)	)	PUNCT
bracis-28360	100	4	and	and	CCONJ
bracis-28360	100	5	(	(	PUNCT
bracis-28360	100	6	7	7	NUM
bracis-28360	100	7	)	)	PUNCT
bracis-28360	100	8	,	,	PUNCT
bracis-28360	100	9	whenever	whenever	SCONJ
bracis-28360	100	10	\(k	\(k	NOUN
bracis-28360	100	11	\ne	\ne	PROPN
bracis-28360	100	12	1\	1\	NUM
bracis-28360	100	13	)	)	PUNCT
bracis-28360	100	14	,	,	PUNCT
bracis-28360	100	15	it	it	PRON
bracis-28360	100	16	follows	follow	VERB
bracis-28360	100	17	that	that	SCONJ
bracis-28360	100	18	:	:	PUNCT
bracis-28360	100	19	$	$	SYM
bracis-28360	100	20	$	$	SYM
bracis-28360	100	21	\begin{aligned	\begin{aligne	VERB
bracis-28360	100	22	}	}	PUNCT
bracis-28360	100	23	&	&	CCONJ
bracis-28360	100	24	\mathfrak	\mathfrak	PROPN
bracis-28360	100	25	{	{	PUNCT
bracis-28360	100	26	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	100	27	,	,	PUNCT
bracis-28360	100	28	m}^c{(1	m}^c{(1	PROPN
bracis-28360	100	29	)	)	PUNCT
bracis-28360	100	30	}	}	PUNCT
bracis-28360	100	31	(	(	PUNCT
bracis-28360	100	32	\boldsymbol{x	\boldsymbol{x	ADP
bracis-28360	100	33	}	}	PUNCT
bracis-28360	100	34	)	)	PUNCT
bracis-28360	100	35	\mathfrak	\mathfrak	PROPN
bracis-28360	100	36	{	{	PUNCT
bracis-28360	100	37	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	100	38	,	,	PUNCT
bracis-28360	100	39	m}^c{(2	m}^c{(2	PROPN
bracis-28360	100	40	)	)	PUNCT
bracis-28360	100	41	}	}	PUNCT
bracis-28360	100	42	(	(	PUNCT
bracis-28360	100	43	\boldsymbol{x	\boldsymbol{x	ADP
bracis-28360	100	44	}	}	PUNCT
bracis-28360	100	45	)	)	PUNCT
bracis-28360	100	46	\\	\\	NOUN
bracis-28360	100	47	&	&	CCONJ
bracis-28360	100	48	=	=	PROPN
bracis-28360	100	49	\delta	\delta	PROPN
bracis-28360	100	50	\left	\left	PROPN
bracis-28360	100	51	(	(	PUNCT
bracis-28360	100	52	c	c	X
bracis-28360	100	53	(	(	PUNCT
bracis-28360	100	54	x_{(k	x_{(k	PROPN
bracis-28360	100	55	)	)	PUNCT
bracis-28360	100	56	}	}	PUNCT
bracis-28360	100	57	,	,	PUNCT
bracis-28360	100	58	m_{(k)}^{(1)}),\	m_{(k)}^{(1)}),\	NOUN
bracis-28360	100	59	c(x_{(k-1	c(x_{(k-1	NUM
bracis-28360	100	60	)	)	PUNCT
bracis-28360	100	61	}	}	PUNCT
bracis-28360	100	62	,	,	PUNCT
bracis-28360	100	63	m_{(k)}^{(1	m_{(k)}^{(1	NOUN
bracis-28360	100	64	)	)	PUNCT
bracis-28360	100	65	}	}	PUNCT
bracis-28360	100	66	)	)	PUNCT
bracis-28360	101	1	\right	\right	PROPN
bracis-28360	101	2	)	)	PUNCT
bracis-28360	101	3	\delta	\delta	PROPN
bracis-28360	101	4	\left	\left	PROPN
bracis-28360	101	5	(	(	PUNCT
bracis-28360	101	6	c(x_{(k	c(x_{(k	NOUN
bracis-28360	101	7	)	)	PUNCT
bracis-28360	101	8	}	}	PUNCT
bracis-28360	101	9	,	,	PUNCT
bracis-28360	101	10	m_{(k)}^{(2)}),\	m_{(k)}^{(2)}),\	NOUN
bracis-28360	101	11	c(x_{(k-1	c(x_{(k-1	NUM
bracis-28360	101	12	)	)	PUNCT
bracis-28360	101	13	}	}	PUNCT
bracis-28360	101	14	,	,	PUNCT
bracis-28360	101	15	m_{(k)}^{(2	m_{(k)}^{(2	PROPN
bracis-28360	101	16	)	)	PUNCT
bracis-28360	101	17	}	}	PUNCT
bracis-28360	101	18	)	)	PUNCT
bracis-28360	101	19	\right	\right	NOUN
bracis-28360	101	20	)	)	PUNCT
bracis-28360	101	21	\\	\\	NOUN
bracis-28360	101	22	&	&	CCONJ
bracis-28360	101	23	=	=	PROPN
bracis-28360	101	24	\delta	\delta	PROPN
bracis-28360	101	25	\bigl	\bigl	PROPN
bracis-28360	101	26	(	(	PUNCT
bracis-28360	101	27	c(x_s	c(x_s	PROPN
bracis-28360	101	28	,	,	PUNCT
bracis-28360	101	29	m(\{s	m(\{s	PROPN
bracis-28360	101	30	,	,	PUNCT
bracis-28360	101	31	(	(	PUNCT
bracis-28360	101	32	k+1	k+1	NOUN
bracis-28360	101	33	)	)	PUNCT
bracis-28360	101	34	,	,	PUNCT
bracis-28360	101	35	\ldots	\ldots	PROPN
bracis-28360	101	36	,	,	PUNCT
bracis-28360	101	37	(	(	PUNCT
bracis-28360	101	38	n)\	n)\	NOUN
bracis-28360	101	39	}	}	PUNCT
bracis-28360	101	40	)	)	PUNCT
bracis-28360	101	41	)	)	PUNCT
bracis-28360	101	42	,	,	PUNCT
bracis-28360	101	43	c(x_r	c(x_r	PROPN
bracis-28360	101	44	,	,	PUNCT
bracis-28360	101	45	m(\{s	m(\{s	PROPN
bracis-28360	101	46	,	,	PUNCT
bracis-28360	101	47	(	(	PUNCT
bracis-28360	101	48	k+1	k+1	NOUN
bracis-28360	101	49	)	)	PUNCT
bracis-28360	101	50	,	,	PUNCT
bracis-28360	101	51	\ldots	\ldots	PROPN
bracis-28360	101	52	,	,	PUNCT
bracis-28360	101	53	(	(	PUNCT
bracis-28360	101	54	n)\	n)\	NOUN
bracis-28360	101	55	}	}	PUNCT
bracis-28360	101	56	)	)	PUNCT
bracis-28360	101	57	)	)	PUNCT
bracis-28360	101	58	\bigr	\bigr	NOUN
bracis-28360	101	59	)	)	PUNCT
bracis-28360	101	60	\\	\\	NOUN
bracis-28360	101	61	&	&	CCONJ
bracis-28360	101	62	\quad	\quad	PROPN
bracis-28360	101	63	\delta	\delta	PROPN
bracis-28360	101	64	\bigl	\bigl	PROPN
bracis-28360	101	65	(	(	PUNCT
bracis-28360	101	66	c(x_r	c(x_r	PROPN
bracis-28360	101	67	,	,	PUNCT
bracis-28360	101	68	m(\{r	m(\{r	PROPN
bracis-28360	101	69	,	,	PUNCT
bracis-28360	101	70	(	(	PUNCT
bracis-28360	101	71	k+1	k+1	NOUN
bracis-28360	101	72	)	)	PUNCT
bracis-28360	101	73	,	,	PUNCT
bracis-28360	101	74	\ldots	\ldots	PROPN
bracis-28360	101	75	,	,	PUNCT
bracis-28360	101	76	(	(	PUNCT
bracis-28360	101	77	n)\	n)\	NOUN
bracis-28360	101	78	}	}	PUNCT
bracis-28360	101	79	)	)	PUNCT
bracis-28360	101	80	)	)	PUNCT
bracis-28360	101	81	,	,	PUNCT
bracis-28360	101	82	c	c	X
bracis-28360	101	83	(	(	PUNCT
bracis-28360	101	84	x_s	x_s	PROPN
bracis-28360	101	85	,	,	PUNCT
bracis-28360	101	86	m	m	VERB
bracis-28360	101	87	(	(	PUNCT
bracis-28360	101	88	\{r	\{r	NOUN
bracis-28360	101	89	,	,	PUNCT
bracis-28360	101	90	(	(	PUNCT
bracis-28360	101	91	k+1	k+1	NOUN
bracis-28360	101	92	)	)	PUNCT
bracis-28360	101	93	,	,	PUNCT
bracis-28360	101	94	\ldots	\ldots	PROPN
bracis-28360	101	95	,	,	PUNCT
bracis-28360	101	96	(	(	PUNCT
bracis-28360	101	97	n)\	n)\	NOUN
bracis-28360	101	98	}	}	PUNCT
bracis-28360	101	99	)	)	PUNCT
bracis-28360	101	100	)	)	PUNCT
bracis-28360	101	101	\bigr	\bigr	NOUN
bracis-28360	101	102	)	)	PUNCT
bracis-28360	101	103	\\	\\	NOUN
bracis-28360	101	104	&	&	CCONJ
bracis-28360	101	105	=	=	PROPN
bracis-28360	101	106	\delta	\delta	PROPN
bracis-28360	101	107	\bigl	\bigl	PROPN
bracis-28360	101	108	(	(	PUNCT
bracis-28360	101	109	c(z	c(z	PROPN
bracis-28360	101	110	,	,	PUNCT
bracis-28360	101	111	m(\{s	m(\{s	PROPN
bracis-28360	101	112	,	,	PUNCT
bracis-28360	101	113	(	(	PUNCT
bracis-28360	101	114	k+1	k+1	NOUN
bracis-28360	101	115	)	)	PUNCT
bracis-28360	101	116	,	,	PUNCT
bracis-28360	101	117	{	{	PUNCT
bracis-28360	101	118	\ldots	\ldot	NOUN
bracis-28360	101	119	}	}	PUNCT
bracis-28360	101	120	,	,	PUNCT
bracis-28360	101	121	(	(	PUNCT
bracis-28360	101	122	n)\	n)\	NOUN
bracis-28360	101	123	}	}	PUNCT
bracis-28360	101	124	)	)	PUNCT
bracis-28360	101	125	)	)	PUNCT
bracis-28360	101	126	,	,	PUNCT
bracis-28360	101	127	c(z	c(z	PROPN
bracis-28360	101	128	,	,	PUNCT
bracis-28360	101	129	m(\{s	m(\{s	PROPN
bracis-28360	101	130	,	,	PUNCT
bracis-28360	101	131	(	(	PUNCT
bracis-28360	101	132	k+1	k+1	NOUN
bracis-28360	101	133	)	)	PUNCT
bracis-28360	101	134	,	,	PUNCT
bracis-28360	101	135	{	{	PUNCT
bracis-28360	101	136	\ldots	\ldot	NOUN
bracis-28360	101	137	}	}	PUNCT
bracis-28360	101	138	,	,	PUNCT
bracis-28360	101	139	(	(	PUNCT
bracis-28360	101	140	n)\	n)\	NOUN
bracis-28360	101	141	}	}	PUNCT
bracis-28360	101	142	)	)	PUNCT
bracis-28360	101	143	)	)	PUNCT
bracis-28360	101	144	\bigr	\bigr	NOUN
bracis-28360	101	145	)	)	PUNCT
bracis-28360	101	146	\\	\\	NOUN
bracis-28360	101	147	&	&	CCONJ
bracis-28360	101	148	\delta	\delta	PROPN
bracis-28360	101	149	\bigl	\bigl	PROPN
bracis-28360	101	150	(	(	PUNCT
bracis-28360	101	151	c(z	c(z	PROPN
bracis-28360	101	152	,	,	PUNCT
bracis-28360	101	153	m(\{r	m(\{r	NOUN
bracis-28360	101	154	,	,	PUNCT
bracis-28360	101	155	(	(	PUNCT
bracis-28360	101	156	k+1	k+1	NOUN
bracis-28360	101	157	)	)	PUNCT
bracis-28360	101	158	,	,	PUNCT
bracis-28360	101	159	{	{	PUNCT
bracis-28360	101	160	\ldots	\ldot	NOUN
bracis-28360	101	161	}	}	PUNCT
bracis-28360	101	162	,	,	PUNCT
bracis-28360	101	163	(	(	PUNCT
bracis-28360	101	164	n)\	n)\	NOUN
bracis-28360	101	165	}	}	PUNCT
bracis-28360	101	166	)	)	PUNCT
bracis-28360	101	167	)	)	PUNCT
bracis-28360	101	168	,	,	PUNCT
bracis-28360	101	169	c(z	c(z	PROPN
bracis-28360	101	170	,	,	PUNCT
bracis-28360	101	171	m(\{r	m(\{r	NOUN
bracis-28360	101	172	,	,	PUNCT
bracis-28360	101	173	(	(	PUNCT
bracis-28360	101	174	k+1	k+1	NOUN
bracis-28360	101	175	)	)	PUNCT
bracis-28360	101	176	,	,	PUNCT
bracis-28360	101	177	{	{	PUNCT
bracis-28360	101	178	\ldots	\ldot	NOUN
bracis-28360	101	179	}	}	PUNCT
bracis-28360	101	180	,	,	PUNCT
bracis-28360	101	181	(	(	PUNCT
bracis-28360	101	182	n)\	n)\	NOUN
bracis-28360	101	183	}	}	PUNCT
bracis-28360	101	184	)	)	PUNCT
bracis-28360	101	185	\bigr	\bigr	NOUN
bracis-28360	101	186	)	)	PUNCT
bracis-28360	101	187	)	)	PUNCT
bracis-28360	102	1	=	=	SYM
bracis-28360	102	2	0	0	NUM
bracis-28360	102	3	,	,	PUNCT
bracis-28360	102	4	\quad	\quad	PROPN
bracis-28360	102	5	\text	\text	ADV
bracis-28360	102	6	{	{	PUNCT
bracis-28360	102	7	by	by	ADP
bracis-28360	102	8	(	(	PUNCT
bracis-28360	102	9	d3	d3	PROPN
bracis-28360	102	10	)	)	PUNCT
bracis-28360	102	11	,	,	PUNCT
bracis-28360	102	12	}	}	PUNCT
bracis-28360	102	13	\end{aligned}$$	\end{aligned}$$	NOUN
bracis-28360	102	14	which	which	PRON
bracis-28360	102	15	is	be	AUX
bracis-28360	102	16	in	in	ADP
bracis-28360	102	17	contradiction	contradiction	NOUN
bracis-28360	102	18	to	to	ADP
bracis-28360	102	19	eq	eq	PROPN
bracis-28360	102	20	.	.	PUNCT
bracis-28360	102	21	 	 	SPACE
bracis-28360	102	22	(	(	PUNCT
bracis-28360	102	23	8)	8)	NUM
bracis-28360	102	24	.	.	PUNCT
bracis-28360	102	25	similarly	similarly	ADV
bracis-28360	102	26	,	,	PUNCT
bracis-28360	102	27	there	there	PRON
bracis-28360	102	28	is	be	VERB
bracis-28360	102	29	also	also	ADV
bracis-28360	102	30	a	a	DET
bracis-28360	102	31	contradiction	contradiction	NOUN
bracis-28360	102	32	for	for	ADP
bracis-28360	102	33	\(k	\(k	NOUN
bracis-28360	102	34	=	=	SYM
bracis-28360	102	35	1\	1\	NUM
bracis-28360	102	36	)	)	PUNCT
bracis-28360	102	37	.	.	PUNCT
bracis-28360	103	1	the	the	DET
bracis-28360	103	2	result	result	NOUN
bracis-28360	103	3	can	can	AUX
bracis-28360	103	4	be	be	AUX
bracis-28360	103	5	easily	easily	ADV
bracis-28360	103	6	generalized	generalize	VERB
bracis-28360	103	7	for	for	ADP
bracis-28360	103	8	any	any	DET
bracis-28360	103	9	subsets	subset	NOUN
bracis-28360	103	10	of	of	ADP
bracis-28360	103	11	repeated	repeat	VERB
bracis-28360	103	12	elements	element	NOUN
bracis-28360	103	13	in	in	ADP
bracis-28360	103	14	the	the	DET
bracis-28360	103	15	input	input	NOUN
bracis-28360	103	16	\(\boldsymbol{x}\	\(\boldsymbol{x}\	NUM
bracis-28360	103	17	)	)	PUNCT
bracis-28360	103	18	.	.	PUNCT
bracis-28360	104	1	the	the	DET
bracis-28360	104	2	conclusion	conclusion	NOUN
bracis-28360	104	3	is	be	AUX
bracis-28360	104	4	that	that	SCONJ
bracis-28360	104	5	for	for	ADP
bracis-28360	104	6	any	any	DET
bracis-28360	104	7	different	different	ADJ
bracis-28360	104	8	increasing	increase	VERB
bracis-28360	104	9	permutations	permutation	NOUN
bracis-28360	104	10	of	of	ADP
bracis-28360	104	11	the	the	DET
bracis-28360	104	12	same	same	ADJ
bracis-28360	104	13	input	input	NOUN
bracis-28360	104	14	\(\boldsymbol{x}\	\(\boldsymbol{x}\	NUM
bracis-28360	104	15	)	)	PUNCT
bracis-28360	104	16	,	,	PUNCT
bracis-28360	104	17	one	one	PRON
bracis-28360	104	18	always	always	ADV
bracis-28360	104	19	obtains	obtain	VERB
bracis-28360	104	20	the	the	DET
bracis-28360	104	21	same	same	ADJ
bracis-28360	104	22	output	output	NOUN
bracis-28360	104	23	value	value	NOUN
bracis-28360	104	24	of	of	ADP
bracis-28360	104	25	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	104	26	{	{	PUNCT
bracis-28360	104	27	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	104	28	,	,	PUNCT
bracis-28360	104	29	m}^c	m}^c	PROPN
bracis-28360	104	30	(	(	PUNCT
bracis-28360	104	31	\boldsymbol{x})\	\boldsymbol{x})\	NOUN
bracis-28360	104	32	)	)	PUNCT
bracis-28360	104	33	.	.	PUNCT
bracis-28360	105	1	remark	remark	NOUN
bracis-28360	105	2	1	1	NUM
bracis-28360	105	3	note	note	VERB
bracis-28360	105	4	that	that	SCONJ
bracis-28360	105	5	,	,	PUNCT
bracis-28360	105	6	in	in	ADP
bracis-28360	105	7	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	105	8	{	{	PUNCT
bracis-28360	105	9	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	105	10	,	,	PUNCT
bracis-28360	105	11	m}^c	m}^c	ADJ
bracis-28360	105	12	\	\	ADJ
bracis-28360	105	13	)	)	PUNCT
bracis-28360	105	14	definition	definition	NOUN
bracis-28360	105	15	,	,	PUNCT
bracis-28360	105	16	the	the	DET
bracis-28360	105	17	summation	summation	NOUN
bracis-28360	105	18	first	first	ADJ
bracis-28360	105	19	element	element	NOUN
bracis-28360	105	20	is	be	AUX
bracis-28360	105	21	just	just	ADV
bracis-28360	105	22	\(x_{(1)}\	\(x_{(1)}\	PRON
bracis-28360	105	23	)	)	PUNCT
bracis-28360	105	24	instead	instead	ADV
bracis-28360	105	25	of	of	ADP
bracis-28360	105	26	\(\delta	\(\delta	PROPN
bracis-28360	105	27	\left	\left	PROPN
bracis-28360	105	28	(	(	PUNCT
bracis-28360	105	29	c(x_{(1	c(x_{(1	NOUN
bracis-28360	105	30	)	)	PUNCT
bracis-28360	105	31	}	}	PUNCT
bracis-28360	105	32	,	,	PUNCT
bracis-28360	105	33	m_{(1)}),\	m_{(1)}),\	NOUN
bracis-28360	105	34	c(x_{(0)},m_{(1	c(x_{(0)},m_{(1	NOUN
bracis-28360	105	35	)	)	PUNCT
bracis-28360	105	36	}	}	PUNCT
bracis-28360	105	37	)	)	PUNCT
bracis-28360	106	1	\right	\right	NOUN
bracis-28360	106	2	)	)	PUNCT
bracis-28360	106	3	\	\	NOUN
bracis-28360	106	4	)	)	PUNCT
bracis-28360	106	5	.	.	PUNCT
bracis-28360	107	1	according	accord	VERB
bracis-28360	107	2	to	to	ADP
bracis-28360	107	3	[	[	X
bracis-28360	107	4	19	19	NUM
bracis-28360	107	5	,	,	PUNCT
bracis-28360	107	6	29	29	NUM
bracis-28360	107	7	]	]	PUNCT
bracis-28360	107	8	,	,	PUNCT
bracis-28360	107	9	this	this	PRON
bracis-28360	107	10	can	can	AUX
bracis-28360	107	11	be	be	AUX
bracis-28360	107	12	used	use	VERB
bracis-28360	107	13	to	to	PART
bracis-28360	107	14	avoid	avoid	VERB
bracis-28360	107	15	a	a	DET
bracis-28360	107	16	discrepant	discrepant	ADJ
bracis-28360	107	17	behavior	behavior	NOUN
bracis-28360	107	18	of	of	ADP
bracis-28360	107	19	non	non	ADJ
bracis-28360	107	20	-	-	ADJ
bracis-28360	107	21	averagingfootnote	averagingfootnote	ADJ
bracis-28360	107	22	1	1	NUM
bracis-28360	107	23	functions	function	NOUN
bracis-28360	107	24	in	in	ADP
bracis-28360	107	25	the	the	DET
bracis-28360	107	26	initial	initial	ADJ
bracis-28360	107	27	phase	phase	NOUN
bracis-28360	107	28	of	of	ADP
bracis-28360	107	29	the	the	DET
bracis-28360	107	30	aggregation	aggregation	NOUN
bracis-28360	107	31	process	process	NOUN
bracis-28360	107	32	.	.	PUNCT
bracis-28360	108	1	example	example	NOUN
bracis-28360	108	2	1	1	NUM
bracis-28360	108	3	it	it	PRON
bracis-28360	108	4	is	be	AUX
bracis-28360	108	5	immediate	immediate	ADJ
bracis-28360	108	6	that	that	SCONJ
bracis-28360	108	7	any	any	DET
bracis-28360	108	8	choices	choice	NOUN
bracis-28360	108	9	of	of	ADP
bracis-28360	108	10	rdf	rdf	VERB
bracis-28360	108	11	\(\delta	\(\delta	NOUN
bracis-28360	108	12	\	\	NOUN
bracis-28360	108	13	)	)	PUNCT
bracis-28360	108	14	from	from	ADP
bracis-28360	108	15	table	table	NOUN
bracis-28360	108	16	 	 	SPACE
bracis-28360	108	17	2	2	NUM
bracis-28360	108	18	and	and	CCONJ
bracis-28360	108	19	copula	copula	NOUN
bracis-28360	108	20	c	c	PROPN
bracis-28360	108	21	from	from	ADP
bracis-28360	108	22	table	table	NOUN
bracis-28360	108	23	 	 	SPACE
bracis-28360	108	24	1	1	NUM
bracis-28360	108	25	can	can	AUX
bracis-28360	108	26	be	be	AUX
bracis-28360	108	27	combined	combine	VERB
bracis-28360	108	28	to	to	PART
bracis-28360	108	29	obtain	obtain	VERB
bracis-28360	108	30	an	an	DET
bracis-28360	108	31	example	example	NOUN
bracis-28360	108	32	of	of	ADP
bracis-28360	108	33	d	d	PROPN
bracis-28360	108	34	-	-	PUNCT
bracis-28360	108	35	cc	cc	ADJ
bracis-28360	108	36	-	-	ADJ
bracis-28360	108	37	integral	integral	ADJ
bracis-28360	108	38	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	108	39	{	{	PUNCT
bracis-28360	108	40	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	108	41	,	,	PUNCT
bracis-28360	108	42	m}^c\	m}^c\	PROPN
bracis-28360	108	43	)	)	PUNCT
bracis-28360	108	44	.	.	PUNCT
bracis-28360	109	1	in	in	ADP
bracis-28360	109	2	the	the	DET
bracis-28360	109	3	following	following	NOUN
bracis-28360	109	4	,	,	PUNCT
bracis-28360	109	5	we	we	PRON
bracis-28360	109	6	first	first	ADV
bracis-28360	109	7	study	study	VERB
bracis-28360	109	8	some	some	DET
bracis-28360	109	9	general	general	ADJ
bracis-28360	109	10	properties	property	NOUN
bracis-28360	109	11	and	and	CCONJ
bracis-28360	109	12	then	then	ADV
bracis-28360	109	13	monotonicity	monotonicity	NOUN
bracis-28360	109	14	-	-	PUNCT
bracis-28360	109	15	like	like	ADJ
bracis-28360	109	16	properties	property	NOUN
bracis-28360	109	17	,	,	PUNCT
bracis-28360	109	18	for	for	ADP
bracis-28360	109	19	the	the	DET
bracis-28360	109	20	rdfs	rdfs	NOUN
bracis-28360	109	21	of	of	ADP
bracis-28360	109	22	table	table	NOUN
bracis-28360	109	23	 	 	SPACE
bracis-28360	109	24	2	2	NUM
bracis-28360	109	25	,	,	PUNCT
bracis-28360	109	26	any	any	DET
bracis-28360	109	27	fuzzy	fuzzy	ADJ
bracis-28360	109	28	measure	measure	NOUN
bracis-28360	109	29	m	m	NOUN
bracis-28360	109	30	and	and	CCONJ
bracis-28360	109	31	copula	copula	PROPN
bracis-28360	109	32	c.	c.	NOUN
bracis-28360	109	33	3.1	3.1	NUM
bracis-28360	109	34	some	some	DET
bracis-28360	109	35	important	important	ADJ
bracis-28360	109	36	properties	property	NOUN
bracis-28360	109	37	for	for	ADP
bracis-28360	109	38	 	 	SPACE
bracis-28360	109	39	aggregation	aggregation	NOUN
bracis-28360	109	40	-	-	PUNCT
bracis-28360	109	41	like	like	ADJ
bracis-28360	109	42	processes	process	NOUN
bracis-28360	109	43	the	the	DET
bracis-28360	109	44	next	next	ADJ
bracis-28360	109	45	proposition	proposition	NOUN
bracis-28360	109	46	shows	show	VERB
bracis-28360	109	47	that	that	SCONJ
bracis-28360	109	48	whenever	whenever	SCONJ
bracis-28360	109	49	the	the	DET
bracis-28360	109	50	adopted	adopt	VERB
bracis-28360	109	51	rdf	rdf	NOUN
bracis-28360	109	52	is	be	AUX
bracis-28360	109	53	constructed	construct	VERB
bracis-28360	109	54	using	use	VERB
bracis-28360	109	55	proposition	proposition	NOUN
bracis-28360	109	56	2	2	NUM
bracis-28360	109	57	,	,	PUNCT
bracis-28360	109	58	then	then	ADV
bracis-28360	109	59	,	,	PUNCT
bracis-28360	109	60	for	for	ADP
bracis-28360	109	61	some	some	DET
bracis-28360	109	62	choices	choice	NOUN
bracis-28360	109	63	of	of	ADP
bracis-28360	109	64	the	the	DET
bracis-28360	109	65	automorphism	automorphism	NOUN
bracis-28360	109	66	\(\varphi	\(\varphi	PROPN
bracis-28360	109	67	_	_	NOUN
bracis-28360	109	68	2\	2\	NUM
bracis-28360	109	69	)	)	PUNCT
bracis-28360	109	70	,	,	PUNCT
bracis-28360	109	71	the	the	DET
bracis-28360	109	72	result	result	NOUN
bracis-28360	109	73	obtained	obtain	VERB
bracis-28360	109	74	is	be	AUX
bracis-28360	109	75	upper	upper	ADJ
bracis-28360	109	76	limited	limited	ADJ
bracis-28360	109	77	in	in	ADP
bracis-28360	109	78	relation	relation	NOUN
bracis-28360	109	79	to	to	ADP
bracis-28360	109	80	the	the	DET
bracis-28360	109	81	dissimilarities	dissimilarity	NOUN
bracis-28360	109	82	(	(	PUNCT
bracis-28360	109	83	by	by	ADP
bracis-28360	109	84	\(\delta	\(\delta	NOUN
bracis-28360	109	85	_	_	NOUN
bracis-28360	109	86	0\	0\	NUM
bracis-28360	109	87	)	)	PUNCT
bracis-28360	109	88	)	)	PUNCT
bracis-28360	109	89	of	of	ADP
bracis-28360	109	90	the	the	DET
bracis-28360	109	91	inputs	input	NOUN
bracis-28360	109	92	:	:	PUNCT
bracis-28360	109	93	proposition	proposition	NOUN
bracis-28360	109	94	4	4	NUM
bracis-28360	109	95	let	let	VERB
bracis-28360	109	96	\(\delta	\(\delta	NOUN
bracis-28360	109	97	\	\	NOUN
bracis-28360	109	98	)	)	PUNCT
bracis-28360	109	99	be	be	AUX
bracis-28360	109	100	an	an	DET
bracis-28360	109	101	rdf	rdf	NOUN
bracis-28360	109	102	constructed	construct	VERB
bracis-28360	109	103	by	by	ADP
bracis-28360	109	104	proposition	proposition	NOUN
bracis-28360	109	105	 	 	SPACE
bracis-28360	109	106	2	2	NUM
bracis-28360	109	107	,	,	PUNCT
bracis-28360	109	108	for	for	ADP
bracis-28360	109	109	any	any	DET
bracis-28360	109	110	automorphism	automorphism	NOUN
bracis-28360	109	111	\(\varphi	\(\varphi	NOUN
bracis-28360	109	112	_	_	NOUN
bracis-28360	109	113	1\	1\	NUM
bracis-28360	109	114	)	)	PUNCT
bracis-28360	109	115	and	and	CCONJ
bracis-28360	109	116	the	the	DET
bracis-28360	109	117	identity	identity	NOUN
bracis-28360	109	118	as	as	ADP
bracis-28360	109	119	\(\varphi	\(\varphi	NOUN
bracis-28360	109	120	_	_	NOUN
bracis-28360	109	121	2\	2\	NUM
bracis-28360	109	122	)	)	PUNCT
bracis-28360	109	123	.	.	PUNCT
bracis-28360	110	1	let	let	VERB
bracis-28360	110	2	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	110	3	{	{	PUNCT
bracis-28360	110	4	cc}_{\delta	cc}_{\delta	PROPN
bracis-28360	110	5	,	,	PUNCT
bracis-28360	110	6	m}^c	m}^c	ADJ
bracis-28360	110	7	:	:	PUNCT
bracis-28360	111	1	[	[	X
bracis-28360	111	2	0	0	NUM
bracis-28360	111	3	,	,	PUNCT
bracis-28360	111	4	1]^n	1]^n	NUM
bracis-28360	111	5	\rightarrow	\rightarrow	PROPN
bracis-28360	112	1	[	[	X
bracis-28360	112	2	0,1]\	0,1]\	NOUN
bracis-28360	112	3	)	)	PUNCT
bracis-28360	112	4	be	be	VERB
bracis-28360	112	5	the	the	DET
bracis-28360	112	6	derived	derive	VERB
bracis-28360	112	7	d	d	NOUN
bracis-28360	112	8	-	-	PUNCT
bracis-28360	112	9	cc	cc	VERB
bracis-28360	112	10	integral	integral	ADJ
bracis-28360	112	11	for	for	ADP
bracis-28360	112	12	any	any	DET
bracis-28360	112	13	fuzzy	fuzzy	ADJ
bracis-28360	112	14	measure	measure	NOUN
bracis-28360	112	15	\(m\	\(m\	ADJ
bracis-28360	112	16	)	)	PUNCT
bracis-28360	112	17	and	and	CCONJ
bracis-28360	112	18	copula	copula	PROPN
bracis-28360	112	19	c.	c.	NOUN
bracis-28360	112	20	then	then	ADV
bracis-28360	112	21	,	,	PUNCT
bracis-28360	112	22	for	for	ADP
bracis-28360	112	23	all	all	DET
bracis-28360	112	24	\(\boldsymbol{x	\(\boldsymbol{x	ADJ
bracis-28360	112	25	}	}	PUNCT
bracis-28360	112	26	\in	\in	PROPN
bracis-28360	112	27	[	[	NOUN
bracis-28360	112	28	0,1]^n\	0,1]^n\	NOUN
bracis-28360	112	29	)	)	PUNCT
bracis-28360	112	30	,	,	PUNCT
bracis-28360	112	31	it	it	PRON
bracis-28360	112	32	holds	hold	VERB
bracis-28360	112	33	that	that	SCONJ
bracis-28360	112	34	:	:	PUNCT
bracis-28360	112	35	$	$	SYM
bracis-28360	112	36	$	$	SYM
bracis-28360	112	37	\begin{aligned	\begin{aligne	VERB
bracis-28360	112	38	}	}	PUNCT
bracis-28360	112	39	\mathfrak	\mathfrak	PROPN
bracis-28360	112	40	{	{	PUNCT
bracis-28360	112	41	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	112	42	,	,	PUNCT
bracis-28360	112	43	m}^c(\boldsymbol{x	m}^c(\boldsymbol{x	NOUN
bracis-28360	112	44	}	}	PUNCT
bracis-28360	112	45	)	)	PUNCT
bracis-28360	112	46	\le	\le	PROPN
bracis-28360	112	47	x_{(1	x_{(1	NOUN
bracis-28360	112	48	)	)	PUNCT
bracis-28360	112	49	}	}	PUNCT
bracis-28360	112	50	+	+	CCONJ
bracis-28360	113	1	\sum	\sum	NOUN
bracis-28360	113	2	_	_	PUNCT
bracis-28360	113	3	{	{	PUNCT
bracis-28360	113	4	i=2}^{n	i=2}^{n	ADJ
bracis-28360	113	5	}	}	PUNCT
bracis-28360	113	6	\varphi	\varphi	PROPN
bracis-28360	113	7	_	_	PROPN
bracis-28360	113	8	1	1	NUM
bracis-28360	113	9	\left	\left	PROPN
bracis-28360	113	10	(	(	PUNCT
bracis-28360	113	11	x_{(i	x_{(i	PROPN
bracis-28360	113	12	)	)	PUNCT
bracis-28360	113	13	}	}	PUNCT
bracis-28360	113	14	x_{(i-1	x_{(i-1	NUM
bracis-28360	113	15	)	)	PUNCT
bracis-28360	113	16	}	}	PUNCT
bracis-28360	113	17	\right	\right	PROPN
bracis-28360	113	18	)	)	PUNCT
bracis-28360	113	19	=	=	SYM
bracis-28360	113	20	x_{(1	x_{(1	NOUN
bracis-28360	113	21	)	)	PUNCT
bracis-28360	113	22	}	}	PUNCT
bracis-28360	114	1	+	+	CCONJ
bracis-28360	114	2	\sum	\sum	NOUN
bracis-28360	114	3	_	_	PUNCT
bracis-28360	114	4	{	{	PUNCT
bracis-28360	114	5	i=2}^{n	i=2}^{n	ADJ
bracis-28360	114	6	}	}	PUNCT
bracis-28360	114	7	\varphi	\varphi	PROPN
bracis-28360	114	8	_	_	PROPN
bracis-28360	114	9	1	1	NUM
bracis-28360	114	10	\left	\left	PROPN
bracis-28360	114	11	(	(	PUNCT
bracis-28360	114	12	\delta	\delta	PROPN
bracis-28360	114	13	_	_	PROPN
bracis-28360	114	14	0	0	PUNCT
bracis-28360	114	15	(	(	PUNCT
bracis-28360	114	16	x_{(i)},x_{(i-1	x_{(i)},x_{(i-1	NOUN
bracis-28360	114	17	)	)	PUNCT
bracis-28360	114	18	}	}	PUNCT
bracis-28360	114	19	)	)	PUNCT
bracis-28360	115	1	\right	\right	NOUN
bracis-28360	115	2	)	)	PUNCT
bracis-28360	115	3	.	.	PUNCT
bracis-28360	116	1	\end{aligned}$$	\end{aligned}$$	X
bracis-28360	117	1	proof	proof	NOUN
bracis-28360	117	2	let	let	VERB
bracis-28360	117	3	\(\delta	\(\delta	NOUN
bracis-28360	117	4	\	\	NOUN
bracis-28360	117	5	)	)	PUNCT
bracis-28360	117	6	be	be	AUX
bracis-28360	117	7	an	an	DET
bracis-28360	117	8	rdf	rdf	NOUN
bracis-28360	117	9	constructed	construct	VERB
bracis-28360	117	10	by	by	ADP
bracis-28360	117	11	proposition	proposition	NOUN
bracis-28360	117	12	2	2	NUM
bracis-28360	117	13	.	.	PUNCT
bracis-28360	118	1	then	then	ADV
bracis-28360	118	2	,	,	PUNCT
bracis-28360	118	3	since	since	SCONJ
bracis-28360	118	4	\(\varphi	\(\varphi	PROPN
bracis-28360	118	5	_	_	NOUN
bracis-28360	118	6	1\	1\	NUM
bracis-28360	118	7	)	)	PUNCT
bracis-28360	118	8	is	be	AUX
bracis-28360	118	9	an	an	DET
bracis-28360	118	10	automorphism	automorphism	NOUN
bracis-28360	118	11	,	,	PUNCT
bracis-28360	118	12	for	for	ADP
bracis-28360	118	13	any	any	DET
bracis-28360	118	14	\(\boldsymbol{x	\(\boldsymbol{x	ADJ
bracis-28360	118	15	}	}	PUNCT
bracis-28360	118	16	\in	\in	PROPN
bracis-28360	118	17	[	[	NOUN
bracis-28360	118	18	0,1]\	0,1]\	NOUN
bracis-28360	118	19	)	)	PUNCT
bracis-28360	118	20	,	,	PUNCT
bracis-28360	118	21	fm	fm	PROPN
bracis-28360	118	22	\(m\	\(m\	PROPN
bracis-28360	118	23	)	)	PUNCT
bracis-28360	118	24	and	and	CCONJ
bracis-28360	118	25	copula	copula	NOUN
bracis-28360	118	26	c	c	X
bracis-28360	118	27	,	,	PUNCT
bracis-28360	118	28	we	we	PRON
bracis-28360	118	29	have	have	VERB
bracis-28360	118	30	that	that	PRON
bracis-28360	118	31	:	:	PUNCT
bracis-28360	119	1	$	$	SYM
bracis-28360	119	2	$	$	SYM
bracis-28360	119	3	\begin{aligned	\begin{aligne	VERB
bracis-28360	119	4	}	}	PUNCT
bracis-28360	119	5	\mathfrak	\mathfrak	PROPN
bracis-28360	119	6	{	{	PUNCT
bracis-28360	119	7	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	119	8	,	,	PUNCT
bracis-28360	119	9	m}^c(\boldsymbol{x	m}^c(\boldsymbol{x	NOUN
bracis-28360	119	10	}	}	PUNCT
bracis-28360	119	11	)	)	PUNCT
bracis-28360	119	12	&	&	CCONJ
bracis-28360	119	13	=	=	SYM
bracis-28360	119	14	x_{(1	x_{(1	PROPN
bracis-28360	119	15	)	)	PUNCT
bracis-28360	119	16	}	}	PUNCT
bracis-28360	119	17	+	+	CCONJ
bracis-28360	119	18	\sum	\sum	NOUN
bracis-28360	119	19	_	_	PUNCT
bracis-28360	119	20	{	{	PUNCT
bracis-28360	119	21	i=2}^{n	i=2}^{n	ADJ
bracis-28360	119	22	}	}	PUNCT
bracis-28360	119	23	\delta	\delta	PROPN
bracis-28360	119	24	(	(	PUNCT
bracis-28360	119	25	c(x_{(i	c(x_{(i	PROPN
bracis-28360	119	26	)	)	PUNCT
bracis-28360	119	27	}	}	PUNCT
bracis-28360	119	28	,	,	PUNCT
bracis-28360	119	29	m_{(i	m_{(i	PROPN
bracis-28360	119	30	)	)	PUNCT
bracis-28360	119	31	}	}	PUNCT
bracis-28360	119	32	)	)	PUNCT
bracis-28360	119	33	,	,	PUNCT
bracis-28360	119	34	c(x_{(i-1	c(x_{(i-1	NOUN
bracis-28360	119	35	)	)	PUNCT
bracis-28360	119	36	}	}	PUNCT
bracis-28360	119	37	,	,	PUNCT
bracis-28360	119	38	m_{(i	m_{(i	PROPN
bracis-28360	119	39	)	)	PUNCT
bracis-28360	119	40	}	}	PUNCT
bracis-28360	119	41	)	)	PUNCT
bracis-28360	119	42	)	)	PUNCT
bracis-28360	119	43	\\	\\	NOUN
bracis-28360	119	44	&	&	CCONJ
bracis-28360	119	45	=	=	PROPN
bracis-28360	119	46	x_{(1	x_{(1	PROPN
bracis-28360	119	47	)	)	PUNCT
bracis-28360	119	48	}	}	PUNCT
bracis-28360	119	49	+	+	CCONJ
bracis-28360	119	50	\sum	\sum	NOUN
bracis-28360	119	51	_	_	PUNCT
bracis-28360	119	52	{	{	PUNCT
bracis-28360	119	53	i=2}^{n	i=2}^{n	ADJ
bracis-28360	119	54	}	}	PUNCT
bracis-28360	119	55	\varphi	\varphi	PROPN
bracis-28360	119	56	_	_	PROPN
bracis-28360	119	57	1	1	NUM
bracis-28360	119	58	\left	\left	PROPN
bracis-28360	119	59	(	(	PUNCT
bracis-28360	119	60	c(x_{(i	c(x_{(i	PROPN
bracis-28360	119	61	)	)	PUNCT
bracis-28360	119	62	}	}	PUNCT
bracis-28360	119	63	,	,	PUNCT
bracis-28360	119	64	m_{(i	m_{(i	PROPN
bracis-28360	119	65	)	)	PUNCT
bracis-28360	119	66	}	}	PUNCT
bracis-28360	119	67	)	)	PUNCT
bracis-28360	119	68	c(x_{(i-1	c(x_{(i-1	NOUN
bracis-28360	119	69	)	)	PUNCT
bracis-28360	119	70	}	}	PUNCT
bracis-28360	119	71	,	,	PUNCT
bracis-28360	119	72	m_{(i)})\right	m_{(i)})\right	ADJ
bracis-28360	119	73	)	)	PUNCT
bracis-28360	119	74	\text	\text	NOUN
bracis-28360	119	75	{	{	PUNCT
bracis-28360	119	76	by	by	ADP
bracis-28360	119	77	props	prop	NOUN
bracis-28360	119	78	.	.	PUNCT
bracis-28360	119	79	2	2	NUM
bracis-28360	119	80	and	and	CCONJ
bracis-28360	119	81	1(i	1(i	NUM
bracis-28360	119	82	)	)	PUNCT
bracis-28360	119	83	}	}	PUNCT
bracis-28360	119	84	\\	\\	NOUN
bracis-28360	119	85	&	&	CCONJ
bracis-28360	119	86	\le	\le	PROPN
bracis-28360	119	87	x_{(1	x_{(1	PROPN
bracis-28360	119	88	)	)	PUNCT
bracis-28360	119	89	}	}	PUNCT
bracis-28360	120	1	+	+	CCONJ
bracis-28360	120	2	\sum	\sum	NOUN
bracis-28360	120	3	_	_	PUNCT
bracis-28360	120	4	{	{	PUNCT
bracis-28360	120	5	i=2}^{n	i=2}^{n	ADJ
bracis-28360	120	6	}	}	PUNCT
bracis-28360	120	7	\varphi	\varphi	PROPN
bracis-28360	120	8	_	_	PROPN
bracis-28360	120	9	1	1	NUM
bracis-28360	120	10	\left	\left	PROPN
bracis-28360	120	11	(	(	PUNCT
bracis-28360	120	12	x_{(i	x_{(i	PROPN
bracis-28360	120	13	)	)	PUNCT
bracis-28360	120	14	}	}	PUNCT
bracis-28360	120	15	x_{(i-1	x_{(i-1	NUM
bracis-28360	120	16	)	)	PUNCT
bracis-28360	120	17	}	}	PUNCT
bracis-28360	120	18	\right	\right	PROPN
bracis-28360	120	19	)	)	PUNCT
bracis-28360	120	20	\text	\text	NOUN
bracis-28360	120	21	{	{	PUNCT
bracis-28360	120	22	by	by	ADP
bracis-28360	120	23	prop	prop	NOUN
bracis-28360	120	24	.	.	PUNCT
bracis-28360	121	1	1	1	NUM
bracis-28360	121	2	(	(	PUNCT
bracis-28360	121	3	ii	ii	NOUN
bracis-28360	121	4	)	)	PUNCT
bracis-28360	121	5	}	}	PUNCT
bracis-28360	121	6	\end{aligned}$$	\end{aligned}$$	ADP
bracis-28360	121	7	the	the	DET
bracis-28360	121	8	following	follow	VERB
bracis-28360	121	9	three	three	NUM
bracis-28360	121	10	results	result	NOUN
bracis-28360	121	11	are	be	AUX
bracis-28360	121	12	immediate	immediate	ADJ
bracis-28360	121	13	:	:	PUNCT
bracis-28360	121	14	proposition	proposition	NOUN
bracis-28360	121	15	5	5	NUM
bracis-28360	121	16	for	for	ADP
bracis-28360	121	17	\(\delta	\(\delta	NOUN
bracis-28360	121	18	\	\	NOUN
bracis-28360	121	19	)	)	PUNCT
bracis-28360	121	20	,	,	PUNCT
bracis-28360	121	21	m	m	VERB
bracis-28360	121	22	and	and	CCONJ
bracis-28360	121	23	c	c	X
bracis-28360	121	24	,	,	PUNCT
bracis-28360	121	25	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	121	26	{	{	PUNCT
bracis-28360	121	27	cc}_{\delta	cc}_{\delta	PROPN
bracis-28360	121	28	,	,	PUNCT
bracis-28360	121	29	m}^c	m}^c	PROPN
bracis-28360	121	30	(	(	PUNCT
bracis-28360	121	31	\boldsymbol{x	\boldsymbol{x	NOUN
bracis-28360	121	32	}	}	PUNCT
bracis-28360	121	33	)	)	PUNCT
bracis-28360	121	34	\ge	\ge	PROPN
bracis-28360	121	35	\min	\min	PROPN
bracis-28360	121	36	(	(	PUNCT
bracis-28360	121	37	\boldsymbol{x})\	\boldsymbol{x})\	NOUN
bracis-28360	121	38	)	)	PUNCT
bracis-28360	121	39	,	,	PUNCT
bracis-28360	121	40	for	for	ADP
bracis-28360	121	41	all	all	DET
bracis-28360	121	42	\(\boldsymbol{x	\(\boldsymbol{x	ADJ
bracis-28360	121	43	}	}	PUNCT
bracis-28360	121	44	\in	\in	PROPN
bracis-28360	121	45	[	[	NOUN
bracis-28360	121	46	0,1]\	0,1]\	NOUN
bracis-28360	121	47	)	)	PUNCT
bracis-28360	121	48	.	.	PUNCT
bracis-28360	122	1	proposition	proposition	NOUN
bracis-28360	122	2	6	6	NUM
bracis-28360	122	3	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	122	4	{	{	PUNCT
bracis-28360	122	5	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	122	6	,	,	PUNCT
bracis-28360	122	7	m}^c(\boldsymbol{x	m}^c(\boldsymbol{x	NOUN
bracis-28360	122	8	}	}	PUNCT
bracis-28360	122	9	)	)	PUNCT
bracis-28360	122	10	\le	\le	PROPN
bracis-28360	122	11	\max	\max	PROPN
bracis-28360	122	12	(	(	PUNCT
bracis-28360	122	13	\boldsymbol{x})\	\boldsymbol{x})\	NOUN
bracis-28360	122	14	)	)	PUNCT
bracis-28360	123	1	if	if	SCONJ
bracis-28360	123	2	and	and	CCONJ
bracis-28360	123	3	only	only	ADV
bracis-28360	123	4	if	if	SCONJ
bracis-28360	123	5	,	,	PUNCT
bracis-28360	123	6	for	for	ADP
bracis-28360	123	7	all	all	DET
bracis-28360	123	8	\(0	\(0	NUM
bracis-28360	123	9	\le	\le	PROPN
bracis-28360	123	10	a_1	a_1	NOUN
bracis-28360	123	11	\le	\le	PROPN
bracis-28360	123	12	\ldots	\ldots	ADP
bracis-28360	123	13	\le	\le	PROPN
bracis-28360	123	14	a_n	a_n	SYM
bracis-28360	123	15	\	\	NOUN
bracis-28360	123	16	)	)	PUNCT
bracis-28360	123	17	and	and	CCONJ
bracis-28360	123	18	fm	fm	PROPN
bracis-28360	123	19	\(m\	\(m\	PROPN
bracis-28360	123	20	)	)	PUNCT
bracis-28360	123	21	,	,	PUNCT
bracis-28360	123	22	the	the	PRON
bracis-28360	123	23	rdf	rdf	VERB
bracis-28360	123	24	\(\delta	\(\delta	NOUN
bracis-28360	123	25	\	\	NOUN
bracis-28360	123	26	)	)	PUNCT
bracis-28360	123	27	satisfies	satisfie	NOUN
bracis-28360	123	28	:	:	PUNCT
bracis-28360	124	1	\	\	PROPN
bracis-28360	124	2	(	(	PUNCT
bracis-28360	124	3	\sum	\sum	NOUN
bracis-28360	124	4	_	_	PUNCT
bracis-28360	124	5	{	{	PUNCT
bracis-28360	124	6	i=2}^n	i=2}^n	PROPN
bracis-28360	124	7	\delta	\delta	PROPN
bracis-28360	124	8	(	(	PUNCT
bracis-28360	124	9	c(a_i	c(a_i	PROPN
bracis-28360	124	10	,	,	PUNCT
bracis-28360	124	11	m_{i}),\	m_{i}),\	NOUN
bracis-28360	124	12	c(a_{i-1	c(a_{i-1	NUM
bracis-28360	124	13	}	}	PUNCT
bracis-28360	124	14	,	,	PUNCT
bracis-28360	124	15	m_{i	m_{i	ADJ
bracis-28360	124	16	}	}	PUNCT
bracis-28360	124	17	)	)	PUNCT
bracis-28360	124	18	)	)	PUNCT
bracis-28360	124	19	\le	\le	PROPN
bracis-28360	124	20	a_n	a_n	PUNCT
bracis-28360	124	21	a_1	a_1	NOUN
bracis-28360	124	22	,	,	PUNCT
bracis-28360	124	23	\	\	PROPN
bracis-28360	124	24	)	)	PUNCT
bracis-28360	124	25	where	where	SCONJ
bracis-28360	124	26	\(m_i	\(m_i	ADV
bracis-28360	124	27	=	=	SYM
bracis-28360	124	28	m(a_{i})\	m(a_{i})\	NOUN
bracis-28360	124	29	)	)	PUNCT
bracis-28360	124	30	,	,	PUNCT
bracis-28360	124	31	for	for	ADP
bracis-28360	124	32	\(a_i	\(a_i	NOUN
bracis-28360	124	33	=	=	SYM
bracis-28360	124	34	\{i	\{i	NOUN
bracis-28360	124	35	,	,	PUNCT
bracis-28360	124	36	\ldots	\ldots	INTJ
bracis-28360	124	37	,	,	PUNCT
bracis-28360	124	38	n\}\	n\}\	ADJ
bracis-28360	124	39	)	)	PUNCT
bracis-28360	124	40	.	.	PUNCT
bracis-28360	125	1	corollary	corollary	ADJ
bracis-28360	125	2	1	1	NUM
bracis-28360	125	3	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	125	4	{	{	PUNCT
bracis-28360	125	5	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	125	6	,	,	PUNCT
bracis-28360	125	7	m}^c\	m}^c\	PROPN
bracis-28360	125	8	)	)	PUNCT
bracis-28360	125	9	is	be	AUX
bracis-28360	125	10	averaging	average	VERB
bracis-28360	125	11	if	if	SCONJ
bracis-28360	125	12	and	and	CCONJ
bracis-28360	125	13	only	only	ADV
bracis-28360	125	14	if	if	SCONJ
bracis-28360	125	15	it	it	PRON
bracis-28360	125	16	satisfies	satisfy	VERB
bracis-28360	125	17	proposition	proposition	NOUN
bracis-28360	125	18	6	6	NUM
bracis-28360	125	19	.	.	PUNCT
bracis-28360	125	20	proposition	proposition	NOUN
bracis-28360	125	21	7	7	NUM
bracis-28360	125	22	for	for	ADP
bracis-28360	125	23	any	any	DET
bracis-28360	125	24	rdf	rdf	NOUN
bracis-28360	125	25	\(\delta	\(\delta	NOUN
bracis-28360	125	26	\	\	NOUN
bracis-28360	125	27	)	)	PUNCT
bracis-28360	125	28	,	,	PUNCT
bracis-28360	125	29	fm	fm	PROPN
bracis-28360	125	30	m	m	PROPN
bracis-28360	125	31	and	and	CCONJ
bracis-28360	125	32	copula	copula	VERB
bracis-28360	126	1	c	c	X
bracis-28360	126	2	,	,	PUNCT
bracis-28360	126	3	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	126	4	{	{	PUNCT
bracis-28360	126	5	cc}_{\delta	cc}_{\delta	PROPN
bracis-28360	126	6	,	,	PUNCT
bracis-28360	126	7	m}^c\	m}^c\	PROPN
bracis-28360	126	8	)	)	PUNCT
bracis-28360	126	9	is	be	AUX
bracis-28360	126	10	idempotent	idempotent	ADJ
bracis-28360	126	11	.	.	PUNCT
bracis-28360	127	1	proof	proof	NOUN
bracis-28360	127	2	if	if	SCONJ
bracis-28360	127	3	\(\boldsymbol{x	\(\boldsymbol{x	NOUN
bracis-28360	127	4	}	}	PUNCT
bracis-28360	127	5	=	=	SYM
bracis-28360	127	6	(	(	PUNCT
bracis-28360	127	7	x	x	X
bracis-28360	127	8	,	,	PUNCT
bracis-28360	127	9	\ldots	\ldots	INTJ
bracis-28360	127	10	,	,	PUNCT
bracis-28360	127	11	x)\	x)\	PROPN
bracis-28360	127	12	)	)	PUNCT
bracis-28360	127	13	,	,	PUNCT
bracis-28360	127	14	then	then	ADV
bracis-28360	127	15	,	,	PUNCT
bracis-28360	127	16	by	by	ADP
bracis-28360	127	17	(	(	PUNCT
bracis-28360	127	18	d3	d3	PROPN
bracis-28360	127	19	)	)	PUNCT
bracis-28360	127	20	,	,	PUNCT
bracis-28360	127	21	one	one	PRON
bracis-28360	127	22	has	have	VERB
bracis-28360	127	23	that	that	PRON
bracis-28360	127	24	:	:	PUNCT
bracis-28360	127	25	$	$	SYM
bracis-28360	127	26	$	$	SYM
bracis-28360	127	27	\begin{aligned	\begin{aligne	VERB
bracis-28360	127	28	}	}	PUNCT
bracis-28360	127	29	\mathfrak	\mathfrak	PROPN
bracis-28360	127	30	{	{	PUNCT
bracis-28360	127	31	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	127	32	,	,	PUNCT
bracis-28360	127	33	m}^c(\boldsymbol{x	m}^c(\boldsymbol{x	NOUN
bracis-28360	127	34	}	}	PUNCT
bracis-28360	127	35	)	)	PUNCT
bracis-28360	128	1	=	=	PUNCT
bracis-28360	128	2	x	x	PUNCT
bracis-28360	129	1	+	+	PUNCT
bracis-28360	129	2	\sum	\sum	NOUN
bracis-28360	129	3	_	_	PUNCT
bracis-28360	129	4	{	{	PUNCT
bracis-28360	129	5	i=2}^{n	i=2}^{n	ADJ
bracis-28360	129	6	}	}	PUNCT
bracis-28360	129	7	\delta	\delta	PROPN
bracis-28360	129	8	\left	\left	PROPN
bracis-28360	129	9	(	(	PUNCT
bracis-28360	129	10	c(x	c(x	PROPN
bracis-28360	129	11	,	,	PUNCT
bracis-28360	129	12	m_{(i	m_{(i	PROPN
bracis-28360	129	13	)	)	PUNCT
bracis-28360	129	14	}	}	PUNCT
bracis-28360	129	15	)	)	PUNCT
bracis-28360	129	16	,	,	PUNCT
bracis-28360	129	17	c(x	c(x	NOUN
bracis-28360	129	18	,	,	PUNCT
bracis-28360	129	19	m_{(i)})\right	m_{(i)})\right	ADJ
bracis-28360	129	20	)	)	PUNCT
bracis-28360	129	21	=	=	SYM
bracis-28360	129	22	x	x	PUNCT
bracis-28360	130	1	+	+	NOUN
bracis-28360	130	2	0	0	NUM
bracis-28360	130	3	=	=	SYM
bracis-28360	130	4	x.	x.	NOUN
bracis-28360	130	5	\end{aligned}$$	\end{aligned}$$	NOUN
bracis-28360	130	6	since	since	SCONJ
bracis-28360	130	7	the	the	DET
bracis-28360	130	8	range	range	NOUN
bracis-28360	130	9	of	of	ADP
bracis-28360	130	10	the	the	DET
bracis-28360	130	11	dcc	dcc	NOUN
bracis-28360	130	12	-	-	PUNCT
bracis-28360	130	13	integral	integral	ADJ
bracis-28360	130	14	is	be	AUX
bracis-28360	130	15	[	[	X
bracis-28360	130	16	0	0	NUM
bracis-28360	130	17	,	,	PUNCT
bracis-28360	130	18	 	 	SPACE
bracis-28360	130	19	n	n	CCONJ
bracis-28360	130	20	]	]	PUNCT
bracis-28360	130	21	,	,	PUNCT
bracis-28360	130	22	we	we	PRON
bracis-28360	130	23	avoid	avoid	VERB
bracis-28360	130	24	the	the	DET
bracis-28360	130	25	term	term	NOUN
bracis-28360	130	26	“	"	PUNCT
bracis-28360	130	27	boundary	boundary	ADJ
bracis-28360	130	28	condition	condition	NOUN
bracis-28360	130	29	”	"	PUNCT
bracis-28360	130	30	when	when	SCONJ
bracis-28360	130	31	referring	refer	VERB
bracis-28360	130	32	to	to	ADP
bracis-28360	130	33	condition	condition	NOUN
bracis-28360	130	34	(	(	PUNCT
bracis-28360	130	35	a2	a2	PROPN
bracis-28360	130	36	)	)	PUNCT
bracis-28360	130	37	in	in	ADP
bracis-28360	130	38	this	this	DET
bracis-28360	130	39	context	context	NOUN
bracis-28360	130	40	.	.	PUNCT
bracis-28360	131	1	instead	instead	ADV
bracis-28360	131	2	,	,	PUNCT
bracis-28360	131	3	we	we	PRON
bracis-28360	131	4	simply	simply	ADV
bracis-28360	131	5	call	call	VERB
bracis-28360	131	6	it	it	PRON
bracis-28360	131	7	0	0	NUM
bracis-28360	131	8	,	,	PUNCT
bracis-28360	131	9	 	 	SPACE
bracis-28360	131	10	1	1	NUM
bracis-28360	131	11	-	-	PUNCT
bracis-28360	131	12	condition	condition	NOUN
bracis-28360	131	13	.	.	PUNCT
bracis-28360	132	1	the	the	DET
bracis-28360	132	2	same	same	ADJ
bracis-28360	132	3	term	term	NOUN
bracis-28360	132	4	was	be	AUX
bracis-28360	132	5	also	also	ADV
bracis-28360	132	6	adopted	adopt	VERB
bracis-28360	132	7	in	in	ADP
bracis-28360	132	8	[	[	X
bracis-28360	132	9	29	29	NUM
bracis-28360	132	10	]	]	PUNCT
bracis-28360	132	11	.	.	PUNCT
bracis-28360	133	1	from	from	ADP
bracis-28360	133	2	proposition	proposition	NOUN
bracis-28360	133	3	7	7	NUM
bracis-28360	133	4	,	,	PUNCT
bracis-28360	133	5	the	the	DET
bracis-28360	133	6	following	following	ADJ
bracis-28360	133	7	result	result	NOUN
bracis-28360	133	8	is	be	AUX
bracis-28360	133	9	immediate	immediate	ADJ
bracis-28360	133	10	:	:	PUNCT
bracis-28360	133	11	corollary	corollary	ADJ
bracis-28360	133	12	2	2	NUM
bracis-28360	133	13	the	the	DET
bracis-28360	133	14	d	d	NOUN
bracis-28360	133	15	-	-	PUNCT
bracis-28360	133	16	cc	cc	VERB
bracis-28360	133	17	integral	integral	ADJ
bracis-28360	133	18	satisfies	satisfie	NOUN
bracis-28360	133	19	the	the	DET
bracis-28360	133	20	0	0	NUM
bracis-28360	133	21	,	,	PUNCT
bracis-28360	133	22	 	 	SPACE
bracis-28360	133	23	1	1	NUM
bracis-28360	133	24	-	-	PUNCT
bracis-28360	133	25	condition	condition	NOUN
bracis-28360	133	26	for	for	ADP
bracis-28360	133	27	any	any	DET
bracis-28360	133	28	m	m	NOUN
bracis-28360	133	29	,	,	PUNCT
bracis-28360	133	30	\(\delta	\(\delta	NOUN
bracis-28360	133	31	\	\	NOUN
bracis-28360	133	32	)	)	PUNCT
bracis-28360	133	33	and	and	CCONJ
bracis-28360	133	34	c.	c.	PROPN
bracis-28360	133	35	3.2	3.2	NUM
bracis-28360	133	36	monotonicity	monotonicity	NOUN
bracis-28360	133	37	-	-	PUNCT
bracis-28360	133	38	like	like	ADJ
bracis-28360	133	39	properties	property	NOUN
bracis-28360	133	40	of	of	ADP
bracis-28360	133	41	d	d	NOUN
bracis-28360	133	42	-	-	PUNCT
bracis-28360	133	43	cc	cc	NOUN
bracis-28360	133	44	integrals	integral	NOUN
bracis-28360	133	45	as	as	SCONJ
bracis-28360	133	46	explained	explain	VERB
bracis-28360	133	47	in	in	ADP
bracis-28360	133	48	[	[	PUNCT
bracis-28360	133	49	13	13	NUM
bracis-28360	133	50	]	]	PUNCT
bracis-28360	133	51	,	,	PUNCT
bracis-28360	133	52	one	one	NUM
bracis-28360	133	53	important	important	ADJ
bracis-28360	133	54	property	property	NOUN
bracis-28360	133	55	of	of	ADP
bracis-28360	133	56	aggregation	aggregation	NOUN
bracis-28360	133	57	-	-	PUNCT
bracis-28360	133	58	like	like	ADJ
bracis-28360	133	59	operators	operator	NOUN
bracis-28360	133	60	is	be	AUX
bracis-28360	133	61	to	to	PART
bracis-28360	133	62	present	present	VERB
bracis-28360	133	63	some	some	DET
bracis-28360	133	64	kind	kind	NOUN
bracis-28360	133	65	of	of	ADP
bracis-28360	133	66	“	"	PUNCT
bracis-28360	133	67	increasingness	increasingness	ADJ
bracis-28360	133	68	property	property	NOUN
bracis-28360	133	69	”	"	PUNCT
bracis-28360	133	70	to	to	PART
bracis-28360	133	71	guarantee	guarantee	VERB
bracis-28360	133	72	that	that	SCONJ
bracis-28360	133	73	the	the	DET
bracis-28360	133	74	more	more	ADJ
bracis-28360	133	75	information	information	NOUN
bracis-28360	133	76	is	be	AUX
bracis-28360	133	77	provided	provide	VERB
bracis-28360	133	78	the	the	DET
bracis-28360	133	79	higher	high	ADJ
bracis-28360	133	80	the	the	DET
bracis-28360	133	81	aggregated	aggregate	VERB
bracis-28360	133	82	value	value	NOUN
bracis-28360	133	83	is	be	AUX
bracis-28360	133	84	in	in	ADP
bracis-28360	133	85	the	the	DET
bracis-28360	133	86	considered	consider	VERB
bracis-28360	133	87	direction	direction	NOUN
bracis-28360	133	88	.	.	PUNCT
bracis-28360	134	1	from	from	ADP
bracis-28360	134	2	the	the	DET
bracis-28360	134	3	discussions	discussion	NOUN
bracis-28360	134	4	in	in	ADP
bracis-28360	134	5	[	[	X
bracis-28360	134	6	29	29	NUM
bracis-28360	134	7	]	]	PUNCT
bracis-28360	134	8	,	,	PUNCT
bracis-28360	134	9	it	it	PRON
bracis-28360	134	10	is	be	AUX
bracis-28360	134	11	immediate	immediate	ADJ
bracis-28360	134	12	that	that	SCONJ
bracis-28360	134	13	d	d	X
bracis-28360	134	14	-	-	PUNCT
bracis-28360	134	15	cc	cc	ADP
bracis-28360	134	16	integrals	integral	NOUN
bracis-28360	134	17	can	can	AUX
bracis-28360	134	18	not	not	PART
bracis-28360	134	19	be	be	AUX
bracis-28360	134	20	fully	fully	ADV
bracis-28360	134	21	monotonic	monotonic	ADJ
bracis-28360	134	22	,	,	PUNCT
bracis-28360	134	23	in	in	ADP
bracis-28360	134	24	general	general	ADJ
bracis-28360	134	25	,	,	PUNCT
bracis-28360	134	26	since	since	SCONJ
bracis-28360	134	27	they	they	PRON
bracis-28360	134	28	have	have	VERB
bracis-28360	134	29	to	to	PART
bracis-28360	134	30	satisfy	satisfy	VERB
bracis-28360	134	31	the	the	DET
bracis-28360	134	32	following	following	ADJ
bracis-28360	134	33	conditions	condition	NOUN
bracis-28360	134	34	:	:	PUNCT
bracis-28360	134	35	(	(	PUNCT
bracis-28360	134	36	i	i	NOUN
bracis-28360	134	37	)	)	PUNCT
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bracis-28360	134	39	\(z_1	\(z_1	PROPN
bracis-28360	134	40	,	,	PUNCT
bracis-28360	134	41	z_2	z_2	NOUN
bracis-28360	134	42	,	,	PUNCT
bracis-28360	134	43	z_3	z_3	NOUN
bracis-28360	134	44	,	,	PUNCT
bracis-28360	134	45	z_4	z_4	X
bracis-28360	134	46	\in	\in	PROPN
bracis-28360	135	1	[	[	X
bracis-28360	135	2	0,1]\	0,1]\	NOUN
bracis-28360	135	3	)	)	PUNCT
bracis-28360	135	4	,	,	PUNCT
bracis-28360	135	5	with	with	ADP
bracis-28360	135	6	\(z_1	\(z_1	PROPN
bracis-28360	135	7	\le	\le	PROPN
bracis-28360	135	8	z_2	z_2	PROPN
bracis-28360	135	9	\le	\le	PROPN
bracis-28360	135	10	z_3	z_3	PROPN
bracis-28360	135	11	\le	\le	NOUN
bracis-28360	135	12	z_4\	z_4\	NUM
bracis-28360	135	13	)	)	PUNCT
bracis-28360	135	14	,	,	PUNCT
bracis-28360	135	15	\(w_1	\(w_1	NUM
bracis-28360	135	16	,	,	PUNCT
bracis-28360	135	17	w_2	w_2	PROPN
bracis-28360	135	18	\in	\in	PROPN
bracis-28360	135	19	[	[	X
bracis-28360	135	20	0,1]\	0,1]\	NOUN
bracis-28360	135	21	)	)	PUNCT
bracis-28360	135	22	,	,	PUNCT
bracis-28360	135	23	with	with	ADP
bracis-28360	135	24	\(w_1	\(w_1	NUM
bracis-28360	135	25	\ge	\ge	PROPN
bracis-28360	135	26	w_2\	w_2\	NUM
bracis-28360	135	27	)	)	PUNCT
bracis-28360	135	28	,	,	PUNCT
bracis-28360	135	29	we	we	PRON
bracis-28360	135	30	have	have	VERB
bracis-28360	135	31	:	:	PUNCT
bracis-28360	135	32	\(\delta	\(\delta	NOUN
bracis-28360	135	33	(	(	PUNCT
bracis-28360	135	34	c(z_1	c(z_1	ADV
bracis-28360	135	35	,	,	PUNCT
bracis-28360	135	36	w_1	w_1	PROPN
bracis-28360	135	37	)	)	PUNCT
bracis-28360	135	38	,	,	PUNCT
bracis-28360	135	39	c(z_3	c(z_3	NOUN
bracis-28360	135	40	,	,	PUNCT
bracis-28360	135	41	w_1	w_1	NOUN
bracis-28360	135	42	)	)	PUNCT
bracis-28360	135	43	)	)	PUNCT
bracis-28360	136	1	+	+	CCONJ
bracis-28360	136	2	\delta	\delta	PROPN
bracis-28360	136	3	(	(	PUNCT
bracis-28360	136	4	c(z_3	c(z_3	NOUN
bracis-28360	136	5	,	,	PUNCT
bracis-28360	136	6	w_2	w_2	PROPN
bracis-28360	136	7	)	)	PUNCT
bracis-28360	136	8	,	,	PUNCT
bracis-28360	136	9	c(z_4	c(z_4	PROPN
bracis-28360	136	10	,	,	PUNCT
bracis-28360	136	11	w_2	w_2	PROPN
bracis-28360	136	12	)	)	PUNCT
bracis-28360	136	13	)	)	PUNCT
bracis-28360	136	14	\ge	\ge	PROPN
bracis-28360	136	15	\delta	\delta	PROPN
bracis-28360	136	16	(	(	PUNCT
bracis-28360	136	17	c(z_1,w_1	c(z_1,w_1	PROPN
bracis-28360	136	18	)	)	PUNCT
bracis-28360	136	19	,	,	PUNCT
bracis-28360	136	20	c(z_2	c(z_2	NOUN
bracis-28360	136	21	,	,	PUNCT
bracis-28360	136	22	w_1))\	w_1))\	NOUN
bracis-28360	136	23	)	)	PUNCT
bracis-28360	136	24	\(+	\(+	PROPN
bracis-28360	136	25	\delta	\delta	PROPN
bracis-28360	136	26	(	(	PUNCT
bracis-28360	136	27	c(z_2	c(z_2	PROPN
bracis-28360	136	28	,	,	PUNCT
bracis-28360	136	29	w_2	w_2	PROPN
bracis-28360	136	30	)	)	PUNCT
bracis-28360	136	31	,	,	PUNCT
bracis-28360	136	32	c(z_4	c(z_4	PROPN
bracis-28360	136	33	,	,	PUNCT
bracis-28360	136	34	w_2))\	w_2))\	PROPN
bracis-28360	136	35	)	)	PUNCT
bracis-28360	136	36	;	;	PUNCT
bracis-28360	136	37	(	(	PUNCT
bracis-28360	136	38	ii	ii	NOUN
bracis-28360	136	39	)	)	PUNCT
bracis-28360	136	40	for	for	ADP
bracis-28360	136	41	all	all	DET
bracis-28360	136	42	\(z_1	\(z_1	PROPN
bracis-28360	136	43	,	,	PUNCT
bracis-28360	136	44	z_2	z_2	NOUN
bracis-28360	136	45	,	,	PUNCT
bracis-28360	136	46	z_3	z_3	ADP
bracis-28360	136	47	\in	\in	ADJ
bracis-28360	136	48	[	[	X
bracis-28360	136	49	0	0	NUM
bracis-28360	136	50	,	,	PUNCT
bracis-28360	136	51	1]\	1]\	PROPN
bracis-28360	136	52	)	)	PUNCT
bracis-28360	136	53	,	,	PUNCT
bracis-28360	136	54	with	with	ADP
bracis-28360	136	55	\(z_1	\(z_1	PROPN
bracis-28360	136	56	\le	\le	PROPN
bracis-28360	136	57	z_2	z_2	PROPN
bracis-28360	136	58	\le	\le	PROPN
bracis-28360	136	59	z_3\	z_3\	NUM
bracis-28360	136	60	)	)	PUNCT
bracis-28360	136	61	,	,	PUNCT
bracis-28360	136	62	\(w	\(w	NUM
bracis-28360	136	63	\in	\in	PROPN
bracis-28360	136	64	[	[	X
bracis-28360	136	65	0,1]\	0,1]\	NOUN
bracis-28360	136	66	)	)	PUNCT
bracis-28360	136	67	,	,	PUNCT
bracis-28360	136	68	we	we	PRON
bracis-28360	136	69	have	have	VERB
bracis-28360	136	70	:	:	PUNCT
bracis-28360	136	71	\(z_2	\(z_2	PROPN
bracis-28360	136	72	+	+	PROPN
bracis-28360	136	73	\delta	\delta	PROPN
bracis-28360	136	74	(	(	PUNCT
bracis-28360	136	75	c(z_3	c(z_3	PROPN
bracis-28360	136	76	,	,	PUNCT
bracis-28360	136	77	w	w	NOUN
bracis-28360	136	78	)	)	PUNCT
bracis-28360	136	79	,	,	PUNCT
bracis-28360	136	80	c(z_2	c(z_2	NOUN
bracis-28360	136	81	,	,	PUNCT
bracis-28360	136	82	w	w	NOUN
bracis-28360	136	83	)	)	PUNCT
bracis-28360	136	84	)	)	PUNCT
bracis-28360	136	85	\ge	\ge	PROPN
bracis-28360	136	86	z_1	z_1	PROPN
bracis-28360	137	1	+	+	CCONJ
bracis-28360	137	2	\delta	\delta	PROPN
bracis-28360	137	3	(	(	PUNCT
bracis-28360	137	4	c(z_3	c(z_3	PROPN
bracis-28360	137	5	,	,	PUNCT
bracis-28360	137	6	w	w	NOUN
bracis-28360	137	7	)	)	PUNCT
bracis-28360	137	8	,	,	PUNCT
bracis-28360	137	9	c(z_1	c(z_1	ADV
bracis-28360	137	10	,	,	PUNCT
bracis-28360	137	11	w)).\	w)).\	X
bracis-28360	137	12	)	)	PUNCT
bracis-28360	137	13	considering	consider	VERB
bracis-28360	137	14	the	the	DET
bracis-28360	137	15	rdfs	rdfs	NOUN
bracis-28360	137	16	of	of	ADP
bracis-28360	137	17	table	table	NOUN
bracis-28360	137	18	 	 	SPACE
bracis-28360	137	19	2	2	NUM
bracis-28360	137	20	,	,	PUNCT
bracis-28360	137	21	for	for	ADP
bracis-28360	137	22	any	any	DET
bracis-28360	137	23	copula	copula	NOUN
bracis-28360	137	24	c	c	PROPN
bracis-28360	137	25	and	and	CCONJ
bracis-28360	137	26	fm	fm	PROPN
bracis-28360	137	27	m	m	PROPN
bracis-28360	137	28	,	,	PUNCT
bracis-28360	137	29	only	only	ADV
bracis-28360	137	30	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	137	31	{	{	PUNCT
bracis-28360	137	32	cc}_{\delta	cc}_{\delta	VERB
bracis-28360	137	33	_	_	NOUN
bracis-28360	137	34	0,m}^c\	0,m}^c\	NUM
bracis-28360	137	35	)	)	PUNCT
bracis-28360	137	36	is	be	AUX
bracis-28360	137	37	increasing	increase	VERB
bracis-28360	137	38	,	,	PUNCT
bracis-28360	137	39	since	since	SCONJ
bracis-28360	137	40	it	it	PRON
bracis-28360	137	41	satisfies	satisfy	VERB
bracis-28360	137	42	both	both	DET
bracis-28360	137	43	conditions	condition	NOUN
bracis-28360	137	44	.	.	PUNCT
bracis-28360	138	1	observe	observe	VERB
bracis-28360	138	2	that	that	SCONJ
bracis-28360	138	3	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	138	4	{	{	PUNCT
bracis-28360	138	5	cc}_{\delta	cc}_{\delta	VERB
bracis-28360	138	6	_	_	NOUN
bracis-28360	138	7	0,m}^c\	0,m}^c\	NUM
bracis-28360	138	8	)	)	PUNCT
bracis-28360	138	9	is	be	AUX
bracis-28360	138	10	,	,	PUNCT
bracis-28360	138	11	in	in	ADP
bracis-28360	138	12	fact	fact	NOUN
bracis-28360	138	13	,	,	PUNCT
bracis-28360	138	14	a	a	DET
bracis-28360	138	15	cc	cc	NOUN
bracis-28360	138	16	-	-	ADJ
bracis-28360	138	17	integral	integral	ADJ
bracis-28360	138	18	[	[	X
bracis-28360	138	19	22	22	NUM
bracis-28360	138	20	]	]	PUNCT
bracis-28360	138	21	,	,	PUNCT
bracis-28360	138	22	which	which	PRON
bracis-28360	138	23	is	be	AUX
bracis-28360	138	24	fully	fully	ADV
bracis-28360	138	25	monotonic	monotonic	ADJ
bracis-28360	138	26	,	,	PUNCT
bracis-28360	138	27	for	for	ADP
bracis-28360	138	28	any	any	DET
bracis-28360	138	29	copula	copula	NOUN
bracis-28360	138	30	c.	c.	NOUN
bracis-28360	138	31	when	when	SCONJ
bracis-28360	138	32	c	c	PROPN
bracis-28360	138	33	is	be	AUX
bracis-28360	138	34	the	the	DET
bracis-28360	138	35	product	product	NOUN
bracis-28360	138	36	,	,	PUNCT
bracis-28360	138	37	both	both	PRON
bracis-28360	138	38	coincide	coincide	VERB
bracis-28360	138	39	with	with	ADP
bracis-28360	138	40	the	the	DET
bracis-28360	138	41	d	d	PROPN
bracis-28360	138	42	-	-	PUNCT
bracis-28360	138	43	xc	xc	PROPN
bracis-28360	138	44	integral	integral	ADJ
bracis-28360	138	45	(	(	PUNCT
bracis-28360	138	46	definition	definition	NOUN
bracis-28360	138	47	2	2	NUM
bracis-28360	138	48	)	)	PUNCT
bracis-28360	138	49	for	for	ADP
bracis-28360	138	50	\(\delta	\(\delta	NOUN
bracis-28360	138	51	_	_	PROPN
bracis-28360	138	52	0\	0\	NUM
bracis-28360	138	53	)	)	PUNCT
bracis-28360	138	54	,	,	PUNCT
bracis-28360	138	55	which	which	PRON
bracis-28360	138	56	is	be	AUX
bracis-28360	138	57	the	the	DET
bracis-28360	138	58	standard	standard	ADJ
bracis-28360	138	59	ci	ci	NOUN
bracis-28360	138	60	in	in	ADP
bracis-28360	138	61	the	the	DET
bracis-28360	138	62	expanded	expand	VERB
bracis-28360	138	63	form	form	NOUN
bracis-28360	138	64	.	.	PUNCT
bracis-28360	139	1	nevertheless	nevertheless	ADV
bracis-28360	139	2	,	,	PUNCT
bracis-28360	139	3	d	d	X
bracis-28360	139	4	-	-	PUNCT
bracis-28360	139	5	cc	cc	ADP
bracis-28360	139	6	integrals	integral	NOUN
bracis-28360	139	7	do	do	AUX
bracis-28360	139	8	satisfy	satisfy	VERB
bracis-28360	139	9	weaker	weak	ADJ
bracis-28360	139	10	forms	form	NOUN
bracis-28360	139	11	of	of	ADP
bracis-28360	139	12	monotonicity	monotonicity	NOUN
bracis-28360	139	13	,	,	PUNCT
bracis-28360	139	14	as	as	SCONJ
bracis-28360	139	15	we	we	PRON
bracis-28360	139	16	discuss	discuss	VERB
bracis-28360	139	17	in	in	ADP
bracis-28360	139	18	this	this	DET
bracis-28360	139	19	section	section	NOUN
bracis-28360	139	20	.	.	PUNCT
bracis-28360	140	1	directional	directional	ADJ
bracis-28360	140	2	monotonicity	monotonicity	NOUN
bracis-28360	140	3	of	of	ADP
bracis-28360	140	4	d	d	PROPN
bracis-28360	140	5	-	-	PUNCT
bracis-28360	140	6	cc	cc	NOUN
bracis-28360	140	7	integrals	integral	NOUN
bracis-28360	140	8	.	.	PUNCT
bracis-28360	141	1	directional	directional	ADJ
bracis-28360	141	2	monotonicity	monotonicity	NOUN
bracis-28360	141	3	is	be	AUX
bracis-28360	141	4	one	one	NUM
bracis-28360	141	5	of	of	ADP
bracis-28360	141	6	the	the	DET
bracis-28360	141	7	most	most	ADV
bracis-28360	141	8	adopted	adopt	VERB
bracis-28360	141	9	weaker	weak	ADJ
bracis-28360	141	10	notions	notion	NOUN
bracis-28360	141	11	of	of	ADP
bracis-28360	141	12	monotonicity	monotonicity	NOUN
bracis-28360	141	13	,	,	PUNCT
bracis-28360	141	14	which	which	PRON
bracis-28360	141	15	enlarged	enlarge	VERB
bracis-28360	141	16	the	the	DET
bracis-28360	141	17	scope	scope	NOUN
bracis-28360	141	18	of	of	ADP
bracis-28360	141	19	aggregation	aggregation	NOUN
bracis-28360	141	20	processes	process	NOUN
bracis-28360	141	21	in	in	ADP
bracis-28360	141	22	applications	application	NOUN
bracis-28360	141	23	(	(	PUNCT
bracis-28360	141	24	e.g.	e.g.	ADV
bracis-28360	141	25	,	,	PUNCT
bracis-28360	141	26	[	[	X
bracis-28360	141	27	13	13	NUM
bracis-28360	141	28	,	,	PUNCT
bracis-28360	141	29	18	18	NUM
bracis-28360	141	30	,	,	PUNCT
bracis-28360	141	31	24	24	NUM
bracis-28360	141	32	,	,	PUNCT
bracis-28360	141	33	25	25	NUM
bracis-28360	141	34	]	]	PUNCT
bracis-28360	141	35	)	)	PUNCT
bracis-28360	141	36	.	.	PUNCT
bracis-28360	142	1	definition	definition	NOUN
bracis-28360	142	2	4	4	NUM
bracis-28360	142	3	[	[	X
bracis-28360	142	4	5	5	NUM
bracis-28360	142	5	]	]	PUNCT
bracis-28360	142	6	.	.	PUNCT
bracis-28360	143	1	let	let	VERB
bracis-28360	143	2	\(\boldsymbol{r	\(\boldsymbol{r	ADJ
bracis-28360	143	3	}	}	PUNCT
bracis-28360	143	4	=	=	SYM
bracis-28360	143	5	(	(	PUNCT
bracis-28360	143	6	r_1	r_1	NOUN
bracis-28360	143	7	,	,	PUNCT
bracis-28360	143	8	\dots	\dot	NOUN
bracis-28360	143	9	,	,	PUNCT
bracis-28360	143	10	r_n)\	r_n)\	NUM
bracis-28360	143	11	)	)	PUNCT
bracis-28360	143	12	be	be	AUX
bracis-28360	143	13	a	a	DET
bracis-28360	143	14	real	real	ADJ
bracis-28360	143	15	\(n\)-dimensional	\(n\)-dimensional	ADJ
bracis-28360	143	16	vector	vector	NOUN
bracis-28360	143	17	such	such	ADJ
bracis-28360	143	18	that	that	SCONJ
bracis-28360	143	19	\(\boldsymbol{r	\(\boldsymbol{r	ADJ
bracis-28360	143	20	}	}	PUNCT
bracis-28360	143	21	\ne	\ne	PROPN
bracis-28360	143	22	\boldsymbol{0	\boldsymbol{0	NOUN
bracis-28360	143	23	}	}	PUNCT
bracis-28360	143	24	=	=	SYM
bracis-28360	143	25	(	(	PUNCT
bracis-28360	143	26	0	0	NUM
bracis-28360	143	27	,	,	PUNCT
bracis-28360	143	28	\ldots	\ldots	INTJ
bracis-28360	143	29	,	,	PUNCT
bracis-28360	143	30	0)\	0)\	NUM
bracis-28360	143	31	)	)	PUNCT
bracis-28360	143	32	.	.	PUNCT
bracis-28360	144	1	a	a	DET
bracis-28360	144	2	function	function	NOUN
bracis-28360	144	3	\(f	\(f	X
bracis-28360	144	4	:	:	PUNCT
bracis-28360	145	1	[	[	X
bracis-28360	145	2	0,1]^n	0,1]^n	X
bracis-28360	145	3	\rightarrow	\rightarrow	PROPN
bracis-28360	146	1	[	[	X
bracis-28360	146	2	0,1]\	0,1]\	NOUN
bracis-28360	146	3	)	)	PUNCT
bracis-28360	146	4	is	be	AUX
bracis-28360	146	5	said	say	VERB
bracis-28360	146	6	to	to	PART
bracis-28360	146	7	be	be	AUX
bracis-28360	146	8	\(\boldsymbol{r}\)-increasing	\(\boldsymbol{r}\)-increase	VERB
bracis-28360	146	9	if	if	SCONJ
bracis-28360	146	10	,	,	PUNCT
bracis-28360	146	11	for	for	ADP
bracis-28360	146	12	all	all	DET
bracis-28360	146	13	\(\boldsymbol{x}=	\(\boldsymbol{x}=	PROPN
bracis-28360	146	14	(	(	PUNCT
bracis-28360	146	15	x_1,\dots	x_1,\dot	NOUN
bracis-28360	146	16	,	,	PUNCT
bracis-28360	146	17	x_n	x_n	NUM
bracis-28360	146	18	)	)	PUNCT
bracis-28360	146	19	\in	\in	PROPN
bracis-28360	146	20	[	[	NOUN
bracis-28360	146	21	0,1]^n\	0,1]^n\	NOUN
bracis-28360	146	22	)	)	PUNCT
bracis-28360	146	23	and	and	CCONJ
bracis-28360	146	24	\(c	\(c	NOUN
bracis-28360	146	25	>	>	X
bracis-28360	146	26	0\	0\	PROPN
bracis-28360	146	27	)	)	PUNCT
bracis-28360	146	28	such	such	ADJ
bracis-28360	146	29	that	that	SCONJ
bracis-28360	146	30	\(\boldsymbol{x	\(\boldsymbol{x	ADJ
bracis-28360	146	31	}	}	PUNCT
bracis-28360	146	32	+	+	NUM
bracis-28360	146	33	c{\textbf	c{\textbf	NOUN
bracis-28360	146	34	{	{	PUNCT
bracis-28360	146	35	r	r	NOUN
bracis-28360	146	36	}	}	PUNCT
bracis-28360	146	37	}	}	PUNCT
bracis-28360	146	38	=	=	SYM
bracis-28360	146	39	(	(	PUNCT
bracis-28360	146	40	x_1	x_1	PROPN
bracis-28360	146	41	+	+	CCONJ
bracis-28360	146	42	c	c	PROPN
bracis-28360	146	43	r_1	r_1	NOUN
bracis-28360	146	44	,	,	PUNCT
bracis-28360	146	45	\dots	\dot	NOUN
bracis-28360	146	46	,	,	PUNCT
bracis-28360	146	47	x_n	x_n	PROPN
bracis-28360	147	1	+	+	CCONJ
bracis-28360	147	2	c	c	NOUN
bracis-28360	147	3	r_n	r_n	ADJ
bracis-28360	147	4	)	)	PUNCT
bracis-28360	147	5	\in	\in	PROPN
bracis-28360	147	6	[	[	NOUN
bracis-28360	147	7	0,1]^n\	0,1]^n\	NOUN
bracis-28360	147	8	)	)	PUNCT
bracis-28360	148	1	,	,	PUNCT
bracis-28360	148	2	it	it	PRON
bracis-28360	148	3	holds	hold	VERB
bracis-28360	148	4	that	that	SCONJ
bracis-28360	148	5	\(f(\boldsymbol{x	\(f(\boldsymbol{x	ADP
bracis-28360	148	6	}	}	PUNCT
bracis-28360	148	7	+	+	ADJ
bracis-28360	148	8	c\boldsymbol{r	c\boldsymbol{r	ADJ
bracis-28360	148	9	}	}	PUNCT
bracis-28360	148	10	)	)	PUNCT
bracis-28360	148	11	\ge	\ge	PROPN
bracis-28360	148	12	f(\boldsymbol{x})\	f(\boldsymbol{x})\	NOUN
bracis-28360	148	13	)	)	PUNCT
bracis-28360	148	14	.	.	PUNCT
bracis-28360	149	1	theorem	theorem	NOUN
bracis-28360	149	2	1	1	NUM
bracis-28360	149	3	let	let	VERB
bracis-28360	149	4	\(m	\(m	ADV
bracis-28360	149	5	:	:	PUNCT
bracis-28360	149	6	2^n	2^n	NUM
bracis-28360	149	7	\rightarrow	\rightarrow	PROPN
bracis-28360	149	8	[	[	X
bracis-28360	149	9	0,1]\	0,1]\	NOUN
bracis-28360	149	10	)	)	PUNCT
bracis-28360	149	11	,	,	PUNCT
bracis-28360	149	12	\(\delta	\(\delta	NOUN
bracis-28360	149	13	:	:	PUNCT
bracis-28360	150	1	[	[	X
bracis-28360	150	2	0,1]^2	0,1]^2	NUM
bracis-28360	150	3	\rightarrow	\rightarrow	PROPN
bracis-28360	150	4	[	[	X
bracis-28360	150	5	0,1]\	0,1]\	NUM
bracis-28360	150	6	)	)	PUNCT
bracis-28360	150	7	and	and	CCONJ
bracis-28360	150	8	\(c	\(c	NOUN
bracis-28360	150	9	:	:	PUNCT
bracis-28360	151	1	[	[	X
bracis-28360	151	2	0,1]^2	0,1]^2	NUM
bracis-28360	151	3	\rightarrow	\rightarrow	PROPN
bracis-28360	151	4	[	[	X
bracis-28360	151	5	0,1]\	0,1]\	NOUN
bracis-28360	151	6	)	)	PUNCT
bracis-28360	151	7	be	be	VERB
bracis-28360	151	8	an	an	DET
bracis-28360	151	9	fm	fm	NOUN
bracis-28360	151	10	,	,	PUNCT
bracis-28360	151	11	an	an	DET
bracis-28360	151	12	rdf	rdf	NOUN
bracis-28360	151	13	,	,	PUNCT
bracis-28360	151	14	and	and	CCONJ
bracis-28360	151	15	a	a	DET
bracis-28360	151	16	copula	copula	NOUN
bracis-28360	151	17	,	,	PUNCT
bracis-28360	151	18	respectively	respectively	ADV
bracis-28360	151	19	.	.	PUNCT
bracis-28360	152	1	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	152	2	{	{	PUNCT
bracis-28360	152	3	cc}_{\delta	cc}_{\delta	PROPN
bracis-28360	152	4	,	,	PUNCT
bracis-28360	152	5	m}^c\	m}^c\	PROPN
bracis-28360	152	6	)	)	PUNCT
bracis-28360	152	7	is	be	AUX
bracis-28360	152	8	\(\boldsymbol{1}\)-increasing	\(\boldsymbol{1}\)-increase	VERB
bracis-28360	152	9	if	if	SCONJ
bracis-28360	152	10	and	and	CCONJ
bracis-28360	152	11	only	only	ADV
bracis-28360	152	12	if	if	SCONJ
bracis-28360	152	13	one	one	NUM
bracis-28360	152	14	of	of	ADP
bracis-28360	152	15	the	the	DET
bracis-28360	152	16	following	follow	VERB
bracis-28360	152	17	conditions	condition	NOUN
bracis-28360	152	18	hold	hold	VERB
bracis-28360	152	19	:	:	PUNCT
bracis-28360	152	20	(	(	PUNCT
bracis-28360	152	21	i	i	NOUN
bracis-28360	152	22	)	)	PUNCT
bracis-28360	152	23	the	the	PRON
bracis-28360	152	24	rdf	rdf	NOUN
bracis-28360	152	25	\(\delta	\(\delta	NOUN
bracis-28360	152	26	\	\	NOUN
bracis-28360	152	27	)	)	PUNCT
bracis-28360	152	28	is	be	AUX
bracis-28360	152	29	\(\boldsymbol{1}\)-increasing	\(\boldsymbol{1}\)-increase	VERB
bracis-28360	152	30	;	;	PUNCT
bracis-28360	152	31	(	(	PUNCT
bracis-28360	152	32	ii	ii	NOUN
bracis-28360	152	33	)	)	PUNCT
bracis-28360	152	34	for	for	ADP
bracis-28360	152	35	all	all	DET
bracis-28360	152	36	\(0	\(0	NUM
bracis-28360	152	37	\le	\le	PROPN
bracis-28360	152	38	z_1	z_1	PROPN
bracis-28360	152	39	\le	\le	PROPN
bracis-28360	152	40	\ldots	\ldots	ADP
bracis-28360	152	41	\le	\le	PROPN
bracis-28360	152	42	z_n	z_n	PROPN
bracis-28360	152	43	\le	\le	PROPN
bracis-28360	152	44	1\	1\	NUM
bracis-28360	152	45	)	)	PUNCT
bracis-28360	152	46	and	and	CCONJ
bracis-28360	152	47	\(c>0\	\(c>0\	NOUN
bracis-28360	152	48	)	)	PUNCT
bracis-28360	152	49	,	,	PUNCT
bracis-28360	152	50	such	such	ADJ
bracis-28360	152	51	that	that	SCONJ
bracis-28360	152	52	\	\	PROPN
bracis-28360	152	53	(	(	PUNCT
bracis-28360	152	54	z_i	z_i	PUNCT
bracis-28360	153	1	+	+	NUM
bracis-28360	153	2	c	c	X
bracis-28360	153	3	\in	\in	PROPN
bracis-28360	153	4	[	[	X
bracis-28360	153	5	0,1]\	0,1]\	NOUN
bracis-28360	153	6	)	)	PUNCT
bracis-28360	153	7	,	,	PUNCT
bracis-28360	153	8	for	for	ADP
bracis-28360	153	9	all	all	DET
bracis-28360	153	10	\(i	\(i	NOUN
bracis-28360	153	11	=	=	SYM
bracis-28360	153	12	1	1	NUM
bracis-28360	153	13	,	,	PUNCT
bracis-28360	153	14	\ldots	\ldots	INTJ
bracis-28360	153	15	,	,	PUNCT
bracis-28360	153	16	n\	n\	PROPN
bracis-28360	153	17	):	):	PUNCT
bracis-28360	153	18	$	$	SYM
bracis-28360	153	19	$	$	SYM
bracis-28360	153	20	\begin{aligned	\begin{aligne	VERB
bracis-28360	153	21	}	}	PUNCT
bracis-28360	153	22	&	&	CCONJ
bracis-28360	153	23	\sum	\sum	NOUN
bracis-28360	153	24	_	_	PUNCT
bracis-28360	153	25	{	{	PUNCT
bracis-28360	153	26	i=2}^{n	i=2}^{n	ADJ
bracis-28360	153	27	}	}	PUNCT
bracis-28360	153	28	\delta	\delta	PROPN
bracis-28360	153	29	(	(	PUNCT
bracis-28360	153	30	c(z_i	c(z_i	VERB
bracis-28360	153	31	+	+	CCONJ
bracis-28360	153	32	c	c	X
bracis-28360	153	33	,	,	PUNCT
bracis-28360	153	34	m_{i	m_{i	ADJ
bracis-28360	153	35	}	}	PUNCT
bracis-28360	153	36	)	)	PUNCT
bracis-28360	153	37	,	,	PUNCT
bracis-28360	153	38	c(z_{i-1}+	c(z_{i-1}+	PROPN
bracis-28360	153	39	c	c	NOUN
bracis-28360	153	40	,	,	PUNCT
bracis-28360	153	41	\cdot	\cdot	NOUN
bracis-28360	153	42	m_{i	m_{i	ADJ
bracis-28360	153	43	}	}	PUNCT
bracis-28360	153	44	)	)	PUNCT
bracis-28360	153	45	)	)	PUNCT
bracis-28360	153	46	\ge	\ge	PROPN
bracis-28360	153	47	\sum	\sum	NOUN
bracis-28360	153	48	_	_	PUNCT
bracis-28360	153	49	{	{	PUNCT
bracis-28360	153	50	i=2}^{n}\delta	i=2}^{n}\delta	PROPN
bracis-28360	153	51	(	(	PUNCT
bracis-28360	153	52	c(z_i	c(z_i	ADJ
bracis-28360	153	53	\cdot	\cdot	NOUN
bracis-28360	153	54	m_{i	m_{i	NOUN
bracis-28360	153	55	}	}	PUNCT
bracis-28360	153	56	)	)	PUNCT
bracis-28360	153	57	,	,	PUNCT
bracis-28360	153	58	c(z_{i-1	c(z_{i-1	NUM
bracis-28360	153	59	}	}	PUNCT
bracis-28360	153	60	\cdot	\cdot	NOUN
bracis-28360	153	61	m_{i	m_{i	ADJ
bracis-28360	153	62	}	}	PUNCT
bracis-28360	153	63	)	)	PUNCT
bracis-28360	153	64	)	)	PUNCT
bracis-28360	154	1	c	c	X
bracis-28360	154	2	,	,	PUNCT
bracis-28360	154	3	\end{aligned}$$	\end{aligned}$$	VERB
bracis-28360	154	4	where	where	SCONJ
bracis-28360	154	5	\(m_i	\(m_i	ADV
bracis-28360	154	6	=	=	SYM
bracis-28360	154	7	m(a_{i})\	m(a_{i})\	NOUN
bracis-28360	154	8	)	)	PUNCT
bracis-28360	154	9	,	,	PUNCT
bracis-28360	154	10	for	for	ADP
bracis-28360	154	11	\(a_i	\(a_i	NOUN
bracis-28360	154	12	=	=	SYM
bracis-28360	154	13	\{i	\{i	NOUN
bracis-28360	154	14	,	,	PUNCT
bracis-28360	154	15	\ldots	\ldots	INTJ
bracis-28360	154	16	,	,	PUNCT
bracis-28360	154	17	n\}\	n\}\	ADJ
bracis-28360	154	18	)	)	PUNCT
bracis-28360	154	19	.	.	PUNCT
bracis-28360	155	1	proof	proof	NOUN
bracis-28360	155	2	(	(	PUNCT
bracis-28360	155	3	\(\leftarrow	\(\leftarrow	NOUN
bracis-28360	155	4	\))(i	\))(i	NUM
bracis-28360	155	5	)	)	PUNCT
bracis-28360	155	6	suppose	suppose	VERB
bracis-28360	155	7	that	that	SCONJ
bracis-28360	155	8	\(\delta	\(\delta	NOUN
bracis-28360	155	9	\	\	NOUN
bracis-28360	155	10	)	)	PUNCT
bracis-28360	155	11	is	be	AUX
bracis-28360	155	12	\(\boldsymbol{1}\)-increasing	\(\boldsymbol{1}\)-increase	VERB
bracis-28360	155	13	and	and	CCONJ
bracis-28360	155	14	let	let	VERB
bracis-28360	155	15	\(\boldsymbol{c	\(\boldsymbol{c	PROPN
bracis-28360	155	16	}	}	PUNCT
bracis-28360	155	17	=	=	SYM
bracis-28360	155	18	(	(	PUNCT
bracis-28360	155	19	c	c	X
bracis-28360	155	20	,	,	PUNCT
bracis-28360	155	21	\ldots	\ldots	INTJ
bracis-28360	155	22	,	,	PUNCT
bracis-28360	155	23	c)\	c)\	PROPN
bracis-28360	155	24	)	)	PUNCT
bracis-28360	155	25	,	,	PUNCT
bracis-28360	155	26	\(c>0\	\(c>0\	NOUN
bracis-28360	155	27	)	)	PUNCT
bracis-28360	155	28	,	,	PUNCT
bracis-28360	155	29	such	such	ADJ
bracis-28360	155	30	that	that	SCONJ
bracis-28360	155	31	\(\boldsymbol{x	\(\boldsymbol{x	NOUN
bracis-28360	155	32	}	}	PUNCT
bracis-28360	155	33	,	,	PUNCT
bracis-28360	155	34	\boldsymbol{x	\boldsymbol{x	ADP
bracis-28360	155	35	}	}	PUNCT
bracis-28360	155	36	+	+	CCONJ
bracis-28360	155	37	\boldsymbol{c}\in	\boldsymbol{c}\in	PROPN
bracis-28360	155	38	[	[	X
bracis-28360	155	39	0,1]^n\	0,1]^n\	NUM
bracis-28360	155	40	)	)	PUNCT
bracis-28360	155	41	.	.	PUNCT
bracis-28360	156	1	then	then	ADV
bracis-28360	156	2	:	:	PUNCT
bracis-28360	156	3	$	$	SYM
bracis-28360	156	4	$	$	SYM
bracis-28360	156	5	\begin{aligned	\begin{aligne	VERB
bracis-28360	156	6	}	}	PUNCT
bracis-28360	156	7	&	&	CCONJ
bracis-28360	156	8	\mathfrak	\mathfrak	PROPN
bracis-28360	156	9	{	{	PUNCT
bracis-28360	156	10	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	156	11	,	,	PUNCT
bracis-28360	156	12	m}^c(\boldsymbol{x	m}^c(\boldsymbol{x	NOUN
bracis-28360	156	13	}	}	PUNCT
bracis-28360	156	14	+	+	NUM
bracis-28360	156	15	c	c	PROPN
bracis-28360	156	16	\boldsymbol{1	\boldsymbol{1	PROPN
bracis-28360	156	17	}	}	PUNCT
bracis-28360	156	18	)	)	PUNCT
bracis-28360	157	1	=	=	SYM
bracis-28360	157	2	(	(	PUNCT
bracis-28360	157	3	x_{(1	x_{(1	NOUN
bracis-28360	157	4	)	)	PUNCT
bracis-28360	157	5	}	}	PUNCT
bracis-28360	158	1	+	+	CCONJ
bracis-28360	158	2	c	c	X
bracis-28360	158	3	)	)	PUNCT
bracis-28360	158	4	+	+	CCONJ
bracis-28360	158	5	\sum	\sum	NOUN
bracis-28360	158	6	_	_	PUNCT
bracis-28360	158	7	{	{	PUNCT
bracis-28360	158	8	i=2}^{n	i=2}^{n	ADJ
bracis-28360	158	9	}	}	PUNCT
bracis-28360	158	10	\delta	\delta	PROPN
bracis-28360	158	11	\left	\left	PROPN
bracis-28360	158	12	(	(	PUNCT
bracis-28360	158	13	c	c	PROPN
bracis-28360	158	14	(	(	PUNCT
bracis-28360	158	15	x_{(i	x_{(i	PROPN
bracis-28360	158	16	)	)	PUNCT
bracis-28360	158	17	}	}	PUNCT
bracis-28360	158	18	+	+	CCONJ
bracis-28360	158	19	c	c	X
bracis-28360	158	20	,	,	PUNCT
bracis-28360	158	21	m_{(i	m_{(i	PROPN
bracis-28360	158	22	)	)	PUNCT
bracis-28360	158	23	}	}	PUNCT
bracis-28360	158	24	)	)	PUNCT
bracis-28360	158	25	,	,	PUNCT
bracis-28360	158	26	c	c	X
bracis-28360	158	27	(	(	PUNCT
bracis-28360	158	28	x_{(i-1	x_{(i-1	NUM
bracis-28360	158	29	)	)	PUNCT
bracis-28360	158	30	}	}	PUNCT
bracis-28360	158	31	+	+	CCONJ
bracis-28360	159	1	c	c	X
bracis-28360	159	2	,	,	PUNCT
bracis-28360	159	3	m_{(i	m_{(i	PROPN
bracis-28360	159	4	)	)	PUNCT
bracis-28360	159	5	}	}	PUNCT
bracis-28360	159	6	)	)	PUNCT
bracis-28360	159	7	\right	\right	NOUN
bracis-28360	159	8	)	)	PUNCT
bracis-28360	159	9	\\	\\	NOUN
bracis-28360	159	10	&	&	CCONJ
bracis-28360	159	11	\qquad	\qquad	PROPN
bracis-28360	159	12	\qquad	\qquad	PROPN
bracis-28360	159	13	\quad	\quad	PROPN
bracis-28360	159	14	>	>	X
bracis-28360	159	15	x_{(1	x_{(1	PROPN
bracis-28360	159	16	)	)	PUNCT
bracis-28360	159	17	}	}	PUNCT
bracis-28360	160	1	+	+	CCONJ
bracis-28360	160	2	\sum	\sum	NOUN
bracis-28360	160	3	_	_	PUNCT
bracis-28360	160	4	{	{	PUNCT
bracis-28360	160	5	i=2}^{n	i=2}^{n	ADJ
bracis-28360	160	6	}	}	PUNCT
bracis-28360	160	7	\delta	\delta	PROPN
bracis-28360	160	8	\left	\left	PROPN
bracis-28360	160	9	(	(	PUNCT
bracis-28360	160	10	c(x_{(i	c(x_{(i	PROPN
bracis-28360	160	11	)	)	PUNCT
bracis-28360	160	12	}	}	PUNCT
bracis-28360	160	13	,	,	PUNCT
bracis-28360	160	14	m_{(i	m_{(i	PROPN
bracis-28360	160	15	)	)	PUNCT
bracis-28360	160	16	}	}	PUNCT
bracis-28360	160	17	)	)	PUNCT
bracis-28360	160	18	,	,	PUNCT
bracis-28360	160	19	c(x_{(i-1	c(x_{(i-1	NOUN
bracis-28360	160	20	)	)	PUNCT
bracis-28360	160	21	}	}	PUNCT
bracis-28360	160	22	,	,	PUNCT
bracis-28360	160	23	m_{(i	m_{(i	PROPN
bracis-28360	160	24	)	)	PUNCT
bracis-28360	160	25	}	}	PUNCT
bracis-28360	160	26	)	)	PUNCT
bracis-28360	160	27	\right	\right	NOUN
bracis-28360	160	28	)	)	PUNCT
bracis-28360	160	29	=	=	SYM
bracis-28360	160	30	\mathfrak	\mathfrak	PROPN
bracis-28360	160	31	{	{	PUNCT
bracis-28360	160	32	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	160	33	,	,	PUNCT
bracis-28360	160	34	m}^c(\boldsymbol{x	m}^c(\boldsymbol{x	NOUN
bracis-28360	160	35	}	}	PUNCT
bracis-28360	160	36	)	)	PUNCT
bracis-28360	160	37	.	.	PUNCT
bracis-28360	161	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-28360	161	2	now	now	ADV
bracis-28360	161	3	suppose	suppose	VERB
bracis-28360	161	4	that	that	SCONJ
bracis-28360	161	5	(	(	PUNCT
bracis-28360	161	6	ii	ii	NOUN
bracis-28360	161	7	)	)	PUNCT
bracis-28360	161	8	holds	hold	VERB
bracis-28360	161	9	.	.	PUNCT
bracis-28360	162	1	then	then	ADV
bracis-28360	162	2	,	,	PUNCT
bracis-28360	162	3	for	for	ADP
bracis-28360	162	4	all	all	DET
bracis-28360	162	5	\	\	NOUN
bracis-28360	162	6	(	(	PUNCT
bracis-28360	162	7	\boldsymbol{x	\boldsymbol{x	ADP
bracis-28360	162	8	}	}	PUNCT
bracis-28360	162	9	\in	\in	PROPN
bracis-28360	162	10	[	[	NOUN
bracis-28360	162	11	0,1]^n\	0,1]^n\	NOUN
bracis-28360	162	12	)	)	PUNCT
bracis-28360	162	13	and	and	CCONJ
bracis-28360	162	14	\(\boldsymbol{c	\(\boldsymbol{c	ADJ
bracis-28360	162	15	}	}	PUNCT
bracis-28360	162	16	=	=	SYM
bracis-28360	162	17	(	(	PUNCT
bracis-28360	162	18	c	c	X
bracis-28360	162	19	,	,	PUNCT
bracis-28360	162	20	\ldots	\ldots	INTJ
bracis-28360	162	21	,	,	PUNCT
bracis-28360	162	22	c)\	c)\	PROPN
bracis-28360	162	23	)	)	PUNCT
bracis-28360	162	24	,	,	PUNCT
bracis-28360	162	25	with	with	ADP
bracis-28360	162	26	\(c	\(c	PROPN
bracis-28360	162	27	>	>	X
bracis-28360	162	28	0\	0\	PROPN
bracis-28360	162	29	)	)	PUNCT
bracis-28360	162	30	,	,	PUNCT
bracis-28360	163	1	such	such	ADJ
bracis-28360	163	2	that	that	SCONJ
bracis-28360	163	3	\(x_i	\(x_i	PROPN
bracis-28360	163	4	+	+	NUM
bracis-28360	163	5	c	c	NOUN
bracis-28360	163	6	\in	\in	PROPN
bracis-28360	163	7	[	[	X
bracis-28360	163	8	0,1]\	0,1]\	NOUN
bracis-28360	163	9	)	)	PUNCT
bracis-28360	163	10	,	,	PUNCT
bracis-28360	163	11	\(\forall	\(\forall	ADV
bracis-28360	163	12	i	i	VERB
bracis-28360	163	13	=	=	NOUN
bracis-28360	163	14	1	1	NUM
bracis-28360	163	15	,	,	PUNCT
bracis-28360	163	16	\ldots	\ldots	INTJ
bracis-28360	163	17	,	,	PUNCT
bracis-28360	163	18	n\	n\	PROPN
bracis-28360	163	19	)	)	PUNCT
bracis-28360	163	20	,	,	PUNCT
bracis-28360	163	21	it	it	PRON
bracis-28360	163	22	follows	follow	VERB
bracis-28360	163	23	that	that	PRON
bracis-28360	163	24	\(\sum	\(\sum	PUNCT
bracis-28360	164	1	_	_	PRON
bracis-28360	164	2	{	{	PUNCT
bracis-28360	164	3	i=2}^{n	i=2}^{n	ADJ
bracis-28360	164	4	}	}	PUNCT
bracis-28360	164	5	\delta	\delta	PROPN
bracis-28360	164	6	(	(	PUNCT
bracis-28360	164	7	c(x_{(i	c(x_{(i	PROPN
bracis-28360	164	8	)	)	PUNCT
bracis-28360	164	9	}	}	PUNCT
bracis-28360	165	1	+	+	CCONJ
bracis-28360	165	2	c	c	X
bracis-28360	165	3	,	,	PUNCT
bracis-28360	165	4	m_{(i	m_{(i	PROPN
bracis-28360	165	5	)	)	PUNCT
bracis-28360	165	6	}	}	PUNCT
bracis-28360	165	7	)	)	PUNCT
bracis-28360	165	8	,	,	PUNCT
bracis-28360	165	9	c(x_{(i-1	c(x_{(i-1	NOUN
bracis-28360	165	10	)	)	PUNCT
bracis-28360	165	11	}	}	PUNCT
bracis-28360	165	12	+	+	CCONJ
bracis-28360	165	13	c	c	X
bracis-28360	165	14	,	,	PUNCT
bracis-28360	165	15	m_{(i	m_{(i	PROPN
bracis-28360	165	16	)	)	PUNCT
bracis-28360	165	17	}	}	PUNCT
bracis-28360	165	18	)	)	PUNCT
bracis-28360	165	19	)	)	PUNCT
bracis-28360	165	20	\ge	\ge	PROPN
bracis-28360	165	21	\sum	\sum	NOUN
bracis-28360	165	22	_	_	PUNCT
bracis-28360	165	23	{	{	PUNCT
bracis-28360	165	24	i=2}^{n}\delta	i=2}^{n}\delta	PROPN
bracis-28360	165	25	(	(	PUNCT
bracis-28360	165	26	c(x_{(i	c(x_{(i	PROPN
bracis-28360	165	27	)	)	PUNCT
bracis-28360	165	28	}	}	PUNCT
bracis-28360	165	29	,	,	PUNCT
bracis-28360	165	30	m_{(i	m_{(i	PROPN
bracis-28360	165	31	)	)	PUNCT
bracis-28360	165	32	}	}	PUNCT
bracis-28360	165	33	)	)	PUNCT
bracis-28360	165	34	,	,	PUNCT
bracis-28360	165	35	c	c	X
bracis-28360	165	36	(	(	PUNCT
bracis-28360	165	37	x_{(i-1	x_{(i-1	NUM
bracis-28360	165	38	)	)	PUNCT
bracis-28360	165	39	}	}	PUNCT
bracis-28360	165	40	,	,	PUNCT
bracis-28360	165	41	m_{(i	m_{(i	PROPN
bracis-28360	165	42	)	)	PUNCT
bracis-28360	165	43	}	}	PUNCT
bracis-28360	165	44	)	)	PUNCT
bracis-28360	165	45	)	)	PUNCT
bracis-28360	165	46	c\	c\	NOUN
bracis-28360	165	47	)	)	PUNCT
bracis-28360	165	48	.	.	PUNCT
bracis-28360	166	1	this	this	PRON
bracis-28360	166	2	implies	imply	VERB
bracis-28360	166	3	that	that	SCONJ
bracis-28360	166	4	\((x_{(1	\((x_{(1	NOUN
bracis-28360	166	5	)	)	PUNCT
bracis-28360	166	6	}	}	PUNCT
bracis-28360	166	7	+	+	CCONJ
bracis-28360	167	1	c	c	X
bracis-28360	167	2	)	)	PUNCT
bracis-28360	167	3	+	+	CCONJ
bracis-28360	167	4	\sum	\sum	NOUN
bracis-28360	167	5	_	_	PUNCT
bracis-28360	167	6	{	{	PUNCT
bracis-28360	167	7	i=2}^{n	i=2}^{n	ADJ
bracis-28360	167	8	}	}	PUNCT
bracis-28360	167	9	\delta	\delta	PROPN
bracis-28360	167	10	(	(	PUNCT
bracis-28360	167	11	c(x_{(i	c(x_{(i	PROPN
bracis-28360	167	12	)	)	PUNCT
bracis-28360	167	13	}	}	PUNCT
bracis-28360	168	1	+	+	CCONJ
bracis-28360	168	2	c	c	X
bracis-28360	168	3	,	,	PUNCT
bracis-28360	168	4	m_{(i	m_{(i	PROPN
bracis-28360	168	5	)	)	PUNCT
bracis-28360	168	6	}	}	PUNCT
bracis-28360	168	7	)	)	PUNCT
bracis-28360	168	8	,	,	PUNCT
bracis-28360	168	9	c(x_{(i-1	c(x_{(i-1	NOUN
bracis-28360	168	10	)	)	PUNCT
bracis-28360	168	11	}	}	PUNCT
bracis-28360	168	12	+	+	CCONJ
bracis-28360	168	13	c	c	X
bracis-28360	168	14	,	,	PUNCT
bracis-28360	168	15	m_{(i	m_{(i	PROPN
bracis-28360	168	16	)	)	PUNCT
bracis-28360	168	17	}	}	PUNCT
bracis-28360	168	18	)	)	PUNCT
bracis-28360	168	19	)	)	PUNCT
bracis-28360	168	20	\ge	\ge	PROPN
bracis-28360	168	21	x_{(1	x_{(1	PROPN
bracis-28360	168	22	)	)	PUNCT
bracis-28360	168	23	}	}	PUNCT
bracis-28360	169	1	+	+	CCONJ
bracis-28360	169	2	\sum	\sum	NOUN
bracis-28360	169	3	_	_	PUNCT
bracis-28360	169	4	{	{	PUNCT
bracis-28360	169	5	i=2}^{n}\delta	i=2}^{n}\delta	PROPN
bracis-28360	169	6	(	(	PUNCT
bracis-28360	169	7	c(x_{(i	c(x_{(i	PROPN
bracis-28360	169	8	)	)	PUNCT
bracis-28360	169	9	}	}	PUNCT
bracis-28360	169	10	,	,	PUNCT
bracis-28360	169	11	m_{(i	m_{(i	PROPN
bracis-28360	169	12	)	)	PUNCT
bracis-28360	169	13	}	}	PUNCT
bracis-28360	169	14	)	)	PUNCT
bracis-28360	169	15	,	,	PUNCT
bracis-28360	169	16	c	c	X
bracis-28360	169	17	(	(	PUNCT
bracis-28360	169	18	x_{(i-1	x_{(i-1	NUM
bracis-28360	169	19	)	)	PUNCT
bracis-28360	169	20	}	}	PUNCT
bracis-28360	169	21	,	,	PUNCT
bracis-28360	169	22	m_{(i)}))\	m_{(i)}))\	NOUN
bracis-28360	169	23	)	)	PUNCT
bracis-28360	169	24	.	.	PUNCT
bracis-28360	170	1	then	then	ADV
bracis-28360	170	2	,	,	PUNCT
bracis-28360	170	3	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	170	4	{	{	PUNCT
bracis-28360	170	5	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	170	6	,	,	PUNCT
bracis-28360	170	7	m}^c(\boldsymbol{x	m}^c(\boldsymbol{x	NOUN
bracis-28360	170	8	}	}	PUNCT
bracis-28360	170	9	+	+	NUM
bracis-28360	170	10	\boldsymbol{c	\boldsymbol{c	ADJ
bracis-28360	170	11	}	}	PUNCT
bracis-28360	170	12	)	)	PUNCT
bracis-28360	170	13	\ge	\ge	PROPN
bracis-28360	170	14	\mathfrak	\mathfrak	PROPN
bracis-28360	170	15	{	{	PUNCT
bracis-28360	170	16	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	170	17	,	,	PUNCT
bracis-28360	170	18	m}^c(\boldsymbol{x})\	m}^c(\boldsymbol{x})\	NOUN
bracis-28360	170	19	)	)	PUNCT
bracis-28360	170	20	.	.	PUNCT
bracis-28360	171	1	therefore	therefore	ADV
bracis-28360	171	2	,	,	PUNCT
bracis-28360	171	3	if	if	SCONJ
bracis-28360	171	4	(	(	PUNCT
bracis-28360	171	5	i	i	NOUN
bracis-28360	171	6	)	)	PUNCT
bracis-28360	171	7	or	or	CCONJ
bracis-28360	171	8	(	(	PUNCT
bracis-28360	171	9	ii	ii	NOUN
bracis-28360	171	10	)	)	PUNCT
bracis-28360	171	11	holds	hold	VERB
bracis-28360	171	12	,	,	PUNCT
bracis-28360	171	13	then	then	ADV
bracis-28360	171	14	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	171	15	{	{	PUNCT
bracis-28360	171	16	cc}_{\delta	cc}_{\delta	PROPN
bracis-28360	171	17	,	,	PUNCT
bracis-28360	171	18	m}^c\	m}^c\	PROPN
bracis-28360	171	19	)	)	PUNCT
bracis-28360	171	20	is	be	AUX
bracis-28360	171	21	\(\boldsymbol{1}\)-increasing	\(\boldsymbol{1}\)-increase	VERB
bracis-28360	171	22	.	.	PUNCT
bracis-28360	172	1	(	(	PUNCT
bracis-28360	172	2	\(\rightarrow	\(\rightarrow	NOUN
bracis-28360	172	3	\	\	ADJ
bracis-28360	172	4	)	)	PUNCT
bracis-28360	172	5	)	)	PUNCT
bracis-28360	172	6	suppose	suppose	VERB
bracis-28360	172	7	that	that	SCONJ
bracis-28360	172	8	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	172	9	{	{	PUNCT
bracis-28360	172	10	cc}_{\delta	cc}_{\delta	PROPN
bracis-28360	172	11	,	,	PUNCT
bracis-28360	172	12	m}^c\	m}^c\	PROPN
bracis-28360	172	13	)	)	PUNCT
bracis-28360	172	14	is	be	AUX
bracis-28360	172	15	\(\boldsymbol{1}\)-increasing	\(\boldsymbol{1}\)-increase	VERB
bracis-28360	172	16	,	,	PUNCT
bracis-28360	172	17	that	that	PRON
bracis-28360	172	18	is	is	ADV
bracis-28360	172	19	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	172	20	{	{	PUNCT
bracis-28360	172	21	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	172	22	,	,	PUNCT
bracis-28360	172	23	m}^c(\boldsymbol{x	m}^c(\boldsymbol{x	NOUN
bracis-28360	172	24	}	}	PUNCT
bracis-28360	172	25	+	+	NUM
bracis-28360	172	26	\boldsymbol{c	\boldsymbol{c	ADJ
bracis-28360	172	27	}	}	PUNCT
bracis-28360	172	28	)	)	PUNCT
bracis-28360	172	29	\ge	\ge	PROPN
bracis-28360	172	30	\mathfrak	\mathfrak	PROPN
bracis-28360	172	31	{	{	PUNCT
bracis-28360	172	32	cc}^c_{\delta	cc}^c_{\delta	NOUN
bracis-28360	172	33	,	,	PUNCT
bracis-28360	172	34	m}(\boldsymbol{x})\	m}(\boldsymbol{x})\	PROPN
bracis-28360	172	35	)	)	PUNCT
bracis-28360	172	36	.	.	PUNCT
bracis-28360	173	1	then	then	ADV
bracis-28360	173	2	it	it	PRON
bracis-28360	173	3	follows	follow	VERB
bracis-28360	173	4	that	that	SCONJ
bracis-28360	173	5	\((x_{(1	\((x_{(1	NOUN
bracis-28360	173	6	)	)	PUNCT
bracis-28360	173	7	}	}	PUNCT
bracis-28360	173	8	+	+	CCONJ
bracis-28360	174	1	c	c	X
bracis-28360	174	2	)	)	PUNCT
bracis-28360	174	3	+	+	CCONJ
bracis-28360	174	4	\sum	\sum	NOUN
bracis-28360	174	5	_	_	PUNCT
bracis-28360	174	6	{	{	PUNCT
bracis-28360	174	7	i=2}^{n	i=2}^{n	ADJ
bracis-28360	174	8	}	}	PUNCT
bracis-28360	174	9	\delta	\delta	PROPN
bracis-28360	174	10	(	(	PUNCT
bracis-28360	174	11	c(x_{(i	c(x_{(i	PROPN
bracis-28360	174	12	)	)	PUNCT
bracis-28360	174	13	}	}	PUNCT
bracis-28360	175	1	+	+	CCONJ
bracis-28360	175	2	c	c	X
bracis-28360	175	3	,	,	PUNCT
bracis-28360	175	4	m_{(i	m_{(i	PROPN
bracis-28360	175	5	)	)	PUNCT
bracis-28360	175	6	}	}	PUNCT
bracis-28360	175	7	)	)	PUNCT
bracis-28360	175	8	,	,	PUNCT
bracis-28360	175	9	c	c	X
bracis-28360	175	10	(	(	PUNCT
bracis-28360	175	11	x_{(i-1	x_{(i-1	NUM
bracis-28360	175	12	)	)	PUNCT
bracis-28360	175	13	}	}	PUNCT
bracis-28360	175	14	+	+	CCONJ
bracis-28360	176	1	c	c	X
bracis-28360	176	2	,	,	PUNCT
bracis-28360	176	3	m_{(i	m_{(i	PROPN
bracis-28360	176	4	)	)	PUNCT
bracis-28360	176	5	}	}	PUNCT
bracis-28360	176	6	)	)	PUNCT
bracis-28360	176	7	)	)	PUNCT
bracis-28360	177	1	\	\	NOUN
bracis-28360	177	2	)	)	PUNCT
bracis-28360	177	3	\(\ge	\(\ge	PROPN
bracis-28360	177	4	x_{(1	x_{(1	PROPN
bracis-28360	177	5	)	)	PUNCT
bracis-28360	177	6	}	}	PUNCT
bracis-28360	177	7	+	+	CCONJ
bracis-28360	177	8	\sum	\sum	NOUN
bracis-28360	177	9	_	_	PUNCT
bracis-28360	177	10	{	{	PUNCT
bracis-28360	177	11	i=2}^{n}\delta	i=2}^{n}\delta	PROPN
bracis-28360	177	12	(	(	PUNCT
bracis-28360	177	13	c(x_{(i)},m_{(i	c(x_{(i)},m_{(i	NOUN
bracis-28360	177	14	)	)	PUNCT
bracis-28360	177	15	}	}	PUNCT
bracis-28360	177	16	)	)	PUNCT
bracis-28360	177	17	,	,	PUNCT
bracis-28360	177	18	c(x_{(i-1	c(x_{(i-1	NOUN
bracis-28360	177	19	)	)	PUNCT
bracis-28360	177	20	}	}	PUNCT
bracis-28360	177	21	,	,	PUNCT
bracis-28360	177	22	m_{(i)}))\	m_{(i)}))\	PROPN
bracis-28360	177	23	)	)	PUNCT
bracis-28360	177	24	which	which	PRON
bracis-28360	177	25	implies	imply	VERB
bracis-28360	177	26	that	that	SCONJ
bracis-28360	177	27	condition	condition	NOUN
bracis-28360	177	28	(	(	PUNCT
bracis-28360	177	29	ii	ii	NOUN
bracis-28360	177	30	)	)	PUNCT
bracis-28360	177	31	holds	hold	VERB
bracis-28360	177	32	.	.	PUNCT
bracis-28360	178	1	ordered	order	VERB
bracis-28360	178	2	directional	directional	ADJ
bracis-28360	178	3	monotonicity	monotonicity	NOUN
bracis-28360	178	4	of	of	ADP
bracis-28360	178	5	d	d	PROPN
bracis-28360	178	6	-	-	PUNCT
bracis-28360	178	7	cc	cc	NOUN
bracis-28360	178	8	integrals	integral	NOUN
bracis-28360	178	9	.	.	PUNCT
bracis-28360	179	1	any	any	DET
bracis-28360	179	2	d	d	NOUN
bracis-28360	179	3	-	-	PUNCT
bracis-28360	179	4	cc	cc	VERB
bracis-28360	179	5	integral	integral	ADJ
bracis-28360	179	6	is	be	AUX
bracis-28360	179	7	ordered	order	VERB
bracis-28360	179	8	directionally	directionally	ADV
bracis-28360	179	9	monotonic	monotonic	ADJ
bracis-28360	179	10	 	 	SPACE
bracis-28360	180	1	[	[	X
bracis-28360	180	2	9	9	NUM
bracis-28360	180	3	]	]	PUNCT
bracis-28360	180	4	.	.	PUNCT
bracis-28360	181	1	such	such	ADJ
bracis-28360	181	2	functions	function	NOUN
bracis-28360	181	3	are	be	AUX
bracis-28360	181	4	monotonic	monotonic	ADJ
bracis-28360	181	5	along	along	ADP
bracis-28360	181	6	different	different	ADJ
bracis-28360	181	7	directions	direction	NOUN
bracis-28360	181	8	according	accord	VERB
bracis-28360	181	9	to	to	ADP
bracis-28360	181	10	the	the	DET
bracis-28360	181	11	ordinal	ordinal	ADJ
bracis-28360	181	12	size	size	NOUN
bracis-28360	181	13	of	of	ADP
bracis-28360	181	14	the	the	DET
bracis-28360	181	15	coordinates	coordinate	NOUN
bracis-28360	181	16	of	of	ADP
bracis-28360	181	17	each	each	DET
bracis-28360	181	18	input	input	NOUN
bracis-28360	181	19	.	.	PUNCT
bracis-28360	182	1	definition	definition	NOUN
bracis-28360	182	2	5	5	NUM
bracis-28360	182	3	[	[	X
bracis-28360	182	4	9	9	NUM
bracis-28360	182	5	]	]	PUNCT
bracis-28360	182	6	.	.	PUNCT
bracis-28360	183	1	consider	consider	VERB
bracis-28360	183	2	a	a	DET
bracis-28360	183	3	function	function	NOUN
bracis-28360	183	4	\(f	\(f	NOUN
bracis-28360	183	5	:	:	PUNCT
bracis-28360	184	1	[	[	X
bracis-28360	184	2	0	0	NUM
bracis-28360	184	3	,	,	PUNCT
bracis-28360	184	4	1]^n	1]^n	NUM
bracis-28360	184	5	\rightarrow	\rightarrow	PROPN
bracis-28360	185	1	[	[	X
bracis-28360	185	2	0	0	NUM
bracis-28360	185	3	,	,	PUNCT
bracis-28360	185	4	1]\	1]\	NUM
bracis-28360	185	5	)	)	PUNCT
bracis-28360	185	6	and	and	CCONJ
bracis-28360	185	7	let	let	VERB
bracis-28360	185	8	\(\boldsymbol{r}=(r_1,\dots	\(\boldsymbol{r}=(r_1,\dot	NOUN
bracis-28360	185	9	,	,	PUNCT
bracis-28360	185	10	r_n)\	r_n)\	NUM
bracis-28360	185	11	)	)	PUNCT
bracis-28360	185	12	be	be	AUX
bracis-28360	185	13	a	a	DET
bracis-28360	185	14	real	real	ADJ
bracis-28360	185	15	n	n	CCONJ
bracis-28360	185	16	-	-	PUNCT
bracis-28360	185	17	dimensional	dimensional	ADJ
bracis-28360	185	18	vector	vector	NOUN
bracis-28360	185	19	,	,	PUNCT
bracis-28360	185	20	\(\boldsymbol{r	\(\boldsymbol{r	ADJ
bracis-28360	185	21	}	}	PUNCT
bracis-28360	185	22	\ne	\ne	PROPN
bracis-28360	185	23	\boldsymbol{0}\	\boldsymbol{0}\	NOUN
bracis-28360	185	24	)	)	PUNCT
bracis-28360	185	25	.	.	PUNCT
bracis-28360	186	1	f	f	PROPN
bracis-28360	186	2	is	be	AUX
bracis-28360	186	3	said	say	VERB
bracis-28360	186	4	to	to	PART
bracis-28360	186	5	be	be	AUX
bracis-28360	186	6	ordered	order	VERB
bracis-28360	186	7	directionally	directionally	ADV
bracis-28360	186	8	(	(	PUNCT
bracis-28360	186	9	od	od	NOUN
bracis-28360	186	10	)	)	PUNCT
bracis-28360	186	11	\(\boldsymbol{r}\)-increasing	\(\boldsymbol{r}\)-increase	VERB
bracis-28360	186	12	if	if	SCONJ
bracis-28360	186	13	,	,	PUNCT
bracis-28360	186	14	for	for	ADP
bracis-28360	186	15	each	each	DET
bracis-28360	186	16	\(\boldsymbol{x	\(\boldsymbol{x	ADJ
bracis-28360	186	17	}	}	PUNCT
bracis-28360	186	18	\in	\in	PROPN
bracis-28360	186	19	[	[	X
bracis-28360	186	20	0	0	NUM
bracis-28360	186	21	,	,	PUNCT
bracis-28360	186	22	1]^n\	1]^n\	NUM
bracis-28360	186	23	)	)	PUNCT
bracis-28360	186	24	,	,	PUNCT
bracis-28360	186	25	any	any	DET
bracis-28360	186	26	permutation	permutation	NOUN
bracis-28360	186	27	\(\sigma	\(\sigma	NOUN
bracis-28360	186	28	:	:	PUNCT
bracis-28360	186	29	\{1	\{1	NUM
bracis-28360	186	30	,	,	PUNCT
bracis-28360	186	31	\ldots	\ldots	INTJ
bracis-28360	186	32	,	,	PUNCT
bracis-28360	186	33	n\	n\	PROPN
bracis-28360	186	34	}	}	PUNCT
bracis-28360	186	35	\rightarrow	\rightarrow	PROPN
bracis-28360	186	36	\{1	\{1	PROPN
bracis-28360	186	37	,	,	PUNCT
bracis-28360	186	38	\ldots	\ldots	INTJ
bracis-28360	186	39	,	,	PUNCT
bracis-28360	186	40	n\}\	n\}\	NOUN
bracis-28360	186	41	)	)	PUNCT
bracis-28360	186	42	with	with	ADP
bracis-28360	186	43	\(x_{\sigma	\(x_{\sigma	NUM
bracis-28360	186	44	(	(	PUNCT
bracis-28360	186	45	1	1	NUM
bracis-28360	186	46	)	)	PUNCT
bracis-28360	186	47	}	}	PUNCT
bracis-28360	186	48	\ge	\ge	PROPN
bracis-28360	186	49	\ldots	\ldots	ADP
bracis-28360	186	50	\ge	\ge	PROPN
bracis-28360	186	51	x_{\sigma	x_{\sigma	X
bracis-28360	187	1	(	(	PUNCT
bracis-28360	187	2	n)}\	n)}\	ADJ
bracis-28360	187	3	)	)	PUNCT
bracis-28360	187	4	,	,	PUNCT
bracis-28360	187	5	and	and	CCONJ
bracis-28360	187	6	\(c>0\	\(c>0\	NOUN
bracis-28360	187	7	)	)	PUNCT
bracis-28360	188	1	such	such	ADJ
bracis-28360	188	2	that	that	SCONJ
bracis-28360	188	3	\(1	\(1	PROPN
bracis-28360	188	4	\ge	\ge	PROPN
bracis-28360	188	5	x_{\sigma	x_{\sigma	PUNCT
bracis-28360	188	6	(	(	PUNCT
bracis-28360	188	7	1	1	NUM
bracis-28360	188	8	)	)	PUNCT
bracis-28360	188	9	}	}	PUNCT
bracis-28360	189	1	+	+	CCONJ
bracis-28360	189	2	cr_1	cr_1	ADJ
bracis-28360	189	3	\ge	\ge	PROPN
bracis-28360	189	4	\ldots	\ldot	NOUN
bracis-28360	189	5	\ge	\ge	PROPN
bracis-28360	189	6	x_{\sigma	x_{\sigma	PUNCT
bracis-28360	189	7	(	(	PUNCT
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bracis-28360	189	14	,	,	PUNCT
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bracis-28360	189	19	}	}	PUNCT
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bracis-28360	189	38	r_{\sigma	r_{\sigma	NOUN
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bracis-28360	189	44	,	,	PUNCT
bracis-28360	189	45	r_{\sigma	r_{\sigma	NOUN
bracis-28360	189	46	^{-1}(n)})\	^{-1}(n)})\	NOUN
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bracis-28360	190	2	2	2	NUM
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bracis-28360	190	6	m	m	PROPN
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bracis-28360	190	11	)	)	PUNCT
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bracis-28360	190	28	m}^c\	m}^c\	PROPN
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bracis-28360	191	10	1]^n\	1]^n\	NUM
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bracis-28360	191	33	1	1	NUM
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bracis-28360	191	39	x_{\sigma	x_{\sigma	X
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bracis-28360	196	21	r_{\sigma	r_{\sigma	NOUN
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bracis-28360	202	58	&	&	CCONJ
bracis-28360	202	59	=	=	PROPN
bracis-28360	202	60	x_{(1	x_{(1	PROPN
bracis-28360	202	61	)	)	PUNCT
bracis-28360	202	62	}	}	PUNCT
bracis-28360	202	63	+	+	CCONJ
bracis-28360	202	64	\sum	\sum	NOUN
bracis-28360	202	65	_	_	PUNCT
bracis-28360	202	66	{	{	PUNCT
bracis-28360	202	67	i=2}^{n-1	i=2}^{n-1	PROPN
bracis-28360	202	68	}	}	PUNCT
bracis-28360	202	69	\delta	\delta	PROPN
bracis-28360	202	70	(	(	PUNCT
bracis-28360	202	71	c(x_{(i	c(x_{(i	PROPN
bracis-28360	202	72	)	)	PUNCT
bracis-28360	202	73	}	}	PUNCT
bracis-28360	202	74	,	,	PUNCT
bracis-28360	202	75	m_{(i	m_{(i	PROPN
bracis-28360	202	76	)	)	PUNCT
bracis-28360	202	77	}	}	PUNCT
bracis-28360	202	78	)	)	PUNCT
bracis-28360	202	79	,	,	PUNCT
bracis-28360	202	80	c(x_{(i-1	c(x_{(i-1	NOUN
bracis-28360	202	81	)	)	PUNCT
bracis-28360	202	82	}	}	PUNCT
bracis-28360	202	83	,	,	PUNCT
bracis-28360	202	84	m_{(i	m_{(i	PROPN
bracis-28360	202	85	)	)	PUNCT
bracis-28360	202	86	}	}	PUNCT
bracis-28360	202	87	)	)	PUNCT
bracis-28360	202	88	)	)	PUNCT
bracis-28360	202	89	\\	\\	NOUN
bracis-28360	202	90	&	&	CCONJ
bracis-28360	202	91	\quad	\quad	PROPN
bracis-28360	202	92	+	+	PROPN
bracis-28360	202	93	\delta	\delta	PROPN
bracis-28360	202	94	(	(	PUNCT
bracis-28360	202	95	c	c	X
bracis-28360	202	96	(	(	PUNCT
bracis-28360	202	97	(	(	PUNCT
bracis-28360	202	98	x_{(n	x_{(n	PROPN
bracis-28360	202	99	)	)	PUNCT
bracis-28360	202	100	}	}	PUNCT
bracis-28360	202	101	+	+	CCONJ
bracis-28360	202	102	c\cdot	c\cdot	NOUN
bracis-28360	202	103	k	k	NOUN
bracis-28360	202	104	)	)	PUNCT
bracis-28360	202	105	,	,	PUNCT
bracis-28360	202	106	m_{(n	m_{(n	PROPN
bracis-28360	202	107	)	)	PUNCT
bracis-28360	202	108	}	}	PUNCT
bracis-28360	202	109	)	)	PUNCT
bracis-28360	202	110	,	,	PUNCT
bracis-28360	202	111	c	c	X
bracis-28360	202	112	(	(	PUNCT
bracis-28360	202	113	x_{(n-1	x_{(n-1	NUM
bracis-28360	202	114	)	)	PUNCT
bracis-28360	202	115	}	}	PUNCT
bracis-28360	202	116	,	,	PUNCT
bracis-28360	202	117	m_{(n)}))\\	m_{(n)}))\\	PROPN
bracis-28360	202	118	&	&	CCONJ
bracis-28360	202	119	\ge	\ge	PROPN
bracis-28360	202	120	x_{(1	x_{(1	PROPN
bracis-28360	202	121	)	)	PUNCT
bracis-28360	202	122	}	}	PUNCT
bracis-28360	202	123	+	+	CCONJ
bracis-28360	202	124	\sum	\sum	NOUN
bracis-28360	202	125	_	_	PUNCT
bracis-28360	202	126	{	{	PUNCT
bracis-28360	202	127	i=2}^{n-1	i=2}^{n-1	PROPN
bracis-28360	202	128	}	}	PUNCT
bracis-28360	202	129	\delta	\delta	PROPN
bracis-28360	202	130	(	(	PUNCT
bracis-28360	202	131	c(x_{(i	c(x_{(i	PROPN
bracis-28360	202	132	)	)	PUNCT
bracis-28360	202	133	}	}	PUNCT
bracis-28360	202	134	,	,	PUNCT
bracis-28360	202	135	m_{(i	m_{(i	PROPN
bracis-28360	202	136	)	)	PUNCT
bracis-28360	202	137	}	}	PUNCT
bracis-28360	202	138	)	)	PUNCT
bracis-28360	202	139	,	,	PUNCT
bracis-28360	202	140	c(x_{(i-1	c(x_{(i-1	NOUN
bracis-28360	202	141	)	)	PUNCT
bracis-28360	202	142	}	}	PUNCT
bracis-28360	202	143	,	,	PUNCT
bracis-28360	202	144	m_{(i	m_{(i	PROPN
bracis-28360	202	145	)	)	PUNCT
bracis-28360	202	146	}	}	PUNCT
bracis-28360	202	147	)	)	PUNCT
bracis-28360	203	1	+	+	CCONJ
bracis-28360	203	2	\delta	\delta	PROPN
bracis-28360	203	3	(	(	PUNCT
bracis-28360	203	4	c(x_{(n	c(x_{(n	PROPN
bracis-28360	203	5	)	)	PUNCT
bracis-28360	203	6	}	}	PUNCT
bracis-28360	203	7	,	,	PUNCT
bracis-28360	203	8	m_{(n	m_{(n	NOUN
bracis-28360	203	9	)	)	PUNCT
bracis-28360	203	10	}	}	PUNCT
bracis-28360	203	11	)	)	PUNCT
bracis-28360	203	12	,	,	PUNCT
bracis-28360	203	13	c(x_{(n-1	c(x_{(n-1	X
bracis-28360	203	14	)	)	PUNCT
bracis-28360	203	15	}	}	PUNCT
bracis-28360	203	16	,	,	PUNCT
bracis-28360	203	17	m_{(n	m_{(n	NOUN
bracis-28360	203	18	)	)	PUNCT
bracis-28360	203	19	}	}	PUNCT
bracis-28360	203	20	)	)	PUNCT
bracis-28360	203	21	)	)	PUNCT
bracis-28360	203	22	\\	\\	NOUN
bracis-28360	203	23	{	{	PUNCT
bracis-28360	203	24	}	}	PUNCT
bracis-28360	203	25	&	&	CCONJ
bracis-28360	203	26	=	=	PROPN
bracis-28360	203	27	\mathfrak	\mathfrak	PROPN
bracis-28360	203	28	{	{	PUNCT
bracis-28360	203	29	cc}_{\delta	cc}_{\delta	NOUN
bracis-28360	203	30	,	,	PUNCT
bracis-28360	203	31	m}^c(\boldsymbol{x	m}^c(\boldsymbol{x	NOUN
bracis-28360	203	32	}	}	PUNCT
bracis-28360	203	33	)	)	PUNCT
bracis-28360	204	1	\qquad	\qquad	PROPN
bracis-28360	204	2	\qquad	\qquad	PROPN
bracis-28360	204	3	\qquad	\qquad	PROPN
bracis-28360	204	4	\qquad	\qquad	PROPN
bracis-28360	204	5	\qquad	\qquad	PROPN
bracis-28360	204	6	\qquad	\qquad	PROPN
bracis-28360	204	7	\qquad	\qquad	PROPN
bracis-28360	204	8	\text	\text	PROPN
bracis-28360	204	9	{	{	PUNCT
bracis-28360	204	10	by	by	ADP
bracis-28360	204	11	prop	prop	NOUN
bracis-28360	204	12	.	.	PUNCT
bracis-28360	204	13	1-(i	1-(i	NUM
bracis-28360	204	14	)	)	PUNCT
bracis-28360	204	15	and	and	CCONJ
bracis-28360	204	16	(	(	PUNCT
bracis-28360	204	17	d4)}\\	d4)}\\	NOUN
bracis-28360	204	18	\end{aligned}$$	\end{aligned}$$	ADP
bracis-28360	204	19	4	4	NUM
bracis-28360	204	20	application	application	NOUN
bracis-28360	204	21	of	of	ADP
bracis-28360	204	22	d	d	PROPN
bracis-28360	204	23	-	-	PUNCT
bracis-28360	204	24	cc	cc	NOUN
bracis-28360	204	25	integrals	integral	NOUN
bracis-28360	204	26	in	in	ADP
bracis-28360	204	27	 	 	SPACE
bracis-28360	204	28	classification	classification	VERB
bracis-28360	204	29	a	a	DET
bracis-28360	204	30	classification	classification	NOUN
bracis-28360	204	31	problem	problem	NOUN
bracis-28360	204	32	consists	consist	VERB
bracis-28360	204	33	of	of	ADP
bracis-28360	204	34	p	p	NOUN
bracis-28360	204	35	training	training	NOUN
bracis-28360	204	36	examples	example	NOUN
bracis-28360	204	37	\(\vec	\(\vec	X
bracis-28360	204	38	{	{	PUNCT
bracis-28360	204	39	x_p	x_p	SYM
bracis-28360	204	40	}	}	PUNCT
bracis-28360	204	41	=	=	SYM
bracis-28360	204	42	(	(	PUNCT
bracis-28360	204	43	x_{p1},\ldots	x_{p1},\ldot	NOUN
bracis-28360	204	44	,	,	PUNCT
bracis-28360	204	45	x_{pn})\	x_{pn})\	PROPN
bracis-28360	204	46	)	)	PUNCT
bracis-28360	204	47	,	,	PUNCT
bracis-28360	204	48	\(p	\(p	PROPN
bracis-28360	204	49	\in	\in	PROPN
bracis-28360	204	50	\{1,\ldots	\{1,\ldot	NOUN
bracis-28360	204	51	,	,	PUNCT
bracis-28360	204	52	p\}\	p\}\	NOUN
bracis-28360	204	53	)	)	PUNCT
bracis-28360	204	54	where	where	SCONJ
bracis-28360	204	55	\(x_{pi}\	\(x_{pi}\	NOUN
bracis-28360	204	56	)	)	PUNCT
bracis-28360	204	57	is	be	AUX
bracis-28360	204	58	the	the	DET
bracis-28360	204	59	value	value	NOUN
bracis-28360	204	60	of	of	ADP
bracis-28360	204	61	the	the	DET
bracis-28360	204	62	i	i	PROPN
bracis-28360	204	63	-	-	PUNCT
bracis-28360	204	64	th	th	X
bracis-28360	204	65	variable	variable	NOUN
bracis-28360	204	66	of	of	ADP
bracis-28360	204	67	the	the	DET
bracis-28360	204	68	p	p	PROPN
bracis-28360	204	69	-	-	PUNCT
bracis-28360	204	70	th	th	X
bracis-28360	204	71	example	example	NOUN
bracis-28360	204	72	and	and	CCONJ
bracis-28360	204	73	each	each	DET
bracis-28360	204	74	example	example	NOUN
bracis-28360	204	75	belongs	belong	VERB
bracis-28360	204	76	to	to	ADP
bracis-28360	204	77	one	one	NUM
bracis-28360	204	78	of	of	ADP
bracis-28360	204	79	m	m	PROPN
bracis-28360	204	80	classes	class	NOUN
bracis-28360	204	81	in	in	ADP
bracis-28360	204	82	\(c	\(c	ADJ
bracis-28360	204	83	{	{	PUNCT
bracis-28360	204	84	=	=	NOUN
bracis-28360	204	85	}	}	PUNCT
bracis-28360	204	86	\{c_1	\{c_1	NOUN
bracis-28360	204	87	,	,	PUNCT
bracis-28360	204	88	\ldots	\ldots	INTJ
bracis-28360	204	89	,	,	PUNCT
bracis-28360	204	90	c_m\}\	c_m\}\	NOUN
bracis-28360	204	91	)	)	PUNCT
bracis-28360	204	92	.	.	PUNCT
bracis-28360	205	1	the	the	DET
bracis-28360	205	2	goal	goal	NOUN
bracis-28360	205	3	of	of	ADP
bracis-28360	205	4	the	the	DET
bracis-28360	205	5	learned	learn	VERB
bracis-28360	205	6	classifier	classifier	NOUN
bracis-28360	205	7	is	be	AUX
bracis-28360	205	8	to	to	PART
bracis-28360	205	9	identify	identify	VERB
bracis-28360	205	10	the	the	DET
bracis-28360	205	11	class	class	NOUN
bracis-28360	205	12	of	of	ADP
bracis-28360	205	13	new	new	ADJ
bracis-28360	205	14	/	/	SYM
bracis-28360	205	15	unknown	unknown	ADJ
bracis-28360	205	16	examples	example	NOUN
bracis-28360	205	17	.	.	PUNCT
bracis-28360	206	1	a	a	DET
bracis-28360	206	2	frbcs	frbc	NOUN
bracis-28360	206	3	[	[	X
bracis-28360	206	4	17	17	NUM
bracis-28360	206	5	]	]	PUNCT
bracis-28360	206	6	is	be	AUX
bracis-28360	206	7	a	a	DET
bracis-28360	206	8	type	type	NOUN
bracis-28360	206	9	of	of	ADP
bracis-28360	206	10	classification	classification	NOUN
bracis-28360	206	11	system	system	NOUN
bracis-28360	206	12	that	that	PRON
bracis-28360	206	13	is	be	AUX
bracis-28360	206	14	based	base	VERB
bracis-28360	206	15	on	on	ADP
bracis-28360	206	16	rules	rule	NOUN
bracis-28360	206	17	with	with	ADP
bracis-28360	206	18	linguistic	linguistic	ADJ
bracis-28360	206	19	labels	label	NOUN
bracis-28360	206	20	,	,	PUNCT
bracis-28360	206	21	modeled	model	VERB
bracis-28360	206	22	by	by	ADP
bracis-28360	206	23	fuzzy	fuzzy	ADJ
bracis-28360	206	24	sets	set	NOUN
bracis-28360	206	25	.	.	PUNCT
bracis-28360	207	1	the	the	DET
bracis-28360	207	2	inference	inference	NOUN
bracis-28360	207	3	process	process	NOUN
bracis-28360	207	4	,	,	PUNCT
bracis-28360	207	5	known	know	VERB
bracis-28360	207	6	as	as	ADP
bracis-28360	207	7	the	the	DET
bracis-28360	207	8	fuzzy	fuzzy	ADJ
bracis-28360	207	9	reasoning	reasoning	NOUN
bracis-28360	207	10	method	method	NOUN
bracis-28360	207	11	(	(	PUNCT
bracis-28360	207	12	frm	frm	PROPN
bracis-28360	207	13	)	)	PUNCT
bracis-28360	207	14	,	,	PUNCT
bracis-28360	207	15	is	be	AUX
bracis-28360	207	16	determined	determine	VERB
bracis-28360	207	17	by	by	ADP
bracis-28360	207	18	four	four	NUM
bracis-28360	207	19	sequential	sequential	ADJ
bracis-28360	207	20	steps	step	NOUN
bracis-28360	207	21	:	:	PUNCT
bracis-28360	207	22	(	(	PUNCT
bracis-28360	207	23	1	1	X
bracis-28360	207	24	)	)	PUNCT
bracis-28360	207	25	matching	matching	NOUN
bracis-28360	207	26	degree	degree	NOUN
bracis-28360	207	27	(	(	PUNCT
bracis-28360	207	28	\({a_j}\	\({a_j}\	PROPN
bracis-28360	207	29	)	)	PUNCT
bracis-28360	207	30	)	)	PUNCT
bracis-28360	208	1	it	it	PRON
bracis-28360	208	2	measures	measure	VERB
bracis-28360	208	3	,	,	PUNCT
bracis-28360	208	4	for	for	ADP
bracis-28360	208	5	the	the	DET
bracis-28360	208	6	example	example	NOUN
bracis-28360	208	7	\(x_p\	\(x_p\	PROPN
bracis-28360	208	8	)	)	PUNCT
bracis-28360	208	9	to	to	PART
bracis-28360	208	10	be	be	AUX
bracis-28360	208	11	classified	classify	VERB
bracis-28360	208	12	,	,	PUNCT
bracis-28360	208	13	the	the	DET
bracis-28360	208	14	strength	strength	NOUN
bracis-28360	208	15	of	of	ADP
bracis-28360	208	16	the	the	DET
bracis-28360	208	17	if	if	NOUN
bracis-28360	208	18	-	-	PUNCT
bracis-28360	208	19	part	part	NOUN
bracis-28360	208	20	of	of	ADP
bracis-28360	208	21	a	a	DET
bracis-28360	208	22	rule	rule	NOUN
bracis-28360	208	23	\(r_j\	\(r_j\	NOUN
bracis-28360	208	24	)	)	PUNCT
bracis-28360	208	25	.	.	PUNCT
bracis-28360	209	1	\({a_j}\	\({a_j}\	NOUN
bracis-28360	209	2	)	)	PUNCT
bracis-28360	209	3	is	be	AUX
bracis-28360	209	4	calculated	calculate	VERB
bracis-28360	209	5	by	by	ADP
bracis-28360	209	6	a	a	DET
bracis-28360	209	7	fuzzy	fuzzy	ADJ
bracis-28360	209	8	conjunction	conjunction	NOUN
bracis-28360	209	9	operator	operator	NOUN
bracis-28360	209	10	\(\mathfrak	\(\mathfrak	PROPN
bracis-28360	209	11	{	{	PUNCT
bracis-28360	209	12	c}\	c}\	NUM
bracis-28360	209	13	)	)	PUNCT
bracis-28360	209	14	,	,	PUNCT
bracis-28360	209	15	as	as	SCONJ
bracis-28360	209	16	follows	follow	VERB
bracis-28360	209	17	:	:	PUNCT
bracis-28360	209	18	\({a_j}(x_p	\({a_j}(x_p	X
bracis-28360	209	19	)	)	PUNCT
bracis-28360	209	20	=	=	SYM
bracis-28360	209	21	\mathfrak	\mathfrak	PROPN
bracis-28360	209	22	{	{	PUNCT
bracis-28360	209	23	c}(a_{j1}(x_{p1}),\cdots	c}(a_{j1}(x_{p1}),\cdot	NOUN
bracis-28360	209	24	,	,	PUNCT
bracis-28360	209	25	a_{jn}(x_{pn}))\	a_{jn}(x_{pn}))\	PUNCT
bracis-28360	209	26	)	)	PUNCT
bracis-28360	209	27	.	.	PUNCT
bracis-28360	210	1	(	(	PUNCT
bracis-28360	210	2	2	2	X
bracis-28360	210	3	)	)	PUNCT
bracis-28360	210	4	association	association	NOUN
bracis-28360	210	5	degree	degree	NOUN
bracis-28360	210	6	(	(	PUNCT
bracis-28360	210	7	\(b_j^k\	\(b_j^k\	NOUN
bracis-28360	210	8	)	)	PUNCT
bracis-28360	210	9	)	)	PUNCT
bracis-28360	211	1	it	it	PRON
bracis-28360	211	2	weights	weight	VERB
bracis-28360	211	3	the	the	DET
bracis-28360	211	4	matching	matching	NOUN
bracis-28360	211	5	degree	degree	NOUN
bracis-28360	211	6	\({a_j}\	\({a_j}\	NOUN
bracis-28360	211	7	)	)	PUNCT
bracis-28360	211	8	by	by	ADP
bracis-28360	211	9	the	the	DET
bracis-28360	211	10	rule	rule	NOUN
bracis-28360	211	11	weight	weight	NOUN
bracis-28360	211	12	\(rw_j\	\(rw_j\	PROPN
bracis-28360	211	13	)	)	PUNCT
bracis-28360	211	14	,	,	PUNCT
bracis-28360	211	15	through	through	ADP
bracis-28360	211	16	a	a	DET
bracis-28360	211	17	product	product	NOUN
bracis-28360	211	18	operation	operation	NOUN
bracis-28360	211	19	:	:	PUNCT
bracis-28360	211	20	(	(	PUNCT
bracis-28360	211	21	3	3	X
bracis-28360	211	22	)	)	PUNCT
bracis-28360	211	23	example	example	NOUN
bracis-28360	211	24	classification	classification	NOUN
bracis-28360	211	25	soundness	soundness	NOUN
bracis-28360	211	26	degree	degree	NOUN
bracis-28360	211	27	for	for	ADP
bracis-28360	211	28	all	all	DET
bracis-28360	211	29	classes	class	NOUN
bracis-28360	211	30	(	(	PUNCT
bracis-28360	211	31	\(y_k\	\(y_k\	NUM
bracis-28360	211	32	)	)	PUNCT
bracis-28360	211	33	)	)	PUNCT
bracis-28360	211	34	for	for	ADP
bracis-28360	211	35	each	each	DET
bracis-28360	211	36	class	class	NOUN
bracis-28360	211	37	\(c_k	\(c_k	NOUN
bracis-28360	211	38	\in	\in	PROPN
bracis-28360	211	39	c\	c\	NOUN
bracis-28360	211	40	)	)	PUNCT
bracis-28360	211	41	,	,	PUNCT
bracis-28360	211	42	we	we	PRON
bracis-28360	211	43	aggregate	aggregate	VERB
bracis-28360	211	44	all	all	DET
bracis-28360	211	45	the	the	DET
bracis-28360	211	46	positive	positive	ADJ
bracis-28360	211	47	association	association	NOUN
bracis-28360	211	48	degrees	degree	VERB
bracis-28360	211	49	\(b_j^k\	\(b_j^k\	PROPN
bracis-28360	211	50	)	)	PUNCT
bracis-28360	211	51	that	that	PRON
bracis-28360	211	52	were	be	AUX
bracis-28360	211	53	obtained	obtain	VERB
bracis-28360	211	54	in	in	ADP
bracis-28360	211	55	the	the	DET
bracis-28360	211	56	previous	previous	ADJ
bracis-28360	211	57	step	step	NOUN
bracis-28360	211	58	with	with	ADP
bracis-28360	211	59	respect	respect	NOUN
bracis-28360	211	60	to	to	ADP
bracis-28360	211	61	\(c_k\	\(c_k\	PROPN
bracis-28360	211	62	)	)	PUNCT
bracis-28360	211	63	,	,	PUNCT
bracis-28360	211	64	through	through	ADP
bracis-28360	211	65	an	an	DET
bracis-28360	211	66	aggregation	aggregation	NOUN
bracis-28360	211	67	function	function	NOUN
bracis-28360	211	68	a	a	PRON
bracis-28360	211	69	:	:	PUNCT
bracis-28360	211	70	\(y_k	\(y_k	PROPN
bracis-28360	211	71	=	=	SYM
bracis-28360	211	72	a(b_j^k)\	a(b_j^k)\	PROPN
bracis-28360	211	73	)	)	PUNCT
bracis-28360	211	74	,	,	PUNCT
bracis-28360	211	75	with	with	ADP
bracis-28360	211	76	\(j	\(j	PROPN
bracis-28360	211	77	=	=	SYM
bracis-28360	211	78	1	1	NUM
bracis-28360	211	79	,	,	PUNCT
bracis-28360	211	80	\ldots	\ldots	INTJ
bracis-28360	211	81	,	,	PUNCT
bracis-28360	211	82	l\	l\	ADJ
bracis-28360	211	83	)	)	PUNCT
bracis-28360	211	84	,	,	PUNCT
bracis-28360	211	85	and	and	CCONJ
bracis-28360	211	86	\(b_j^k>0\	\(b_j^k>0\	NUM
bracis-28360	211	87	)	)	PUNCT
bracis-28360	211	88	.	.	PUNCT
bracis-28360	212	1	(	(	PUNCT
bracis-28360	212	2	4	4	X
bracis-28360	212	3	)	)	PUNCT
bracis-28360	212	4	classification	classification	NOUN
bracis-28360	212	5	the	the	DET
bracis-28360	212	6	final	final	ADJ
bracis-28360	212	7	decision	decision	NOUN
bracis-28360	212	8	is	be	AUX
bracis-28360	212	9	made	make	VERB
bracis-28360	212	10	in	in	ADP
bracis-28360	212	11	this	this	DET
bracis-28360	212	12	step	step	NOUN
bracis-28360	212	13	.	.	PUNCT
bracis-28360	213	1	for	for	ADP
bracis-28360	213	2	that	that	PRON
bracis-28360	213	3	,	,	PUNCT
bracis-28360	213	4	a	a	DET
bracis-28360	213	5	function	function	NOUN
bracis-28360	213	6	\(f	\(f	NOUN
bracis-28360	213	7	:	:	PUNCT
bracis-28360	213	8	[	[	X
bracis-28360	213	9	0,1]^m	0,1]^m	X
bracis-28360	213	10	\rightarrow	\rightarrow	PROPN
bracis-28360	213	11	c\	c\	PROPN
bracis-28360	213	12	)	)	PUNCT
bracis-28360	213	13	is	be	AUX
bracis-28360	213	14	applied	apply	VERB
bracis-28360	213	15	over	over	ADP
bracis-28360	213	16	all	all	DET
bracis-28360	213	17	example	example	NOUN
bracis-28360	213	18	classification	classification	NOUN
bracis-28360	213	19	soundness	soundness	NOUN
bracis-28360	213	20	degrees	degree	NOUN
bracis-28360	213	21	calculated	calculate	VERB
bracis-28360	213	22	in	in	ADP
bracis-28360	213	23	the	the	DET
bracis-28360	213	24	previous	previous	ADJ
bracis-28360	213	25	step	step	NOUN
bracis-28360	213	26	:	:	PUNCT
bracis-28360	213	27	\(f(y_1,\ldots	\(f(y_1,\ldot	NOUN
bracis-28360	213	28	,	,	PUNCT
bracis-28360	213	29	y_m)=	y_m)=	PROPN
bracis-28360	213	30	\arg	\arg	ADP
bracis-28360	213	31	\max	\max	PROPN
bracis-28360	213	32	\limits	\limits	PROPN
bracis-28360	213	33	_	_	PUNCT
bracis-28360	213	34	{	{	PUNCT
bracis-28360	213	35	k=1,\ldots	k=1,\ldot	NOUN
bracis-28360	213	36	,	,	PUNCT
bracis-28360	213	37	m}(y_k)\	m}(y_k)\	PROPN
bracis-28360	213	38	)	)	PUNCT
bracis-28360	213	39	.	.	PUNCT
bracis-28360	214	1	in	in	ADP
bracis-28360	214	2	this	this	DET
bracis-28360	214	3	paper	paper	NOUN
bracis-28360	214	4	,	,	PUNCT
bracis-28360	214	5	we	we	PRON
bracis-28360	214	6	will	will	AUX
bracis-28360	214	7	apply	apply	VERB
bracis-28360	214	8	d	d	PROPN
bracis-28360	214	9	-	-	PUNCT
bracis-28360	214	10	cc	cc	NOUN
bracis-28360	214	11	integrals	integral	NOUN
bracis-28360	214	12	as	as	ADP
bracis-28360	214	13	the	the	DET
bracis-28360	214	14	aggregation	aggregation	NOUN
bracis-28360	214	15	operator	operator	NOUN
bracis-28360	214	16	a	a	PRON
bracis-28360	214	17	in	in	ADP
bracis-28360	214	18	the	the	DET
bracis-28360	214	19	third	third	ADJ
bracis-28360	214	20	step	step	NOUN
bracis-28360	214	21	of	of	ADP
bracis-28360	214	22	the	the	DET
bracis-28360	214	23	frm	frm	PROPN
bracis-28360	214	24	to	to	PART
bracis-28360	214	25	analyze	analyze	VERB
bracis-28360	214	26	their	their	PRON
bracis-28360	214	27	effect	effect	NOUN
bracis-28360	214	28	on	on	ADP
bracis-28360	214	29	the	the	DET
bracis-28360	214	30	classification	classification	NOUN
bracis-28360	214	31	process.footnote	process.footnote	NOUN
bracis-28360	214	32	2	2	NUM
bracis-28360	214	33	4.1	4.1	NUM
bracis-28360	214	34	experimental	experimental	ADJ
bracis-28360	214	35	framework	framework	NOUN
bracis-28360	214	36	the	the	DET
bracis-28360	214	37	application	application	NOUN
bracis-28360	214	38	of	of	ADP
bracis-28360	214	39	our	our	PRON
bracis-28360	214	40	new	new	ADJ
bracis-28360	214	41	family	family	NOUN
bracis-28360	214	42	of	of	ADP
bracis-28360	214	43	functions	function	NOUN
bracis-28360	214	44	is	be	AUX
bracis-28360	214	45	based	base	VERB
bracis-28360	214	46	on	on	ADP
bracis-28360	214	47	a	a	DET
bracis-28360	214	48	benchmark	benchmark	NOUN
bracis-28360	214	49	composed	compose	VERB
bracis-28360	214	50	of	of	ADP
bracis-28360	214	51	33	33	NUM
bracis-28360	214	52	different	different	ADJ
bracis-28360	214	53	public	public	ADJ
bracis-28360	214	54	datasets	dataset	NOUN
bracis-28360	214	55	found	find	VERB
bracis-28360	214	56	in	in	ADP
bracis-28360	214	57	keel	keel	NOUN
bracis-28360	214	58	 	 	SPACE
bracis-28360	215	1	[	[	X
bracis-28360	215	2	2	2	NUM
bracis-28360	215	3	]	]	PUNCT
bracis-28360	215	4	dataset	dataset	NOUN
bracis-28360	215	5	repositoryfootnote	repositoryfootnote	VERB
bracis-28360	215	6	3	3	NUM
bracis-28360	215	7	.	.	PUNCT
bracis-28360	216	1	it	it	PRON
bracis-28360	216	2	is	be	AUX
bracis-28360	216	3	important	important	ADJ
bracis-28360	216	4	to	to	PART
bracis-28360	216	5	mention	mention	VERB
bracis-28360	216	6	that	that	SCONJ
bracis-28360	216	7	this	this	DET
bracis-28360	216	8	benchmark	benchmark	NOUN
bracis-28360	216	9	has	have	AUX
bracis-28360	216	10	been	be	AUX
bracis-28360	216	11	used	use	VERB
bracis-28360	216	12	for	for	ADP
bracis-28360	216	13	all	all	DET
bracis-28360	216	14	the	the	DET
bracis-28360	216	15	most	most	ADV
bracis-28360	216	16	important	important	ADJ
bracis-28360	216	17	generalizations	generalization	NOUN
bracis-28360	216	18	of	of	ADP
bracis-28360	216	19	the	the	DET
bracis-28360	216	20	ci	ci	NOUN
bracis-28360	216	21	discussed	discuss	VERB
bracis-28360	216	22	before	before	ADV
bracis-28360	216	23	.	.	PUNCT
bracis-28360	217	1	the	the	DET
bracis-28360	217	2	selection	selection	NOUN
bracis-28360	217	3	of	of	ADP
bracis-28360	217	4	the	the	DET
bracis-28360	217	5	same	same	ADJ
bracis-28360	217	6	datasets	dataset	NOUN
bracis-28360	217	7	and	and	CCONJ
bracis-28360	217	8	partitions	partition	NOUN
bracis-28360	217	9	allows	allow	VERB
bracis-28360	217	10	us	we	PRON
bracis-28360	217	11	to	to	PART
bracis-28360	217	12	directly	directly	ADV
bracis-28360	217	13	compare	compare	VERB
bracis-28360	217	14	the	the	DET
bracis-28360	217	15	methods	method	NOUN
bracis-28360	217	16	and	and	CCONJ
bracis-28360	217	17	consequently	consequently	ADV
bracis-28360	217	18	provide	provide	VERB
bracis-28360	217	19	a	a	DET
bracis-28360	217	20	more	more	ADV
bracis-28360	217	21	complete	complete	ADJ
bracis-28360	217	22	analysis	analysis	NOUN
bracis-28360	217	23	.	.	PUNCT
bracis-28360	218	1	in	in	ADP
bracis-28360	218	2	table	table	NOUN
bracis-28360	218	3	 	 	SPACE
bracis-28360	218	4	3	3	NUM
bracis-28360	218	5	,	,	PUNCT
bracis-28360	218	6	we	we	PRON
bracis-28360	218	7	provide	provide	VERB
bracis-28360	218	8	the	the	DET
bracis-28360	218	9	information	information	NOUN
bracis-28360	218	10	of	of	ADP
bracis-28360	218	11	the	the	DET
bracis-28360	218	12	datasets	dataset	NOUN
bracis-28360	218	13	along	along	ADP
bracis-28360	218	14	with	with	ADP
bracis-28360	218	15	their	their	PRON
bracis-28360	218	16	identification	identification	NOUN
bracis-28360	218	17	(	(	PUNCT
bracis-28360	218	18	i	i	NOUN
bracis-28360	218	19	d	d	PROPN
bracis-28360	218	20	)	)	PUNCT
bracis-28360	218	21	,	,	PUNCT
bracis-28360	218	22	number	number	NOUN
bracis-28360	218	23	of	of	ADP
bracis-28360	218	24	instances	instance	NOUN
bracis-28360	218	25	(	(	PUNCT
bracis-28360	218	26	#	#	SYM
bracis-28360	218	27	noi	noi	PROPN
bracis-28360	218	28	)	)	PUNCT
bracis-28360	218	29	,	,	PUNCT
bracis-28360	218	30	number	number	NOUN
bracis-28360	218	31	of	of	ADP
bracis-28360	218	32	attributes	attribute	NOUN
bracis-28360	218	33	(	(	PUNCT
bracis-28360	218	34	#	#	NOUN
bracis-28360	218	35	noa	noa	NOUN
bracis-28360	218	36	)	)	PUNCT
bracis-28360	218	37	,	,	PUNCT
bracis-28360	218	38	and	and	CCONJ
bracis-28360	218	39	the	the	DET
bracis-28360	218	40	total	total	NOUN
bracis-28360	218	41	of	of	ADP
bracis-28360	218	42	classes	class	NOUN
bracis-28360	218	43	(	(	PUNCT
bracis-28360	218	44	#	#	SYM
bracis-28360	218	45	toc	toc	NOUN
bracis-28360	218	46	)	)	PUNCT
bracis-28360	218	47	.	.	PUNCT
bracis-28360	219	1	table	table	NOUN
bracis-28360	220	1	3	3	NUM
bracis-28360	220	2	.	.	PUNCT
bracis-28360	221	1	summary	summary	NOUN
bracis-28360	221	2	of	of	ADP
bracis-28360	221	3	the	the	DET
bracis-28360	221	4	considered	consider	VERB
bracis-28360	221	5	datasets	dataset	NOUN
bracis-28360	221	6	in	in	ADP
bracis-28360	221	7	the	the	DET
bracis-28360	221	8	experimental	experimental	ADJ
bracis-28360	221	9	study.full	study.full	NOUN
bracis-28360	221	10	size	size	NOUN
bracis-28360	221	11	table	table	NOUN
bracis-28360	221	12	the	the	DET
bracis-28360	221	13	experimental	experimental	ADJ
bracis-28360	221	14	framework	framework	NOUN
bracis-28360	221	15	lies	lie	VERB
bracis-28360	221	16	in	in	ADP
bracis-28360	221	17	the	the	DET
bracis-28360	221	18	same	same	ADJ
bracis-28360	221	19	context	context	NOUN
bracis-28360	221	20	as	as	ADP
bracis-28360	221	21	other	other	ADJ
bracis-28360	221	22	works	work	NOUN
bracis-28360	221	23	in	in	ADP
bracis-28360	221	24	the	the	DET
bracis-28360	221	25	literature	literature	NOUN
bracis-28360	221	26	(	(	PUNCT
bracis-28360	221	27	see	see	VERB
bracis-28360	221	28	 	 	SPACE
bracis-28360	221	29	[	[	X
bracis-28360	221	30	19	19	NUM
bracis-28360	221	31	,	,	PUNCT
bracis-28360	221	32	20	20	NUM
bracis-28360	221	33	,	,	PUNCT
bracis-28360	221	34	23	23	NUM
bracis-28360	221	35	]	]	PUNCT
bracis-28360	221	36	)	)	PUNCT
bracis-28360	221	37	,	,	PUNCT
bracis-28360	221	38	i.e.	i.e.	X
bracis-28360	221	39	a	a	DET
bracis-28360	221	40	5	5	NUM
bracis-28360	221	41	-	-	ADJ
bracis-28360	221	42	fold	fold	ADJ
bracis-28360	221	43	cross	cross	NOUN
bracis-28360	221	44	validation	validation	NOUN
bracis-28360	221	45	approach	approach	NOUN
bracis-28360	221	46	.	.	PUNCT
bracis-28360	222	1	consequently	consequently	ADV
bracis-28360	222	2	,	,	PUNCT
bracis-28360	222	3	the	the	DET
bracis-28360	222	4	results	result	NOUN
bracis-28360	222	5	provided	provide	VERB
bracis-28360	222	6	in	in	ADP
bracis-28360	222	7	sect	sect	NOUN
bracis-28360	222	8	.	.	PUNCT
bracis-28360	222	9	 	 	SPACE
bracis-28360	223	1	5	5	NUM
bracis-28360	223	2	are	be	AUX
bracis-28360	223	3	the	the	DET
bracis-28360	223	4	accuracy	accuracy	NOUN
bracis-28360	223	5	mean	mean	NOUN
bracis-28360	223	6	(	(	PUNCT
bracis-28360	223	7	am	be	AUX
bracis-28360	223	8	)	)	PUNCT
bracis-28360	223	9	related	relate	VERB
bracis-28360	223	10	to	to	ADP
bracis-28360	223	11	these	these	DET
bracis-28360	223	12	folds	fold	NOUN
bracis-28360	223	13	.	.	PUNCT
bracis-28360	224	1	moreover	moreover	ADV
bracis-28360	224	2	,	,	PUNCT
bracis-28360	224	3	following	follow	VERB
bracis-28360	224	4	the	the	DET
bracis-28360	224	5	same	same	ADJ
bracis-28360	224	6	approach	approach	NOUN
bracis-28360	224	7	seen	see	VERB
bracis-28360	224	8	in	in	ADP
bracis-28360	224	9	 	 	SPACE
bracis-28360	224	10	[	[	X
bracis-28360	224	11	22	22	NUM
bracis-28360	224	12	]	]	PUNCT
bracis-28360	224	13	,	,	PUNCT
bracis-28360	224	14	the	the	DET
bracis-28360	224	15	hyperparameters	hyperparameter	NOUN
bracis-28360	224	16	used	use	VERB
bracis-28360	224	17	by	by	ADP
bracis-28360	224	18	the	the	DET
bracis-28360	224	19	model	model	NOUN
bracis-28360	224	20	are	be	AUX
bracis-28360	224	21	the	the	DET
bracis-28360	224	22	same	same	ADJ
bracis-28360	224	23	originally	originally	ADV
bracis-28360	224	24	performed	perform	VERB
bracis-28360	224	25	by	by	ADP
bracis-28360	224	26	farc	farc	PROPN
bracis-28360	224	27	-	-	PUNCT
bracis-28360	224	28	hd	hd	NOUN
bracis-28360	224	29	 	 	SPACE
bracis-28360	224	30	[	[	X
bracis-28360	224	31	1	1	NUM
bracis-28360	224	32	]	]	PUNCT
bracis-28360	224	33	.	.	PUNCT
bracis-28360	225	1	5	5	NUM
bracis-28360	225	2	analysis	analysis	NOUN
bracis-28360	225	3	of	of	ADP
bracis-28360	225	4	 	 	SPACE
bracis-28360	225	5	the	the	DET
bracis-28360	225	6	 	 	SPACE
bracis-28360	225	7	experimental	experimental	ADJ
bracis-28360	225	8	results	result	NOUN
bracis-28360	225	9	this	this	DET
bracis-28360	225	10	section	section	NOUN
bracis-28360	225	11	explores	explore	VERB
bracis-28360	225	12	the	the	DET
bracis-28360	225	13	application	application	NOUN
bracis-28360	225	14	of	of	ADP
bracis-28360	225	15	d	d	PROPN
bracis-28360	225	16	-	-	PUNCT
bracis-28360	225	17	cc	cc	NOUN
bracis-28360	225	18	integrals	integral	NOUN
bracis-28360	225	19	.	.	PUNCT
bracis-28360	226	1	so	so	ADV
bracis-28360	226	2	,	,	PUNCT
bracis-28360	226	3	it	it	PRON
bracis-28360	226	4	is	be	AUX
bracis-28360	226	5	presented	present	VERB
bracis-28360	226	6	the	the	DET
bracis-28360	226	7	performance	performance	NOUN
bracis-28360	226	8	of	of	ADP
bracis-28360	226	9	d	d	NOUN
bracis-28360	226	10	-	-	PUNCT
bracis-28360	226	11	cc	cc	ADP
bracis-28360	226	12	integrals	integral	NOUN
bracis-28360	226	13	over	over	ADP
bracis-28360	226	14	the	the	DET
bracis-28360	226	15	datasets	dataset	NOUN
bracis-28360	226	16	to	to	PART
bracis-28360	226	17	achieve	achieve	VERB
bracis-28360	226	18	it	it	PRON
bracis-28360	226	19	.	.	PUNCT
bracis-28360	227	1	then	then	ADV
bracis-28360	227	2	,	,	PUNCT
bracis-28360	227	3	the	the	DET
bracis-28360	227	4	best	good	ADJ
bracis-28360	227	5	function	function	NOUN
bracis-28360	227	6	is	be	AUX
bracis-28360	227	7	pointed	point	VERB
bracis-28360	227	8	out	out	ADP
bracis-28360	227	9	,	,	PUNCT
bracis-28360	227	10	and	and	CCONJ
bracis-28360	227	11	we	we	PRON
bracis-28360	227	12	compare	compare	VERB
bracis-28360	227	13	it	it	PRON
bracis-28360	227	14	against	against	ADP
bracis-28360	227	15	other	other	ADJ
bracis-28360	227	16	operators	operator	NOUN
bracis-28360	227	17	found	find	VERB
bracis-28360	227	18	in	in	ADP
bracis-28360	227	19	the	the	DET
bracis-28360	227	20	literature	literature	NOUN
bracis-28360	227	21	to	to	PART
bracis-28360	227	22	highlight	highlight	VERB
bracis-28360	227	23	the	the	DET
bracis-28360	227	24	best	well	ADV
bracis-28360	227	25	-	-	PUNCT
bracis-28360	227	26	performing	perform	VERB
bracis-28360	227	27	method	method	NOUN
bracis-28360	227	28	efficiency	efficiency	NOUN
bracis-28360	227	29	.	.	PUNCT
bracis-28360	228	1	5.1	5.1	NUM
bracis-28360	228	2	the	the	DET
bracis-28360	228	3	performance	performance	NOUN
bracis-28360	228	4	of	of	ADP
bracis-28360	228	5	 	 	SPACE
bracis-28360	228	6	the	the	DET
bracis-28360	228	7	d	d	PROPN
bracis-28360	228	8	-	-	PUNCT
bracis-28360	228	9	cc	cc	NOUN
bracis-28360	228	10	integrals	integral	NOUN
bracis-28360	228	11	in	in	ADP
bracis-28360	228	12	 	 	SPACE
bracis-28360	228	13	classification	classification	NOUN
bracis-28360	228	14	this	this	DET
bracis-28360	228	15	section	section	NOUN
bracis-28360	228	16	provides	provide	VERB
bracis-28360	228	17	the	the	DET
bracis-28360	228	18	results	result	NOUN
bracis-28360	228	19	obtained	obtain	VERB
bracis-28360	228	20	by	by	ADP
bracis-28360	228	21	the	the	DET
bracis-28360	228	22	application	application	NOUN
bracis-28360	228	23	of	of	ADP
bracis-28360	228	24	the	the	DET
bracis-28360	228	25	d	d	PROPN
bracis-28360	228	26	-	-	PUNCT
bracis-28360	228	27	cc	cc	ADJ
bracis-28360	228	28	integrals	integral	NOUN
bracis-28360	228	29	in	in	ADP
bracis-28360	228	30	the	the	DET
bracis-28360	228	31	frm	frm	PROPN
bracis-28360	228	32	.	.	PUNCT
bracis-28360	229	1	to	to	PART
bracis-28360	229	2	ease	ease	VERB
bracis-28360	229	3	the	the	DET
bracis-28360	229	4	comprehension	comprehension	NOUN
bracis-28360	229	5	,	,	PUNCT
bracis-28360	229	6	in	in	ADP
bracis-28360	229	7	table	table	NOUN
bracis-28360	229	8	 	 	SPACE
bracis-28360	229	9	4	4	NUM
bracis-28360	229	10	,	,	PUNCT
bracis-28360	229	11	we	we	PRON
bracis-28360	229	12	present	present	VERB
bracis-28360	229	13	the	the	DET
bracis-28360	229	14	combination	combination	NOUN
bracis-28360	229	15	of	of	ADP
bracis-28360	229	16	the	the	DET
bracis-28360	229	17	rdf	rdf	NOUN
bracis-28360	229	18	and	and	CCONJ
bracis-28360	229	19	d	d	NOUN
bracis-28360	229	20	-	-	PUNCT
bracis-28360	229	21	cc	cc	VERB
bracis-28360	229	22	integral	integral	ADJ
bracis-28360	229	23	per	per	ADP
bracis-28360	229	24	dataset	dataset	NOUN
bracis-28360	229	25	that	that	PRON
bracis-28360	229	26	led	lead	VERB
bracis-28360	229	27	to	to	ADP
bracis-28360	229	28	the	the	DET
bracis-28360	229	29	largest	large	ADJ
bracis-28360	229	30	accuracy	accuracy	NOUN
bracis-28360	229	31	.	.	PUNCT
bracis-28360	230	1	moreover	moreover	ADV
bracis-28360	230	2	,	,	PUNCT
bracis-28360	230	3	we	we	PRON
bracis-28360	230	4	show	show	VERB
bracis-28360	230	5	in	in	ADP
bracis-28360	230	6	table	table	NOUN
bracis-28360	230	7	 	 	SPACE
bracis-28360	230	8	5	5	NUM
bracis-28360	230	9	the	the	DET
bracis-28360	230	10	mean	mean	ADJ
bracis-28360	230	11	accuracy	accuracy	NOUN
bracis-28360	230	12	for	for	ADP
bracis-28360	230	13	our	our	PRON
bracis-28360	230	14	approach	approach	NOUN
bracis-28360	230	15	considering	consider	VERB
bracis-28360	230	16	the	the	DET
bracis-28360	230	17	33	33	NUM
bracis-28360	230	18	different	different	ADJ
bracis-28360	230	19	datasetsfootnote	datasetsfootnote	NOUN
bracis-28360	230	20	4	4	NUM
bracis-28360	230	21	in	in	ADP
bracis-28360	230	22	order	order	NOUN
bracis-28360	230	23	to	to	PART
bracis-28360	230	24	provide	provide	VERB
bracis-28360	230	25	a	a	DET
bracis-28360	230	26	better	well	ADJ
bracis-28360	230	27	analysis	analysis	NOUN
bracis-28360	230	28	,	,	PUNCT
bracis-28360	230	29	we	we	PRON
bracis-28360	230	30	also	also	ADV
bracis-28360	230	31	highlight	highlight	VERB
bracis-28360	230	32	,	,	PUNCT
bracis-28360	230	33	per	per	ADP
bracis-28360	230	34	rdf	rdf	NOUN
bracis-28360	230	35	,	,	PUNCT
bracis-28360	230	36	the	the	DET
bracis-28360	230	37	largest	large	ADJ
bracis-28360	230	38	mean	mean	NOUN
bracis-28360	230	39	in	in	ADP
bracis-28360	230	40	boldface	boldface	NOUN
bracis-28360	230	41	.	.	PUNCT
bracis-28360	231	1	table	table	NOUN
bracis-28360	231	2	4	4	NUM
bracis-28360	231	3	.	.	PUNCT
bracis-28360	232	1	the	the	DET
bracis-28360	232	2	best	well	ADV
bracis-28360	232	3	-	-	PUNCT
bracis-28360	232	4	achieved	achieve	VERB
bracis-28360	232	5	results	result	NOUN
bracis-28360	232	6	in	in	ADP
bracis-28360	232	7	a	a	DET
bracis-28360	232	8	test	test	NOUN
bracis-28360	232	9	for	for	ADP
bracis-28360	232	10	each	each	DET
bracis-28360	232	11	dataset.full	dataset.full	PROPN
bracis-28360	232	12	size	size	NOUN
bracis-28360	232	13	table	table	NOUN
bracis-28360	232	14	table	table	NOUN
bracis-28360	232	15	5	5	NUM
bracis-28360	232	16	.	.	NUM
bracis-28360	232	17	obtained	obtain	VERB
bracis-28360	232	18	accuracy	accuracy	NOUN
bracis-28360	232	19	mean	mean	VERB
bracis-28360	232	20	in	in	ADP
bracis-28360	232	21	all	all	DET
bracis-28360	232	22	datasets.full	datasets.full	NUM
bracis-28360	232	23	size	size	NOUN
bracis-28360	232	24	table	table	NOUN
bracis-28360	232	25	the	the	DET
bracis-28360	232	26	combination	combination	NOUN
bracis-28360	232	27	of	of	ADP
bracis-28360	232	28	the	the	DET
bracis-28360	232	29	rdf	rdf	NOUN
bracis-28360	232	30	\(\delta	\(\delta	NOUN
bracis-28360	232	31	_	_	NOUN
bracis-28360	232	32	5\	5\	NOUN
bracis-28360	232	33	)	)	PUNCT
bracis-28360	232	34	and	and	CCONJ
bracis-28360	232	35	copula	copula	PROPN
bracis-28360	232	36	\(o_{mm}\	\(o_{mm}\	PROPN
bracis-28360	232	37	)	)	PUNCT
bracis-28360	232	38	achieves	achieve	VERB
bracis-28360	232	39	the	the	DET
bracis-28360	232	40	largest	large	ADJ
bracis-28360	232	41	am	am	NOUN
bracis-28360	232	42	in	in	ADP
bracis-28360	232	43	the	the	DET
bracis-28360	232	44	study	study	NOUN
bracis-28360	232	45	.	.	PUNCT
bracis-28360	233	1	moreover	moreover	ADV
bracis-28360	233	2	,	,	PUNCT
bracis-28360	233	3	considering	consider	VERB
bracis-28360	233	4	\(\delta	\(\delta	NOUN
bracis-28360	233	5	_	_	NOUN
bracis-28360	233	6	5\	5\	NOUN
bracis-28360	233	7	)	)	PUNCT
bracis-28360	233	8	,	,	PUNCT
bracis-28360	233	9	for	for	ADP
bracis-28360	233	10	more	more	ADJ
bracis-28360	233	11	than	than	ADP
bracis-28360	233	12	half	half	NOUN
bracis-28360	233	13	of	of	ADP
bracis-28360	233	14	the	the	DET
bracis-28360	233	15	considered	consider	VERB
bracis-28360	233	16	d	d	NOUN
bracis-28360	233	17	-	-	PUNCT
bracis-28360	233	18	cc	cc	NOUN
bracis-28360	233	19	integrals	integral	NOUN
bracis-28360	233	20	,	,	PUNCT
bracis-28360	233	21	the	the	DET
bracis-28360	233	22	am	am	NOUN
bracis-28360	233	23	is	be	AUX
bracis-28360	233	24	superior	superior	ADJ
bracis-28360	233	25	to	to	ADP
bracis-28360	233	26	80	80	NUM
bracis-28360	233	27	%	%	NOUN
bracis-28360	233	28	.	.	PUNCT
bracis-28360	234	1	the	the	DET
bracis-28360	234	2	rdf	rdf	NOUN
bracis-28360	234	3	\(\delta	\(\delta	NOUN
bracis-28360	234	4	_	_	NOUN
bracis-28360	234	5	2\	2\	NUM
bracis-28360	234	6	)	)	PUNCT
bracis-28360	234	7	is	be	AUX
bracis-28360	234	8	the	the	DET
bracis-28360	234	9	next	next	ADJ
bracis-28360	234	10	one	one	NUM
bracis-28360	234	11	to	to	PART
bracis-28360	234	12	achieve	achieve	VERB
bracis-28360	234	13	satisfactory	satisfactory	ADJ
bracis-28360	234	14	performance	performance	NOUN
bracis-28360	234	15	.	.	PUNCT
bracis-28360	235	1	in	in	ADP
bracis-28360	235	2	fact	fact	NOUN
bracis-28360	235	3	,	,	PUNCT
bracis-28360	235	4	only	only	ADV
bracis-28360	235	5	for	for	ADP
bracis-28360	235	6	two	two	NUM
bracis-28360	235	7	copulas	copula	NOUN
bracis-28360	235	8	,	,	PUNCT
bracis-28360	235	9	\(t_m\	\(t_m\	NOUN
bracis-28360	235	10	)	)	PUNCT
bracis-28360	235	11	,	,	PUNCT
bracis-28360	235	12	and	and	CCONJ
bracis-28360	235	13	\(t_l\	\(t_l\	PROPN
bracis-28360	235	14	)	)	PUNCT
bracis-28360	235	15	,	,	PUNCT
bracis-28360	235	16	this	this	PRON
bracis-28360	235	17	rdf	rdf	VERB
bracis-28360	235	18	presents	present	NOUN
bracis-28360	235	19	an	an	DET
bracis-28360	235	20	am	am	NOUN
bracis-28360	235	21	inferior	inferior	ADJ
bracis-28360	235	22	to	to	ADP
bracis-28360	235	23	80	80	NUM
bracis-28360	235	24	%	%	NOUN
bracis-28360	235	25	.	.	PUNCT
bracis-28360	236	1	observe	observe	VERB
bracis-28360	236	2	that	that	SCONJ
bracis-28360	236	3	\(\delta	\(\delta	NOUN
bracis-28360	236	4	_	_	NOUN
bracis-28360	236	5	5\	5\	NOUN
bracis-28360	236	6	)	)	PUNCT
bracis-28360	236	7	and	and	CCONJ
bracis-28360	236	8	\(\delta	\(\delta	NOUN
bracis-28360	236	9	_	_	NOUN
bracis-28360	236	10	2\	2\	X
bracis-28360	236	11	)	)	PUNCT
bracis-28360	236	12	also	also	ADV
bracis-28360	236	13	performed	perform	VERB
bracis-28360	236	14	well	well	ADV
bracis-28360	236	15	in	in	ADP
bracis-28360	236	16	 	 	SPACE
bracis-28360	236	17	[	[	X
bracis-28360	236	18	27	27	NUM
bracis-28360	236	19	,	,	PUNCT
bracis-28360	236	20	28	28	NUM
bracis-28360	236	21	]	]	PUNCT
bracis-28360	236	22	.	.	PUNCT
bracis-28360	237	1	additionally	additionally	ADV
bracis-28360	237	2	,	,	PUNCT
bracis-28360	237	3	both	both	PRON
bracis-28360	237	4	\(\delta	\(\delta	NOUN
bracis-28360	237	5	_	_	NOUN
bracis-28360	237	6	0\	0\	NUM
bracis-28360	237	7	)	)	PUNCT
bracis-28360	237	8	and	and	CCONJ
bracis-28360	237	9	\(\delta	\(\delta	NOUN
bracis-28360	237	10	_	_	NOUN
bracis-28360	237	11	3\	3\	NUM
bracis-28360	237	12	)	)	PUNCT
bracis-28360	237	13	presented	present	VERB
bracis-28360	237	14	similar	similar	ADJ
bracis-28360	237	15	ams	am	NOUN
bracis-28360	237	16	,	,	PUNCT
bracis-28360	237	17	around	around	ADV
bracis-28360	237	18	79	79	NUM
bracis-28360	237	19	%	%	NOUN
bracis-28360	237	20	.	.	PUNCT
bracis-28360	238	1	on	on	ADP
bracis-28360	238	2	the	the	DET
bracis-28360	238	3	other	other	ADJ
bracis-28360	238	4	hand	hand	NOUN
bracis-28360	238	5	,	,	PUNCT
bracis-28360	238	6	the	the	DET
bracis-28360	238	7	remaining	remain	VERB
bracis-28360	238	8	cases	case	NOUN
bracis-28360	238	9	(	(	PUNCT
bracis-28360	238	10	\(\delta	\(\delta	NOUN
bracis-28360	238	11	_	_	NOUN
bracis-28360	238	12	1\	1\	NUM
bracis-28360	238	13	)	)	PUNCT
bracis-28360	238	14	and	and	CCONJ
bracis-28360	238	15	\(\delta	\(\delta	NOUN
bracis-28360	238	16	_	_	NOUN
bracis-28360	238	17	4\	4\	NOUN
bracis-28360	238	18	)	)	PUNCT
bracis-28360	238	19	)	)	PUNCT
bracis-28360	238	20	presented	present	VERB
bracis-28360	238	21	the	the	DET
bracis-28360	238	22	worst	bad	ADJ
bracis-28360	238	23	scenarios	scenario	NOUN
bracis-28360	238	24	in	in	ADP
bracis-28360	238	25	this	this	DET
bracis-28360	238	26	study	study	NOUN
bracis-28360	238	27	,	,	PUNCT
bracis-28360	238	28	with	with	ADP
bracis-28360	238	29	ams	am	NOUN
bracis-28360	238	30	around	around	ADP
bracis-28360	238	31	78	78	NUM
bracis-28360	238	32	%	%	NOUN
bracis-28360	238	33	.	.	PUNCT
bracis-28360	239	1	up	up	ADP
bracis-28360	239	2	to	to	ADP
bracis-28360	239	3	this	this	DET
bracis-28360	239	4	point	point	NOUN
bracis-28360	239	5	,	,	PUNCT
bracis-28360	239	6	the	the	DET
bracis-28360	239	7	superiority	superiority	NOUN
bracis-28360	239	8	of	of	ADP
bracis-28360	239	9	\(\delta	\(\delta	NOUN
bracis-28360	239	10	_	_	NOUN
bracis-28360	239	11	2\	2\	NUM
bracis-28360	239	12	)	)	PUNCT
bracis-28360	239	13	and	and	CCONJ
bracis-28360	239	14	\(\delta	\(\delta	NOUN
bracis-28360	239	15	_	_	NOUN
bracis-28360	239	16	5\	5\	X
bracis-28360	239	17	)	)	PUNCT
bracis-28360	239	18	among	among	ADP
bracis-28360	239	19	the	the	DET
bracis-28360	239	20	rdfs	rdfs	NOUN
bracis-28360	239	21	can	can	AUX
bracis-28360	239	22	be	be	AUX
bracis-28360	239	23	perceived	perceive	VERB
bracis-28360	239	24	.	.	PUNCT
bracis-28360	240	1	however	however	ADV
bracis-28360	240	2	,	,	PUNCT
bracis-28360	240	3	to	to	PART
bracis-28360	240	4	complete	complete	VERB
bracis-28360	240	5	the	the	DET
bracis-28360	240	6	analysis	analysis	NOUN
bracis-28360	240	7	we	we	PRON
bracis-28360	240	8	have	have	AUX
bracis-28360	240	9	conducted	conduct	VERB
bracis-28360	240	10	a	a	DET
bracis-28360	240	11	set	set	NOUN
bracis-28360	240	12	of	of	ADP
bracis-28360	240	13	statistical	statistical	ADJ
bracis-28360	240	14	tests	test	NOUN
bracis-28360	240	15	to	to	PART
bracis-28360	240	16	reinforce	reinforce	VERB
bracis-28360	240	17	this	this	DET
bracis-28360	240	18	conclusion	conclusion	NOUN
bracis-28360	240	19	.	.	PUNCT
bracis-28360	241	1	considering	consider	VERB
bracis-28360	241	2	that	that	SCONJ
bracis-28360	241	3	the	the	DET
bracis-28360	241	4	conditions	condition	NOUN
bracis-28360	241	5	necessary	necessary	ADJ
bracis-28360	241	6	to	to	PART
bracis-28360	241	7	perform	perform	VERB
bracis-28360	241	8	parametric	parametric	ADJ
bracis-28360	241	9	tests	test	NOUN
bracis-28360	241	10	are	be	AUX
bracis-28360	241	11	not	not	PART
bracis-28360	241	12	fulfilled	fulfil	VERB
bracis-28360	241	13	,	,	PUNCT
bracis-28360	241	14	we	we	PRON
bracis-28360	241	15	considered	consider	VERB
bracis-28360	241	16	non	non	ADJ
bracis-28360	241	17	-	-	ADJ
bracis-28360	241	18	parametric	parametric	ADJ
bracis-28360	241	19	statistical	statistical	ADJ
bracis-28360	241	20	tests	test	NOUN
bracis-28360	241	21	.	.	PUNCT
bracis-28360	242	1	hence	hence	ADV
bracis-28360	242	2	,	,	PUNCT
bracis-28360	242	3	the	the	DET
bracis-28360	242	4	analysis	analysis	NOUN
bracis-28360	242	5	was	be	AUX
bracis-28360	242	6	made	make	VERB
bracis-28360	242	7	by	by	ADP
bracis-28360	242	8	a	a	DET
bracis-28360	242	9	group	group	NOUN
bracis-28360	242	10	comparison	comparison	NOUN
bracis-28360	242	11	using	use	VERB
bracis-28360	242	12	the	the	DET
bracis-28360	242	13	align	align	ADJ
bracis-28360	242	14	-	-	PUNCT
bracis-28360	242	15	friedman	friedman	NOUN
bracis-28360	242	16	rank	rank	PROPN
bracis-28360	242	17	test	test	NOUN
bracis-28360	242	18	 	 	SPACE
bracis-28360	243	1	[	[	X
bracis-28360	243	2	14	14	NUM
bracis-28360	243	3	]	]	PUNCT
bracis-28360	243	4	,	,	PUNCT
bracis-28360	243	5	and	and	CCONJ
bracis-28360	243	6	the	the	DET
bracis-28360	243	7	results	result	NOUN
bracis-28360	243	8	were	be	AUX
bracis-28360	243	9	analyzed	analyze	VERB
bracis-28360	243	10	in	in	ADP
bracis-28360	243	11	terms	term	NOUN
bracis-28360	243	12	of	of	ADP
bracis-28360	243	13	the	the	DET
bracis-28360	243	14	adjusted	adjust	VERB
bracis-28360	243	15	p	p	NOUN
bracis-28360	243	16	-	-	PUNCT
bracis-28360	243	17	value	value	NOUN
bracis-28360	243	18	(	(	PUNCT
bracis-28360	243	19	apv	apv	PROPN
bracis-28360	243	20	)	)	PUNCT
bracis-28360	243	21	computed	compute	VERB
bracis-28360	243	22	by	by	ADP
bracis-28360	243	23	holm	holm	PROPN
bracis-28360	243	24	’s	’s	PART
bracis-28360	243	25	post	post	X
bracis-28360	243	26	hoc	hoc	X
bracis-28360	243	27	test	test	NOUN
bracis-28360	243	28	 	 	SPACE
bracis-28360	244	1	[	[	X
bracis-28360	244	2	15	15	NUM
bracis-28360	244	3	]	]	PUNCT
bracis-28360	244	4	.	.	PUNCT
bracis-28360	245	1	the	the	DET
bracis-28360	245	2	analysis	analysis	NOUN
bracis-28360	245	3	was	be	AUX
bracis-28360	245	4	done	do	VERB
bracis-28360	245	5	by	by	ADP
bracis-28360	245	6	performing	perform	VERB
bracis-28360	245	7	a	a	DET
bracis-28360	245	8	statistical	statistical	ADJ
bracis-28360	245	9	test	test	NOUN
bracis-28360	245	10	per	per	ADP
bracis-28360	245	11	rdf	rdf	NOUN
bracis-28360	245	12	,	,	PUNCT
bracis-28360	245	13	with	with	ADP
bracis-28360	245	14	a	a	DET
bracis-28360	245	15	local	local	ADJ
bracis-28360	245	16	statistical	statistical	ADJ
bracis-28360	245	17	analysis	analysis	NOUN
bracis-28360	245	18	among	among	ADP
bracis-28360	245	19	the	the	DET
bracis-28360	245	20	different	different	ADJ
bracis-28360	245	21	functions	function	NOUN
bracis-28360	245	22	.	.	PUNCT
bracis-28360	246	1	after	after	ADP
bracis-28360	246	2	that	that	PRON
bracis-28360	246	3	,	,	PUNCT
bracis-28360	246	4	we	we	PRON
bracis-28360	246	5	chose	choose	VERB
bracis-28360	246	6	the	the	DET
bracis-28360	246	7	control	control	NOUN
bracis-28360	246	8	variables	variable	NOUN
bracis-28360	246	9	of	of	ADP
bracis-28360	246	10	each	each	DET
bracis-28360	246	11	group	group	NOUN
bracis-28360	246	12	,	,	PUNCT
bracis-28360	246	13	the	the	DET
bracis-28360	246	14	ones	one	NOUN
bracis-28360	246	15	having	have	VERB
bracis-28360	246	16	the	the	DET
bracis-28360	246	17	lowest	low	ADJ
bracis-28360	246	18	obtained	obtain	VERB
bracis-28360	246	19	rank	rank	NOUN
bracis-28360	246	20	,	,	PUNCT
bracis-28360	246	21	and	and	CCONJ
bracis-28360	246	22	once	once	ADV
bracis-28360	246	23	again	again	ADV
bracis-28360	246	24	we	we	PRON
bracis-28360	246	25	statistically	statistically	ADV
bracis-28360	246	26	compared	compare	VERB
bracis-28360	246	27	them	they	PRON
bracis-28360	246	28	.	.	PUNCT
bracis-28360	247	1	this	this	DET
bracis-28360	247	2	approach	approach	NOUN
bracis-28360	247	3	allowed	allow	VERB
bracis-28360	247	4	us	we	PRON
bracis-28360	247	5	to	to	PART
bracis-28360	247	6	point	point	VERB
bracis-28360	247	7	out	out	ADP
bracis-28360	247	8	the	the	DET
bracis-28360	247	9	best	good	ADJ
bracis-28360	247	10	d	d	ADJ
bracis-28360	247	11	-	-	PUNCT
bracis-28360	247	12	cc	cc	VERB
bracis-28360	247	13	integral	integral	ADJ
bracis-28360	247	14	,	,	PUNCT
bracis-28360	247	15	used	use	VERB
bracis-28360	247	16	to	to	PART
bracis-28360	247	17	compare	compare	VERB
bracis-28360	247	18	against	against	ADP
bracis-28360	247	19	other	other	ADJ
bracis-28360	247	20	aggregation	aggregation	NOUN
bracis-28360	247	21	operators	operator	NOUN
bracis-28360	247	22	.	.	PUNCT
bracis-28360	248	1	the	the	DET
bracis-28360	248	2	results	result	NOUN
bracis-28360	248	3	,	,	PUNCT
bracis-28360	248	4	in	in	ADP
bracis-28360	248	5	table	table	NOUN
bracis-28360	248	6	 	 	SPACE
bracis-28360	248	7	6	6	NUM
bracis-28360	248	8	,	,	PUNCT
bracis-28360	248	9	sort	sort	VERB
bracis-28360	248	10	the	the	DET
bracis-28360	248	11	methods	method	NOUN
bracis-28360	248	12	by	by	ADP
bracis-28360	248	13	ranks	rank	NOUN
bracis-28360	248	14	per	per	ADP
bracis-28360	248	15	rdf	rdf	NOUN
bracis-28360	248	16	.	.	PUNCT
bracis-28360	249	1	the	the	DET
bracis-28360	249	2	last	last	ADJ
bracis-28360	249	3	column	column	NOUN
bracis-28360	249	4	shows	show	VERB
bracis-28360	249	5	a	a	DET
bracis-28360	249	6	comparison	comparison	NOUN
bracis-28360	249	7	among	among	ADP
bracis-28360	249	8	the	the	DET
bracis-28360	249	9	selected	select	VERB
bracis-28360	249	10	control	control	NOUN
bracis-28360	249	11	variables	variable	NOUN
bracis-28360	249	12	.	.	PUNCT
bracis-28360	250	1	if	if	SCONJ
bracis-28360	250	2	the	the	DET
bracis-28360	250	3	obtained	obtain	VERB
bracis-28360	250	4	apv	apv	PROPN
bracis-28360	250	5	is	be	AUX
bracis-28360	250	6	smaller	small	ADJ
bracis-28360	250	7	than	than	ADP
bracis-28360	250	8	0.1	0.1	NUM
bracis-28360	250	9	(	(	PUNCT
bracis-28360	250	10	10	10	NUM
bracis-28360	250	11	%	%	NOUN
bracis-28360	250	12	of	of	ADP
bracis-28360	250	13	significance	significance	NOUN
bracis-28360	250	14	level	level	NOUN
bracis-28360	250	15	)	)	PUNCT
bracis-28360	250	16	,	,	PUNCT
bracis-28360	250	17	it	it	PRON
bracis-28360	250	18	means	mean	VERB
bracis-28360	250	19	the	the	DET
bracis-28360	250	20	methods	method	NOUN
bracis-28360	250	21	are	be	AUX
bracis-28360	250	22	statistically	statistically	ADV
bracis-28360	250	23	different	different	ADJ
bracis-28360	250	24	and	and	CCONJ
bracis-28360	250	25	,	,	PUNCT
bracis-28360	250	26	so	so	ADV
bracis-28360	250	27	,	,	PUNCT
bracis-28360	250	28	we	we	PRON
bracis-28360	250	29	underline	underline	VERB
bracis-28360	250	30	them	they	PRON
bracis-28360	250	31	.	.	PUNCT
bracis-28360	251	1	among	among	ADP
bracis-28360	251	2	the	the	DET
bracis-28360	251	3	groups	group	NOUN
bracis-28360	251	4	of	of	ADP
bracis-28360	251	5	rdfs	rdfs	PROPN
bracis-28360	251	6	,	,	PUNCT
bracis-28360	251	7	in	in	ADP
bracis-28360	251	8	general	general	ADJ
bracis-28360	251	9	,	,	PUNCT
bracis-28360	251	10	the	the	DET
bracis-28360	251	11	number	number	NOUN
bracis-28360	251	12	of	of	ADP
bracis-28360	251	13	statistical	statistical	ADJ
bracis-28360	251	14	differences	difference	NOUN
bracis-28360	251	15	are	be	AUX
bracis-28360	251	16	low	low	ADJ
bracis-28360	251	17	.	.	PUNCT
bracis-28360	252	1	the	the	DET
bracis-28360	252	2	test	test	NOUN
bracis-28360	252	3	rejected	reject	VERB
bracis-28360	252	4	the	the	DET
bracis-28360	252	5	null	null	ADJ
bracis-28360	252	6	hypothesis	hypothesis	NOUN
bracis-28360	252	7	when	when	SCONJ
bracis-28360	252	8	comparing	compare	VERB
bracis-28360	252	9	the	the	DET
bracis-28360	252	10	control	control	NOUN
bracis-28360	252	11	variable	variable	NOUN
bracis-28360	252	12	against	against	ADP
bracis-28360	252	13	three	three	NUM
bracis-28360	252	14	different	different	ADJ
bracis-28360	252	15	approaches	approach	NOUN
bracis-28360	252	16	for	for	ADP
bracis-28360	252	17	\(\delta	\(\delta	NOUN
bracis-28360	252	18	_	_	PROPN
bracis-28360	252	19	4\	4\	PROPN
bracis-28360	252	20	)	)	PUNCT
bracis-28360	252	21	,	,	PUNCT
bracis-28360	252	22	two	two	NUM
bracis-28360	252	23	for	for	ADP
bracis-28360	252	24	\(\delta	\(\delta	NOUN
bracis-28360	252	25	_	_	PUNCT
bracis-28360	252	26	0\	0\	NUM
bracis-28360	252	27	)	)	PUNCT
bracis-28360	252	28	and	and	CCONJ
bracis-28360	252	29	\(\delta	\(\delta	NOUN
bracis-28360	252	30	_	_	NOUN
bracis-28360	252	31	2\	2\	X
bracis-28360	252	32	)	)	PUNCT
bracis-28360	252	33	,	,	PUNCT
bracis-28360	252	34	one	one	NUM
bracis-28360	252	35	for	for	ADP
bracis-28360	252	36	\(\delta	\(\delta	NOUN
bracis-28360	252	37	_	_	NOUN
bracis-28360	252	38	5\	5\	NOUN
bracis-28360	252	39	)	)	PUNCT
bracis-28360	252	40	and	and	CCONJ
bracis-28360	252	41	none	none	NOUN
bracis-28360	252	42	for	for	ADP
bracis-28360	252	43	\(\delta	\(\delta	NOUN
bracis-28360	252	44	_	_	NOUN
bracis-28360	252	45	1\	1\	NUM
bracis-28360	252	46	)	)	PUNCT
bracis-28360	252	47	and	and	CCONJ
bracis-28360	252	48	\(\delta	\(\delta	NOUN
bracis-28360	252	49	_	_	NOUN
bracis-28360	252	50	2\	2\	NUM
bracis-28360	252	51	)	)	PUNCT
bracis-28360	252	52	.	.	PUNCT
bracis-28360	253	1	table	table	NOUN
bracis-28360	253	2	6	6	NUM
bracis-28360	253	3	.	.	PUNCT
bracis-28360	254	1	align	align	PROPN
bracis-28360	254	2	friedman	friedman	PROPN
bracis-28360	254	3	rank	rank	PROPN
bracis-28360	254	4	test	test	PROPN
bracis-28360	254	5	and	and	CCONJ
bracis-28360	254	6	holm	holm	PROPN
bracis-28360	254	7	’s	’s	PART
bracis-28360	254	8	post	post	X
bracis-28360	254	9	hoc	hoc	X
bracis-28360	254	10	test	test	NOUN
bracis-28360	254	11	for	for	ADP
bracis-28360	254	12	the	the	DET
bracis-28360	254	13	d	d	PROPN
bracis-28360	254	14	-	-	PUNCT
bracis-28360	254	15	cc	cc	ADP
bracis-28360	254	16	integrals.full	integrals.full	NOUN
bracis-28360	254	17	size	size	NOUN
bracis-28360	254	18	table	table	NOUN
bracis-28360	254	19	the	the	DET
bracis-28360	254	20	last	last	ADJ
bracis-28360	254	21	column	column	NOUN
bracis-28360	254	22	performs	perform	VERB
bracis-28360	254	23	a	a	DET
bracis-28360	254	24	group	group	NOUN
bracis-28360	254	25	comparison	comparison	NOUN
bracis-28360	254	26	among	among	ADP
bracis-28360	254	27	the	the	DET
bracis-28360	254	28	control	control	NOUN
bracis-28360	254	29	variables	variable	NOUN
bracis-28360	254	30	of	of	ADP
bracis-28360	254	31	each	each	DET
bracis-28360	254	32	family	family	NOUN
bracis-28360	254	33	based	base	VERB
bracis-28360	254	34	on	on	ADP
bracis-28360	254	35	an	an	DET
bracis-28360	254	36	rdf	rdf	NOUN
bracis-28360	254	37	.	.	PUNCT
bracis-28360	255	1	see	see	VERB
bracis-28360	255	2	that	that	SCONJ
bracis-28360	255	3	the	the	DET
bracis-28360	255	4	d	d	NOUN
bracis-28360	255	5	-	-	PUNCT
bracis-28360	255	6	cc	cc	ADV
bracis-28360	255	7	integral	integral	ADJ
bracis-28360	255	8	with	with	ADP
bracis-28360	255	9	\(\delta	\(\delta	NOUN
bracis-28360	255	10	_	_	NOUN
bracis-28360	255	11	5\	5\	NOUN
bracis-28360	255	12	)	)	PUNCT
bracis-28360	255	13	and	and	CCONJ
bracis-28360	255	14	\(o_{mm}\	\(o_{mm}\	ADJ
bracis-28360	255	15	)	)	PUNCT
bracis-28360	255	16	,	,	PUNCT
bracis-28360	255	17	when	when	SCONJ
bracis-28360	255	18	compared	compare	VERB
bracis-28360	255	19	against	against	ADP
bracis-28360	255	20	almost	almost	ADV
bracis-28360	255	21	all	all	PRON
bracis-28360	255	22	approaches	approach	NOUN
bracis-28360	255	23	,	,	PUNCT
bracis-28360	255	24	is	be	AUX
bracis-28360	255	25	statically	statically	ADV
bracis-28360	255	26	superior	superior	ADJ
bracis-28360	255	27	.	.	PUNCT
bracis-28360	256	1	but	but	CCONJ
bracis-28360	256	2	this	this	PRON
bracis-28360	256	3	does	do	AUX
bracis-28360	256	4	not	not	PART
bracis-28360	256	5	hold	hold	VERB
bracis-28360	256	6	when	when	SCONJ
bracis-28360	256	7	\(\delta	\(\delta	NOUN
bracis-28360	256	8	_	_	NOUN
bracis-28360	256	9	2\	2\	NUM
bracis-28360	256	10	)	)	PUNCT
bracis-28360	256	11	and	and	CCONJ
bracis-28360	256	12	\(o_{\alpha	\(o_{\alpha	ADP
bracis-28360	256	13	}	}	PUNCT
bracis-28360	256	14	\	\	NOUN
bracis-28360	256	15	)	)	PUNCT
bracis-28360	256	16	are	be	AUX
bracis-28360	256	17	considered	consider	VERB
bracis-28360	256	18	.	.	PUNCT
bracis-28360	257	1	finally	finally	ADV
bracis-28360	257	2	,	,	PUNCT
bracis-28360	257	3	\(\delta	\(\delta	NOUN
bracis-28360	257	4	_	_	NOUN
bracis-28360	257	5	5	5	NUM
bracis-28360	257	6	-	-	SYM
bracis-28360	257	7	o_{mm}\	o_{mm}\	ADV
bracis-28360	257	8	)	)	PUNCT
bracis-28360	257	9	provides	provide	VERB
bracis-28360	257	10	the	the	DET
bracis-28360	257	11	winning	win	VERB
bracis-28360	257	12	combination	combination	NOUN
bracis-28360	257	13	in	in	ADP
bracis-28360	257	14	this	this	DET
bracis-28360	257	15	first	first	ADJ
bracis-28360	257	16	analysis	analysis	NOUN
bracis-28360	257	17	and	and	CCONJ
bracis-28360	257	18	so	so	ADV
bracis-28360	257	19	,	,	PUNCT
bracis-28360	257	20	it	it	PRON
bracis-28360	257	21	is	be	AUX
bracis-28360	257	22	the	the	DET
bracis-28360	257	23	representing	represent	VERB
bracis-28360	257	24	method	method	NOUN
bracis-28360	257	25	of	of	ADP
bracis-28360	257	26	the	the	DET
bracis-28360	257	27	class	class	NOUN
bracis-28360	257	28	of	of	ADP
bracis-28360	257	29	d	d	PROPN
bracis-28360	257	30	-	-	PUNCT
bracis-28360	257	31	cc	cc	NOUN
bracis-28360	257	32	integrals	integral	NOUN
bracis-28360	257	33	.	.	PUNCT
bracis-28360	258	1	5.2	5.2	NUM
bracis-28360	258	2	comparing	compare	VERB
bracis-28360	258	3	the	the	DET
bracis-28360	258	4	best	good	ADJ
bracis-28360	258	5	d	d	NOUN
bracis-28360	258	6	-	-	PUNCT
bracis-28360	258	7	cc	cc	VERB
bracis-28360	258	8	integral	integral	ADJ
bracis-28360	258	9	against	against	ADP
bracis-28360	258	10	classical	classical	ADJ
bracis-28360	258	11	operators	operator	NOUN
bracis-28360	258	12	this	this	DET
bracis-28360	258	13	subsection	subsection	NOUN
bracis-28360	258	14	states	state	VERB
bracis-28360	258	15	the	the	DET
bracis-28360	258	16	position	position	NOUN
bracis-28360	258	17	of	of	ADP
bracis-28360	258	18	the	the	DET
bracis-28360	258	19	d	d	PROPN
bracis-28360	258	20	-	-	PUNCT
bracis-28360	258	21	cc	cc	ADP
bracis-28360	258	22	integrals	integral	NOUN
bracis-28360	258	23	among	among	ADP
bracis-28360	258	24	the	the	DET
bracis-28360	258	25	generalizations	generalization	NOUN
bracis-28360	258	26	of	of	ADP
bracis-28360	258	27	the	the	DET
bracis-28360	258	28	ci	ci	PROPN
bracis-28360	258	29	as	as	ADV
bracis-28360	258	30	well	well	ADV
bracis-28360	258	31	as	as	ADP
bracis-28360	258	32	known	know	VERB
bracis-28360	258	33	frms	frm	NOUN
bracis-28360	258	34	found	find	VERB
bracis-28360	258	35	in	in	ADP
bracis-28360	258	36	the	the	DET
bracis-28360	258	37	literature	literature	NOUN
bracis-28360	258	38	.	.	PUNCT
bracis-28360	259	1	we	we	PRON
bracis-28360	259	2	have	have	AUX
bracis-28360	259	3	selected	select	VERB
bracis-28360	259	4	averaging	averaging	NOUN
bracis-28360	259	5	and	and	CCONJ
bracis-28360	259	6	non	non	ADJ
bracis-28360	259	7	-	-	ADJ
bracis-28360	259	8	averaging	average	VERB
bracis-28360	259	9	operators	operator	NOUN
bracis-28360	259	10	:	:	PUNCT
bracis-28360	259	11	averaging	average	VERB
bracis-28360	259	12	operators	operator	NOUN
bracis-28360	259	13	:	:	PUNCT
bracis-28360	260	1	[	[	X
bracis-28360	260	2	wr	wr	X
bracis-28360	260	3	]	]	X
bracis-28360	260	4	(	(	PUNCT
bracis-28360	260	5	winning	win	VERB
bracis-28360	260	6	rule	rule	NOUN
bracis-28360	260	7	 	 	SPACE
bracis-28360	260	8	[	[	X
bracis-28360	260	9	11	11	NUM
bracis-28360	260	10	]	]	PUNCT
bracis-28360	260	11	,	,	PUNCT
bracis-28360	260	12	based	base	VERB
bracis-28360	260	13	on	on	ADP
bracis-28360	260	14	the	the	DET
bracis-28360	260	15	maximum	maximum	NOUN
bracis-28360	260	16	as	as	ADP
bracis-28360	260	17	aggregation	aggregation	NOUN
bracis-28360	260	18	function	function	NOUN
bracis-28360	260	19	)	)	PUNCT
bracis-28360	260	20	,	,	PUNCT
bracis-28360	260	21	[	[	X
bracis-28360	260	22	cho	cho	X
bracis-28360	260	23	]	]	X
bracis-28360	260	24	(	(	PUNCT
bracis-28360	260	25	ci	ci	NOUN
bracis-28360	260	26	)	)	PUNCT
bracis-28360	260	27	,	,	PUNCT
bracis-28360	261	1	[	[	X
bracis-28360	261	2	cc	cc	X
bracis-28360	261	3	]	]	X
bracis-28360	261	4	(	(	PUNCT
bracis-28360	261	5	the	the	DET
bracis-28360	261	6	best	good	ADJ
bracis-28360	261	7	cc	cc	NOUN
bracis-28360	261	8	-	-	ADJ
bracis-28360	261	9	integral	integral	ADJ
bracis-28360	261	10	 	 	SPACE
bracis-28360	261	11	[	[	X
bracis-28360	261	12	22	22	NUM
bracis-28360	261	13	]	]	PUNCT
bracis-28360	261	14	)	)	PUNCT
bracis-28360	261	15	,	,	PUNCT
bracis-28360	262	1	[	[	X
bracis-28360	262	2	\(c_t\	\(c_t\	NOUN
bracis-28360	262	3	)	)	PUNCT
bracis-28360	262	4	]	]	PUNCT
bracis-28360	262	5	(	(	PUNCT
bracis-28360	262	6	the	the	DET
bracis-28360	262	7	best	good	ADJ
bracis-28360	262	8	\(c_t\)-integral	\(c_t\)-integral	ADJ
bracis-28360	262	9	,	,	PUNCT
bracis-28360	262	10	a	a	DET
bracis-28360	262	11	ci	ci	NOUN
bracis-28360	262	12	generalization	generalization	NOUN
bracis-28360	262	13	by	by	ADP
bracis-28360	262	14	t	t	PROPN
bracis-28360	262	15	-	-	PUNCT
bracis-28360	262	16	norms	norm	NOUN
bracis-28360	262	17	 	 	SPACE
bracis-28360	262	18	[	[	X
bracis-28360	262	19	20	20	NUM
bracis-28360	262	20	]	]	NUM
bracis-28360	262	21	)	)	PUNCT
bracis-28360	262	22	,	,	PUNCT
bracis-28360	263	1	[	[	X
bracis-28360	263	2	\(c^f_{avg}\	\(c^f_{avg}\	NOUN
bracis-28360	263	3	)	)	PUNCT
bracis-28360	263	4	]	]	PUNCT
bracis-28360	263	5	(	(	PUNCT
bracis-28360	263	6	the	the	DET
bracis-28360	263	7	best	well	ADV
bracis-28360	263	8	averaging	average	VERB
bracis-28360	263	9	\(c_f\)-integral	\(c_f\)-integral	ADJ
bracis-28360	263	10	 	 	SPACE
bracis-28360	264	1	[	[	X
bracis-28360	264	2	23	23	NUM
bracis-28360	264	3	]	]	PUNCT
bracis-28360	264	4	)	)	PUNCT
bracis-28360	264	5	,	,	PUNCT
bracis-28360	265	1	[	[	X
bracis-28360	265	2	d	d	X
bracis-28360	265	3	-	-	PUNCT
bracis-28360	265	4	cf	cf	NOUN
bracis-28360	265	5	]	]	X
bracis-28360	265	6	(	(	PUNCT
bracis-28360	265	7	the	the	DET
bracis-28360	265	8	best	good	ADJ
bracis-28360	265	9	averaging	average	VERB
bracis-28360	265	10	d	d	NOUN
bracis-28360	265	11	-	-	PUNCT
bracis-28360	265	12	cf	cf	ADJ
bracis-28360	265	13	integral	integral	ADJ
bracis-28360	265	14	 	 	SPACE
bracis-28360	265	15	[	[	X
bracis-28360	265	16	28	28	NUM
bracis-28360	265	17	]	]	NUM
bracis-28360	265	18	)	)	PUNCT
bracis-28360	265	19	.	.	PUNCT
bracis-28360	266	1	non	non	ADJ
bracis-28360	266	2	-	-	ADJ
bracis-28360	266	3	averaging	average	VERB
bracis-28360	266	4	functions	function	NOUN
bracis-28360	266	5	:	:	PUNCT
bracis-28360	267	1	[	[	X
bracis-28360	267	2	ac	ac	X
bracis-28360	267	3	]	]	X
bracis-28360	267	4	(	(	PUNCT
bracis-28360	267	5	the	the	DET
bracis-28360	267	6	additive	additive	ADJ
bracis-28360	267	7	combination	combination	NOUN
bracis-28360	267	8	 	 	SPACE
bracis-28360	267	9	[	[	X
bracis-28360	267	10	12	12	NUM
bracis-28360	267	11	]	]	PUNCT
bracis-28360	267	12	,	,	PUNCT
bracis-28360	267	13	based	base	VERB
bracis-28360	267	14	on	on	ADP
bracis-28360	267	15	the	the	DET
bracis-28360	267	16	normalized	normalized	ADJ
bracis-28360	267	17	sum	sum	NOUN
bracis-28360	267	18	,	,	PUNCT
bracis-28360	267	19	farc	farc	NOUN
bracis-28360	267	20	-	-	PUNCT
bracis-28360	267	21	hd	hd	NOUN
bracis-28360	267	22	algorithm	algorithm	NOUN
bracis-28360	267	23	basis	basis	NOUN
bracis-28360	267	24	)	)	PUNCT
bracis-28360	267	25	,	,	PUNCT
bracis-28360	267	26	[	[	X
bracis-28360	267	27	ps	ps	X
bracis-28360	267	28	]	]	X
bracis-28360	267	29	(	(	PUNCT
bracis-28360	267	30	the	the	DET
bracis-28360	267	31	probabilistic	probabilistic	ADJ
bracis-28360	267	32	sum	sum	NOUN
bracis-28360	267	33	 	 	SPACE
bracis-28360	268	1	[	[	X
bracis-28360	268	2	12	12	NUM
bracis-28360	268	3	]	]	NUM
bracis-28360	268	4	)	)	PUNCT
bracis-28360	268	5	,	,	PUNCT
bracis-28360	269	1	[	[	X
bracis-28360	269	2	\(c_{f1f2}\	\(c_{f1f2}\	NOUN
bracis-28360	269	3	)	)	PUNCT
bracis-28360	269	4	]	]	PUNCT
bracis-28360	269	5	(	(	PUNCT
bracis-28360	269	6	the	the	DET
bracis-28360	269	7	\(c_{f1f2}\)-integral	\(c_{f1f2}\)-integral	PROPN
bracis-28360	269	8	 	 	SPACE
bracis-28360	270	1	[	[	X
bracis-28360	270	2	19	19	NUM
bracis-28360	270	3	]	]	PUNCT
bracis-28360	270	4	,	,	PUNCT
bracis-28360	270	5	being	be	AUX
bracis-28360	270	6	the	the	DET
bracis-28360	270	7	state	state	NOUN
bracis-28360	270	8	-	-	PUNCT
bracis-28360	270	9	of	of	ADP
bracis-28360	270	10	-	-	PUNCT
bracis-28360	270	11	the	the	DET
bracis-28360	270	12	-	-	PUNCT
bracis-28360	270	13	art	art	NOUN
bracis-28360	270	14	)	)	PUNCT
bracis-28360	270	15	,	,	PUNCT
bracis-28360	271	1	[	[	X
bracis-28360	271	2	\(c^f_{n	\(c^f_{n	PROPN
bracis-28360	271	3	-	-	PUNCT
bracis-28360	271	4	avg}\	avg}\	NOUN
bracis-28360	271	5	)	)	PUNCT
bracis-28360	271	6	]	]	X
bracis-28360	271	7	(	(	PUNCT
bracis-28360	271	8	the	the	DET
bracis-28360	271	9	best	good	ADJ
bracis-28360	271	10	on	on	ADP
bracis-28360	271	11	-	-	PUNCT
bracis-28360	271	12	averaging	average	VERB
bracis-28360	271	13	\(c_f\)-integral	\(c_f\)-integral	ADJ
bracis-28360	271	14	 	 	SPACE
bracis-28360	272	1	[	[	X
bracis-28360	272	2	23	23	NUM
bracis-28360	272	3	]	]	PUNCT
bracis-28360	272	4	)	)	PUNCT
bracis-28360	272	5	.	.	PUNCT
bracis-28360	273	1	the	the	DET
bracis-28360	273	2	obtained	obtain	VERB
bracis-28360	273	3	results	result	NOUN
bracis-28360	273	4	are	be	AUX
bracis-28360	273	5	in	in	ADP
bracis-28360	273	6	table	table	NOUN
bracis-28360	273	7	 	 	SPACE
bracis-28360	273	8	7	7	NUM
bracis-28360	273	9	,	,	PUNCT
bracis-28360	273	10	detailed	detail	VERB
bracis-28360	273	11	per	per	ADP
bracis-28360	273	12	dataset	dataset	NOUN
bracis-28360	273	13	.	.	PUNCT
bracis-28360	274	1	we	we	PRON
bracis-28360	274	2	highlight	highlight	VERB
bracis-28360	274	3	in	in	ADP
bracis-28360	274	4	boldface	boldface	NOUN
bracis-28360	274	5	the	the	DET
bracis-28360	274	6	largest	large	ADJ
bracis-28360	274	7	obtained	obtain	VERB
bracis-28360	274	8	am	am	NOUN
bracis-28360	274	9	among	among	ADP
bracis-28360	274	10	all	all	DET
bracis-28360	274	11	results	result	NOUN
bracis-28360	274	12	.	.	PUNCT
bracis-28360	275	1	table	table	NOUN
bracis-28360	275	2	7	7	NUM
bracis-28360	275	3	.	.	PUNCT
bracis-28360	275	4	comparing	compare	VERB
bracis-28360	275	5	the	the	DET
bracis-28360	275	6	best	good	ADJ
bracis-28360	275	7	d	d	NOUN
bracis-28360	275	8	-	-	PUNCT
bracis-28360	275	9	cc	cc	VERB
bracis-28360	275	10	integral	integral	ADJ
bracis-28360	275	11	with	with	ADP
bracis-28360	275	12	other	other	ADJ
bracis-28360	275	13	operators	operator	NOUN
bracis-28360	275	14	in	in	ADP
bracis-28360	275	15	the	the	DET
bracis-28360	275	16	literature.full	literature.full	NOUN
bracis-28360	275	17	size	size	NOUN
bracis-28360	275	18	table	table	NOUN
bracis-28360	275	19	we	we	PRON
bracis-28360	275	20	observed	observe	VERB
bracis-28360	275	21	that	that	SCONJ
bracis-28360	275	22	the	the	DET
bracis-28360	275	23	\(c_{f1f2}\)-integral	\(c_{f1f2}\)-integral	PROPN
bracis-28360	275	24	is	be	AUX
bracis-28360	275	25	the	the	DET
bracis-28360	275	26	approach	approach	NOUN
bracis-28360	275	27	having	have	VERB
bracis-28360	275	28	the	the	DET
bracis-28360	275	29	largest	large	ADJ
bracis-28360	275	30	am	am	NOUN
bracis-28360	275	31	in	in	ADP
bracis-28360	275	32	the	the	DET
bracis-28360	275	33	study	study	NOUN
bracis-28360	275	34	.	.	PUNCT
bracis-28360	276	1	however	however	ADV
bracis-28360	276	2	,	,	PUNCT
bracis-28360	276	3	the	the	DET
bracis-28360	276	4	d	d	NOUN
bracis-28360	276	5	-	-	PUNCT
bracis-28360	276	6	cc	cc	VERB
bracis-28360	276	7	integral	integral	ADJ
bracis-28360	276	8	(	(	PUNCT
bracis-28360	276	9	our	our	PRON
bracis-28360	276	10	new	new	ADJ
bracis-28360	276	11	approach	approach	NOUN
bracis-28360	276	12	)	)	PUNCT
bracis-28360	276	13	is	be	AUX
bracis-28360	276	14	the	the	DET
bracis-28360	276	15	second	second	ADJ
bracis-28360	276	16	one	one	NUM
bracis-28360	276	17	,	,	PUNCT
bracis-28360	276	18	followed	follow	VERB
bracis-28360	276	19	by	by	ADP
bracis-28360	276	20	the	the	DET
bracis-28360	276	21	\(c_f\	\(c_f\	PROPN
bracis-28360	276	22	)	)	PUNCT
bracis-28360	276	23	and	and	CCONJ
bracis-28360	276	24	the	the	DET
bracis-28360	276	25	d	d	ADJ
bracis-28360	276	26	-	-	PUNCT
bracis-28360	276	27	cf	cf	NOUN
bracis-28360	276	28	integrals	integral	NOUN
bracis-28360	276	29	.	.	PUNCT
bracis-28360	277	1	it	it	PRON
bracis-28360	277	2	is	be	AUX
bracis-28360	277	3	also	also	ADV
bracis-28360	277	4	noticeable	noticeable	ADJ
bracis-28360	277	5	that	that	SCONJ
bracis-28360	277	6	the	the	DET
bracis-28360	277	7	d	d	PROPN
bracis-28360	277	8	-	-	PUNCT
bracis-28360	277	9	cc	cc	VERB
bracis-28360	277	10	integral	integral	ADJ
bracis-28360	277	11	achieves	achieve	VERB
bracis-28360	277	12	a	a	DET
bracis-28360	277	13	superior	superior	ADJ
bracis-28360	277	14	mean	mean	NOUN
bracis-28360	277	15	than	than	ADP
bracis-28360	277	16	the	the	DET
bracis-28360	277	17	classical	classical	ADJ
bracis-28360	277	18	frms	frm	NOUN
bracis-28360	277	19	of	of	ADP
bracis-28360	277	20	ac	ac	PROPN
bracis-28360	277	21	and	and	CCONJ
bracis-28360	277	22	ps	ps	PROPN
bracis-28360	277	23	.	.	PUNCT
bracis-28360	278	1	considering	consider	VERB
bracis-28360	278	2	the	the	DET
bracis-28360	278	3	methods	method	NOUN
bracis-28360	278	4	that	that	PRON
bracis-28360	278	5	present	present	ADJ
bracis-28360	278	6	averaging	average	VERB
bracis-28360	278	7	characteristics	characteristic	NOUN
bracis-28360	278	8	and	and	CCONJ
bracis-28360	278	9	their	their	PRON
bracis-28360	278	10	obtained	obtain	VERB
bracis-28360	278	11	am	am	NOUN
bracis-28360	278	12	,	,	PUNCT
bracis-28360	278	13	it	it	PRON
bracis-28360	278	14	is	be	AUX
bracis-28360	278	15	easy	easy	ADJ
bracis-28360	278	16	to	to	PART
bracis-28360	278	17	see	see	VERB
bracis-28360	278	18	that	that	SCONJ
bracis-28360	278	19	their	their	PRON
bracis-28360	278	20	performance	performance	NOUN
bracis-28360	278	21	is	be	AUX
bracis-28360	278	22	,	,	PUNCT
bracis-28360	278	23	in	in	ADP
bracis-28360	278	24	general	general	ADJ
bracis-28360	278	25	,	,	PUNCT
bracis-28360	278	26	inferior	inferior	ADJ
bracis-28360	278	27	to	to	ADP
bracis-28360	278	28	the	the	DET
bracis-28360	278	29	non	non	ADJ
bracis-28360	278	30	-	-	ADJ
bracis-28360	278	31	averaging	averaging	ADJ
bracis-28360	278	32	ones	one	NOUN
bracis-28360	278	33	.	.	PUNCT
bracis-28360	279	1	the	the	DET
bracis-28360	279	2	accuracy	accuracy	NOUN
bracis-28360	279	3	in	in	ADP
bracis-28360	279	4	these	these	DET
bracis-28360	279	5	cases	case	NOUN
bracis-28360	279	6	is	be	AUX
bracis-28360	279	7	around	around	ADV
bracis-28360	279	8	79	79	NUM
bracis-28360	279	9	%	%	NOUN
bracis-28360	279	10	which	which	PRON
bracis-28360	279	11	is	be	AUX
bracis-28360	279	12	inferior	inferior	ADJ
bracis-28360	279	13	to	to	ADP
bracis-28360	279	14	the	the	DET
bracis-28360	279	15	best	good	ADJ
bracis-28360	279	16	d	d	ADJ
bracis-28360	279	17	-	-	PUNCT
bracis-28360	279	18	cc	cc	VERB
bracis-28360	279	19	integral	integral	ADJ
bracis-28360	279	20	,	,	PUNCT
bracis-28360	279	21	with	with	ADP
bracis-28360	279	22	the	the	DET
bracis-28360	279	23	exception	exception	NOUN
bracis-28360	279	24	of	of	ADP
bracis-28360	279	25	the	the	DET
bracis-28360	279	26	d	d	NOUN
bracis-28360	279	27	-	-	PUNCT
bracis-28360	279	28	cf	cf	NOUN
bracis-28360	279	29	integral	integral	ADJ
bracis-28360	279	30	.	.	PUNCT
bracis-28360	280	1	once	once	ADV
bracis-28360	280	2	again	again	ADV
bracis-28360	280	3	,	,	PUNCT
bracis-28360	280	4	we	we	PRON
bracis-28360	280	5	performed	perform	VERB
bracis-28360	280	6	a	a	DET
bracis-28360	280	7	set	set	NOUN
bracis-28360	280	8	of	of	ADP
bracis-28360	280	9	analyses	analysis	NOUN
bracis-28360	280	10	to	to	PART
bracis-28360	280	11	statistically	statistically	ADV
bracis-28360	280	12	compare	compare	VERB
bracis-28360	280	13	the	the	DET
bracis-28360	280	14	approaches	approach	NOUN
bracis-28360	280	15	.	.	PUNCT
bracis-28360	281	1	therefore	therefore	ADV
bracis-28360	281	2	,	,	PUNCT
bracis-28360	281	3	we	we	PRON
bracis-28360	281	4	have	have	AUX
bracis-28360	281	5	compared	compare	VERB
bracis-28360	281	6	the	the	DET
bracis-28360	281	7	best	good	ADJ
bracis-28360	281	8	d	d	NOUN
bracis-28360	281	9	-	-	PUNCT
bracis-28360	281	10	cc	cc	VERB
bracis-28360	281	11	integral	integral	ADJ
bracis-28360	281	12	(	(	PUNCT
bracis-28360	281	13	based	base	VERB
bracis-28360	281	14	on	on	ADP
bracis-28360	281	15	omm	omm	NOUN
bracis-28360	281	16	and	and	CCONJ
bracis-28360	281	17	\(\delta	\(\delta	NOUN
bracis-28360	281	18	_	_	PROPN
bracis-28360	281	19	5\	5\	NOUN
bracis-28360	281	20	)	)	PUNCT
bracis-28360	281	21	)	)	PUNCT
bracis-28360	281	22	against	against	ADP
bracis-28360	281	23	the	the	DET
bracis-28360	281	24	averaging	averaging	NOUN
bracis-28360	281	25	and	and	CCONJ
bracis-28360	281	26	non	non	ADJ
bracis-28360	281	27	-	-	ADJ
bracis-28360	281	28	averaging	average	VERB
bracis-28360	281	29	approaches	approach	NOUN
bracis-28360	281	30	.	.	PUNCT
bracis-28360	282	1	the	the	DET
bracis-28360	282	2	results	result	NOUN
bracis-28360	282	3	are	be	AUX
bracis-28360	282	4	presented	present	VERB
bracis-28360	282	5	in	in	ADP
bracis-28360	282	6	table	table	NOUN
bracis-28360	282	7	 	 	SPACE
bracis-28360	282	8	8	8	NUM
bracis-28360	282	9	,	,	PUNCT
bracis-28360	282	10	following	follow	VERB
bracis-28360	282	11	the	the	DET
bracis-28360	282	12	same	same	ADJ
bracis-28360	282	13	structure	structure	NOUN
bracis-28360	282	14	used	use	VERB
bracis-28360	282	15	in	in	ADP
bracis-28360	282	16	the	the	DET
bracis-28360	282	17	previous	previous	ADJ
bracis-28360	282	18	analysis	analysis	NOUN
bracis-28360	282	19	.	.	PUNCT
bracis-28360	283	1	table	table	NOUN
bracis-28360	283	2	8	8	NUM
bracis-28360	283	3	.	.	PUNCT
bracis-28360	284	1	statistical	statistical	ADJ
bracis-28360	284	2	analysis	analysis	NOUN
bracis-28360	284	3	comparing	compare	VERB
bracis-28360	284	4	the	the	DET
bracis-28360	284	5	d	d	NOUN
bracis-28360	284	6	-	-	PUNCT
bracis-28360	284	7	cc	cc	ADV
bracis-28360	284	8	integral	integral	ADJ
bracis-28360	284	9	against	against	ADP
bracis-28360	284	10	classical	classical	ADJ
bracis-28360	284	11	operators.full	operators.full	NUM
bracis-28360	284	12	size	size	NOUN
bracis-28360	284	13	table	table	NOUN
bracis-28360	284	14	regarding	regard	VERB
bracis-28360	284	15	the	the	DET
bracis-28360	284	16	results	result	NOUN
bracis-28360	284	17	obtained	obtain	VERB
bracis-28360	284	18	when	when	SCONJ
bracis-28360	284	19	comparing	compare	VERB
bracis-28360	284	20	the	the	DET
bracis-28360	284	21	d	d	NOUN
bracis-28360	284	22	-	-	PUNCT
bracis-28360	284	23	cc	cc	ADV
bracis-28360	284	24	integral	integral	ADJ
bracis-28360	284	25	against	against	ADP
bracis-28360	284	26	the	the	DET
bracis-28360	284	27	averaging	averaging	NOUN
bracis-28360	284	28	approaches	approach	NOUN
bracis-28360	284	29	,	,	PUNCT
bracis-28360	284	30	we	we	PRON
bracis-28360	284	31	see	see	VERB
bracis-28360	284	32	that	that	SCONJ
bracis-28360	284	33	it	it	PRON
bracis-28360	284	34	is	be	AUX
bracis-28360	284	35	statistically	statistically	ADV
bracis-28360	284	36	superior	superior	ADJ
bracis-28360	284	37	to	to	ADP
bracis-28360	284	38	all	all	DET
bracis-28360	284	39	other	other	ADJ
bracis-28360	284	40	approaches	approach	NOUN
bracis-28360	284	41	,	,	PUNCT
bracis-28360	284	42	with	with	ADP
bracis-28360	284	43	the	the	DET
bracis-28360	284	44	exception	exception	NOUN
bracis-28360	284	45	of	of	ADP
bracis-28360	284	46	the	the	PRON
bracis-28360	284	47	d	d	NOUN
bracis-28360	284	48	-	-	PUNCT
bracis-28360	284	49	cf	cf	NOUN
bracis-28360	284	50	integral	integral	ADJ
bracis-28360	284	51	,	,	PUNCT
bracis-28360	284	52	considered	consider	VERB
bracis-28360	284	53	equivalent	equivalent	ADJ
bracis-28360	284	54	.	.	PUNCT
bracis-28360	285	1	it	it	PRON
bracis-28360	285	2	is	be	AUX
bracis-28360	285	3	noteworthy	noteworthy	ADJ
bracis-28360	285	4	that	that	SCONJ
bracis-28360	285	5	the	the	DET
bracis-28360	285	6	cc	cc	NOUN
bracis-28360	285	7	-	-	ADJ
bracis-28360	285	8	integral	integral	ADJ
bracis-28360	285	9	is	be	AUX
bracis-28360	285	10	among	among	ADP
bracis-28360	285	11	the	the	DET
bracis-28360	285	12	surpassed	surpass	VERB
bracis-28360	285	13	methods	method	NOUN
bracis-28360	285	14	,	,	PUNCT
bracis-28360	285	15	pointing	point	VERB
bracis-28360	285	16	out	out	ADP
bracis-28360	285	17	that	that	SCONJ
bracis-28360	285	18	its	its	PRON
bracis-28360	285	19	generalization	generalization	NOUN
bracis-28360	285	20	by	by	ADP
bracis-28360	285	21	rfds	rfds	NOUN
bracis-28360	285	22	resulted	result	VERB
bracis-28360	285	23	in	in	ADP
bracis-28360	285	24	better	well	ADJ
bracis-28360	285	25	performances	performance	NOUN
bracis-28360	285	26	.	.	PUNCT
bracis-28360	286	1	if	if	SCONJ
bracis-28360	286	2	the	the	DET
bracis-28360	286	3	non	non	ADJ
bracis-28360	286	4	-	-	ADJ
bracis-28360	286	5	averaging	average	VERB
bracis-28360	286	6	approaches	approach	NOUN
bracis-28360	286	7	are	be	AUX
bracis-28360	286	8	considered	consider	VERB
bracis-28360	286	9	,	,	PUNCT
bracis-28360	286	10	it	it	PRON
bracis-28360	286	11	is	be	AUX
bracis-28360	286	12	noticeable	noticeable	ADJ
bracis-28360	286	13	that	that	SCONJ
bracis-28360	286	14	our	our	PRON
bracis-28360	286	15	new	new	ADJ
bracis-28360	286	16	method	method	NOUN
bracis-28360	286	17	is	be	AUX
bracis-28360	286	18	the	the	DET
bracis-28360	286	19	only	only	ADJ
bracis-28360	286	20	one	one	NUM
bracis-28360	286	21	that	that	PRON
bracis-28360	286	22	is	be	AUX
bracis-28360	286	23	able	able	ADJ
bracis-28360	286	24	to	to	PART
bracis-28360	286	25	be	be	AUX
bracis-28360	286	26	considered	consider	VERB
bracis-28360	286	27	statistically	statistically	ADV
bracis-28360	286	28	equivalent	equivalent	ADJ
bracis-28360	286	29	to	to	ADP
bracis-28360	286	30	the	the	DET
bracis-28360	286	31	state	state	NOUN
bracis-28360	286	32	-	-	PUNCT
bracis-28360	286	33	of	of	ADP
bracis-28360	286	34	-	-	PUNCT
bracis-28360	286	35	the	the	DET
bracis-28360	286	36	-	-	PUNCT
bracis-28360	286	37	art	art	NOUN
bracis-28360	286	38	.	.	PUNCT
bracis-28360	287	1	for	for	ADP
bracis-28360	287	2	all	all	DET
bracis-28360	287	3	the	the	DET
bracis-28360	287	4	other	other	ADJ
bracis-28360	287	5	cases	case	NOUN
bracis-28360	287	6	,	,	PUNCT
bracis-28360	287	7	the	the	DET
bracis-28360	287	8	\(c_{f1f2}\)-integral	\(c_{f1f2}\)-integral	PROPN
bracis-28360	287	9	is	be	AUX
bracis-28360	287	10	still	still	ADV
bracis-28360	287	11	superior	superior	ADJ
bracis-28360	287	12	.	.	PUNCT
bracis-28360	288	1	6	6	NUM
bracis-28360	288	2	conclusions	conclusion	NOUN
bracis-28360	288	3	new	new	ADJ
bracis-28360	288	4	generalizations	generalization	NOUN
bracis-28360	288	5	of	of	ADP
bracis-28360	288	6	the	the	DET
bracis-28360	288	7	discrete	discrete	ADJ
bracis-28360	288	8	ci	ci	NOUN
bracis-28360	288	9	have	have	AUX
bracis-28360	288	10	been	be	AUX
bracis-28360	288	11	developed	develop	VERB
bracis-28360	288	12	in	in	ADP
bracis-28360	288	13	recent	recent	ADJ
bracis-28360	288	14	years	year	NOUN
bracis-28360	288	15	,	,	PUNCT
bracis-28360	288	16	by	by	ADP
bracis-28360	288	17	generalizing	generalize	VERB
bracis-28360	288	18	the	the	DET
bracis-28360	288	19	product	product	NOUN
bracis-28360	288	20	and/or	and/or	CCONJ
bracis-28360	288	21	the	the	DET
bracis-28360	288	22	difference	difference	NOUN
bracis-28360	288	23	operations	operation	NOUN
bracis-28360	288	24	from	from	ADP
bracis-28360	288	25	the	the	DET
bracis-28360	288	26	original	original	ADJ
bracis-28360	288	27	expression	expression	NOUN
bracis-28360	288	28	or	or	CCONJ
bracis-28360	288	29	its	its	PRON
bracis-28360	288	30	expanded	expand	VERB
bracis-28360	288	31	form	form	NOUN
bracis-28360	288	32	.	.	PUNCT
bracis-28360	289	1	the	the	DET
bracis-28360	289	2	study	study	NOUN
bracis-28360	289	3	of	of	ADP
bracis-28360	289	4	those	those	DET
bracis-28360	289	5	generalizations	generalization	NOUN
bracis-28360	289	6	has	have	AUX
bracis-28360	289	7	proven	prove	VERB
bracis-28360	289	8	to	to	PART
bracis-28360	289	9	be	be	AUX
bracis-28360	289	10	worthwhile	worthwhile	ADJ
bracis-28360	289	11	since	since	SCONJ
bracis-28360	289	12	they	they	PRON
bracis-28360	289	13	can	can	AUX
bracis-28360	289	14	provide	provide	VERB
bracis-28360	289	15	promising	promising	ADJ
bracis-28360	289	16	results	result	NOUN
bracis-28360	289	17	in	in	ADP
bracis-28360	289	18	applications	application	NOUN
bracis-28360	289	19	.	.	PUNCT
bracis-28360	290	1	in	in	ADP
bracis-28360	290	2	this	this	DET
bracis-28360	290	3	paper	paper	NOUN
bracis-28360	290	4	,	,	PUNCT
bracis-28360	290	5	we	we	PRON
bracis-28360	290	6	continue	continue	VERB
bracis-28360	290	7	this	this	DET
bracis-28360	290	8	trend	trend	NOUN
bracis-28360	290	9	by	by	ADP
bracis-28360	290	10	focusing	focus	VERB
bracis-28360	290	11	on	on	ADP
bracis-28360	290	12	the	the	DET
bracis-28360	290	13	generalization	generalization	NOUN
bracis-28360	290	14	of	of	ADP
bracis-28360	290	15	the	the	DET
bracis-28360	290	16	cc	cc	NOUN
bracis-28360	290	17	-	-	NOUN
bracis-28360	290	18	integral	integral	ADJ
bracis-28360	290	19	by	by	ADP
bracis-28360	290	20	means	mean	NOUN
bracis-28360	290	21	of	of	ADP
bracis-28360	290	22	rdfs	rdfs	NOUN
bracis-28360	290	23	,	,	PUNCT
bracis-28360	290	24	calling	call	VERB
bracis-28360	290	25	them	they	PRON
bracis-28360	290	26	d	d	PROPN
bracis-28360	290	27	-	-	PUNCT
bracis-28360	290	28	cc	cc	NOUN
bracis-28360	290	29	-	-	NOUN
bracis-28360	290	30	integrals	integral	NOUN
bracis-28360	290	31	.	.	PUNCT
bracis-28360	291	1	then	then	ADV
bracis-28360	291	2	,	,	PUNCT
bracis-28360	291	3	we	we	PRON
bracis-28360	291	4	studied	study	VERB
bracis-28360	291	5	some	some	DET
bracis-28360	291	6	relevant	relevant	ADJ
bracis-28360	291	7	properties	property	NOUN
bracis-28360	291	8	for	for	ADP
bracis-28360	291	9	application	application	NOUN
bracis-28360	291	10	purposes	purpose	NOUN
bracis-28360	291	11	.	.	PUNCT
bracis-28360	292	1	the	the	DET
bracis-28360	292	2	final	final	ADJ
bracis-28360	292	3	part	part	NOUN
bracis-28360	292	4	of	of	ADP
bracis-28360	292	5	our	our	PRON
bracis-28360	292	6	work	work	NOUN
bracis-28360	292	7	applied	apply	VERB
bracis-28360	292	8	the	the	DET
bracis-28360	292	9	d	d	PROPN
bracis-28360	292	10	-	-	PUNCT
bracis-28360	292	11	cc	cc	NOUN
bracis-28360	292	12	-	-	PUNCT
bracis-28360	292	13	integrals	integral	NOUN
bracis-28360	292	14	in	in	ADP
bracis-28360	292	15	a	a	DET
bracis-28360	292	16	classification	classification	NOUN
bracis-28360	292	17	problem	problem	NOUN
bracis-28360	292	18	,	,	PUNCT
bracis-28360	292	19	followed	follow	VERB
bracis-28360	292	20	by	by	ADP
bracis-28360	292	21	a	a	DET
bracis-28360	292	22	two	two	NUM
bracis-28360	292	23	-	-	PUNCT
bracis-28360	292	24	step	step	NOUN
bracis-28360	292	25	analysis	analysis	NOUN
bracis-28360	292	26	.	.	PUNCT
bracis-28360	293	1	first	first	ADV
bracis-28360	293	2	,	,	PUNCT
bracis-28360	293	3	we	we	PRON
bracis-28360	293	4	compared	compare	VERB
bracis-28360	293	5	different	different	ADJ
bracis-28360	293	6	d	d	PROPN
bracis-28360	293	7	-	-	PUNCT
bracis-28360	293	8	cc	cc	NOUN
bracis-28360	293	9	-	-	PUNCT
bracis-28360	293	10	integrals	integral	NOUN
bracis-28360	293	11	and	and	CCONJ
bracis-28360	293	12	identified	identify	VERB
bracis-28360	293	13	that	that	SCONJ
bracis-28360	293	14	the	the	DET
bracis-28360	293	15	one	one	NOUN
bracis-28360	293	16	based	base	VERB
bracis-28360	293	17	on	on	ADP
bracis-28360	293	18	the	the	DET
bracis-28360	293	19	copula	copula	ADJ
bracis-28360	293	20	omm	omm	NOUN
bracis-28360	293	21	and	and	CCONJ
bracis-28360	293	22	the	the	DET
bracis-28360	293	23	rdf	rdf	NOUN
bracis-28360	293	24	\(\delta	\(\delta	NOUN
bracis-28360	293	25	_	_	PUNCT
bracis-28360	293	26	5\	5\	X
bracis-28360	293	27	)	)	PUNCT
bracis-28360	293	28	had	have	VERB
bracis-28360	293	29	the	the	DET
bracis-28360	293	30	best	good	ADJ
bracis-28360	293	31	overall	overall	ADJ
bracis-28360	293	32	performance	performance	NOUN
bracis-28360	293	33	.	.	PUNCT
bracis-28360	294	1	then	then	ADV
bracis-28360	294	2	,	,	PUNCT
bracis-28360	294	3	we	we	PRON
bracis-28360	294	4	compared	compare	VERB
bracis-28360	294	5	this	this	DET
bracis-28360	294	6	particular	particular	ADJ
bracis-28360	294	7	d	d	ADJ
bracis-28360	294	8	-	-	PUNCT
bracis-28360	294	9	cc	cc	NOUN
bracis-28360	294	10	-	-	NOUN
bracis-28360	294	11	integral	integral	ADJ
bracis-28360	294	12	with	with	ADP
bracis-28360	294	13	other	other	ADJ
bracis-28360	294	14	methods	method	NOUN
bracis-28360	294	15	from	from	ADP
bracis-28360	294	16	the	the	DET
bracis-28360	294	17	literature	literature	NOUN
bracis-28360	294	18	,	,	PUNCT
bracis-28360	294	19	showing	show	VERB
bracis-28360	294	20	that	that	SCONJ
bracis-28360	294	21	it	it	PRON
bracis-28360	294	22	is	be	AUX
bracis-28360	294	23	statistically	statistically	ADV
bracis-28360	294	24	equivalent	equivalent	ADJ
bracis-28360	294	25	to	to	ADP
bracis-28360	294	26	the	the	DET
bracis-28360	294	27	state	state	NOUN
bracis-28360	294	28	-	-	PUNCT
bracis-28360	294	29	of	of	ADP
bracis-28360	294	30	-	-	PUNCT
bracis-28360	294	31	the	the	DET
bracis-28360	294	32	-	-	PUNCT
bracis-28360	294	33	art	art	NOUN
bracis-28360	294	34	\(c_{f1f2}\)-integral	\(c_{f1f2}\)-integral	NOUN
bracis-28360	294	35	and	and	CCONJ
bracis-28360	294	36	surpasses	surpasse	NOUN
bracis-28360	294	37	most	most	ADJ
bracis-28360	294	38	of	of	ADP
bracis-28360	294	39	the	the	DET
bracis-28360	294	40	other	other	ADJ
bracis-28360	294	41	considered	consider	VERB
bracis-28360	294	42	approaches	approach	NOUN
bracis-28360	294	43	,	,	PUNCT
bracis-28360	294	44	including	include	VERB
bracis-28360	294	45	the	the	DET
bracis-28360	294	46	cc	cc	NOUN
bracis-28360	294	47	-	-	ADJ
bracis-28360	294	48	integral	integral	ADJ
bracis-28360	294	49	.	.	PUNCT
bracis-28360	295	1	notes	note	VERB
bracis-28360	295	2	1.a	1.a	NUM
bracis-28360	295	3	function	function	NOUN
bracis-28360	295	4	f	f	PROPN
bracis-28360	295	5	is	be	AUX
bracis-28360	295	6	said	say	VERB
bracis-28360	295	7	to	to	PART
bracis-28360	295	8	be	be	AUX
bracis-28360	295	9	averaging	average	VERB
bracis-28360	295	10	if	if	SCONJ
bracis-28360	295	11	\(min	\(min	PROPN
bracis-28360	295	12	\le	\le	PROPN
bracis-28360	295	13	f	f	PROPN
bracis-28360	295	14	\le	\le	PROPN
bracis-28360	295	15	max\	max\	PROPN
bracis-28360	295	16	)	)	PUNCT
bracis-28360	295	17	.	.	PUNCT
bracis-28360	296	1	2.for	2.for	ADP
bracis-28360	296	2	more	more	ADJ
bracis-28360	296	3	information	information	NOUN
bracis-28360	296	4	about	about	ADP
bracis-28360	296	5	this	this	DET
bracis-28360	296	6	approach	approach	NOUN
bracis-28360	296	7	see	see	VERB
bracis-28360	296	8	 	 	SPACE
bracis-28360	297	1	[	[	X
bracis-28360	297	2	19	19	NUM
bracis-28360	297	3	,	,	PUNCT
bracis-28360	297	4	20	20	NUM
bracis-28360	297	5	,	,	PUNCT
bracis-28360	297	6	23	23	NUM
bracis-28360	297	7	]	]	PUNCT
bracis-28360	297	8	.	.	PUNCT
bracis-28360	298	1	3.https://keel.es	3.https://keel.es	NUM
bracis-28360	298	2	.	.	PUNCT
bracis-28360	299	1	4.to	4.to	NUM
bracis-28360	299	2	analyze	analyze	VERB
bracis-28360	299	3	the	the	DET
bracis-28360	299	4	particular	particular	ADJ
bracis-28360	299	5	cases	case	NOUN
bracis-28360	299	6	and	and	CCONJ
bracis-28360	299	7	results	result	NOUN
bracis-28360	299	8	per	per	ADP
bracis-28360	299	9	fold	fold	NOUN
bracis-28360	299	10	please	please	INTJ
bracis-28360	299	11	check	check	VERB
bracis-28360	299	12	the	the	DET
bracis-28360	299	13	folowing	folowing	NOUN
bracis-28360	299	14	link	link	PROPN
bracis-28360	299	15	https://github.com/giancarlo-lucca/d-cc-integrals-generalizing-cc-integrals-by-restricted-dissimilarity-functions	https://github.com/giancarlo-lucca/d-cc-integrals-generalizing-cc-integrals-by-restricted-dissimilarity-function	NOUN
bracis-28360	299	16	.	.	PUNCT
bracis-28360	300	1	references	reference	NOUN
bracis-28360	300	2	alcala	alcala	PROPN
bracis-28360	300	3	-	-	PUNCT
bracis-28360	300	4	fdez	fdez	PROPN
bracis-28360	300	5	,	,	PUNCT
bracis-28360	300	6	j.	j.	PROPN
bracis-28360	300	7	,	,	PUNCT
bracis-28360	300	8	alcala	alcala	PROPN
bracis-28360	300	9	,	,	PUNCT
bracis-28360	300	10	r.	r.	PROPN
bracis-28360	300	11	,	,	PUNCT
bracis-28360	300	12	herrera	herrera	PROPN
bracis-28360	300	13	,	,	PUNCT
bracis-28360	300	14	f.	f.	PROPN
bracis-28360	300	15	:	:	PUNCT
bracis-28360	300	16	a	a	DET
bracis-28360	300	17	fuzzy	fuzzy	ADJ
bracis-28360	300	18	association	association	NOUN
bracis-28360	300	19	rule	rule	NOUN
bracis-28360	300	20	-	-	PUNCT
bracis-28360	300	21	based	base	VERB
bracis-28360	300	22	classification	classification	NOUN
bracis-28360	300	23	model	model	NOUN
bracis-28360	300	24	for	for	ADP
bracis-28360	300	25	high	high	ADJ
bracis-28360	300	26	-	-	PUNCT
bracis-28360	300	27	dimensional	dimensional	ADJ
bracis-28360	300	28	problems	problem	NOUN
bracis-28360	300	29	with	with	ADP
bracis-28360	300	30	genetic	genetic	ADJ
bracis-28360	300	31	rule	rule	NOUN
bracis-28360	300	32	selection	selection	NOUN
bracis-28360	300	33	and	and	CCONJ
bracis-28360	300	34	lateral	lateral	ADJ
bracis-28360	300	35	tuning	tuning	NOUN
bracis-28360	300	36	.	.	PUNCT
bracis-28360	301	1	ieee	ieee	PROPN
bracis-28360	301	2	trans	trans	PROPN
bracis-28360	301	3	.	.	PUNCT
bracis-28360	301	4	fuzzy	fuzzy	ADJ
bracis-28360	301	5	syst	syst	PROPN
bracis-28360	301	6	.	.	PUNCT
bracis-28360	302	1	19(5	19(5	NUM
bracis-28360	302	2	)	)	PUNCT
bracis-28360	302	3	,	,	PUNCT
bracis-28360	302	4	857–872	857–872	NUM
bracis-28360	302	5	(	(	PUNCT
bracis-28360	302	6	2011	2011	NUM
bracis-28360	302	7	)	)	PUNCT
bracis-28360	302	8	article	article	NOUN
bracis-28360	302	9	  	  	SPACE
bracis-28360	302	10	google	google	PROPN
bracis-28360	302	11	scholar	scholar	NOUN
bracis-28360	302	12	  	  	SPACE
bracis-28360	302	13	alcalá	alcalá	ADJ
bracis-28360	302	14	-	-	PUNCT
bracis-28360	302	15	fdez	fdez	PROPN
bracis-28360	302	16	,	,	PUNCT
bracis-28360	302	17	j.	j.	PROPN
bracis-28360	302	18	,	,	PUNCT
bracis-28360	302	19	et	et	PROPN
bracis-28360	302	20	al	al	PROPN
bracis-28360	302	21	.	.	PUNCT
bracis-28360	302	22	:	:	PUNCT
bracis-28360	303	1	keel	keel	NOUN
bracis-28360	303	2	:	:	PUNCT
bracis-28360	303	3	a	a	DET
bracis-28360	303	4	software	software	NOUN
bracis-28360	303	5	tool	tool	NOUN
bracis-28360	303	6	to	to	PART
bracis-28360	303	7	assess	assess	VERB
bracis-28360	303	8	evolutionary	evolutionary	ADJ
bracis-28360	303	9	algorithms	algorithm	NOUN
bracis-28360	303	10	for	for	ADP
bracis-28360	303	11	data	data	NOUN
bracis-28360	303	12	mining	mining	NOUN
bracis-28360	303	13	problems	problem	NOUN
bracis-28360	303	14	.	.	PUNCT
bracis-28360	304	1	soft	soft	ADJ
bracis-28360	304	2	.	.	PUNCT
bracis-28360	305	1	comput	comput	NOUN
bracis-28360	305	2	.	.	PUNCT
bracis-28360	306	1	13(3	13(3	NUM
bracis-28360	306	2	)	)	PUNCT
bracis-28360	306	3	,	,	PUNCT
bracis-28360	306	4	307–318	307–318	NUM
bracis-28360	306	5	(	(	PUNCT
bracis-28360	306	6	2009	2009	NUM
bracis-28360	306	7	)	)	PUNCT
bracis-28360	306	8	article	article	NOUN
bracis-28360	306	9	  	  	SPACE
bracis-28360	306	10	google	google	PROPN
bracis-28360	306	11	scholar	scholar	NOUN
bracis-28360	306	12	  	  	SPACE
bracis-28360	306	13	alsina	alsina	NOUN
bracis-28360	306	14	,	,	PUNCT
bracis-28360	306	15	c.	c.	PROPN
bracis-28360	306	16	,	,	PUNCT
bracis-28360	306	17	frank	frank	PROPN
bracis-28360	306	18	,	,	PUNCT
bracis-28360	306	19	m.j	m.j	PROPN
bracis-28360	306	20	.	.	PROPN
bracis-28360	306	21	,	,	PUNCT
bracis-28360	306	22	schweizer	schweizer	PROPN
bracis-28360	306	23	,	,	PUNCT
bracis-28360	306	24	b.	b.	PROPN
bracis-28360	306	25	:	:	PUNCT
bracis-28360	306	26	associative	associative	ADJ
bracis-28360	306	27	functions	function	NOUN
bracis-28360	306	28	:	:	PUNCT
bracis-28360	306	29	triangular	triangular	NOUN
bracis-28360	306	30	norms	norm	NOUN
bracis-28360	306	31	and	and	CCONJ
bracis-28360	306	32	copulas	copula	NOUN
bracis-28360	306	33	.	.	PUNCT
bracis-28360	307	1	world	world	NOUN
bracis-28360	307	2	scientific	scientific	ADJ
bracis-28360	307	3	publishing	publishing	NOUN
bracis-28360	307	4	company	company	NOUN
bracis-28360	307	5	,	,	PUNCT
bracis-28360	307	6	singapore	singapore	PROPN
bracis-28360	307	7	(	(	PUNCT
bracis-28360	307	8	2006	2006	NUM
bracis-28360	307	9	)	)	PUNCT
bracis-28360	307	10	book	book	NOUN
bracis-28360	307	11	  	  	SPACE
bracis-28360	307	12	math	math	NOUN
bracis-28360	307	13	  	  	SPACE
bracis-28360	307	14	google	google	PROPN
bracis-28360	307	15	scholar	scholar	NOUN
bracis-28360	307	16	  	  	SPACE
bracis-28360	307	17	boczek	boczek	NOUN
bracis-28360	307	18	,	,	PUNCT
bracis-28360	307	19	m.	m.	NOUN
bracis-28360	307	20	,	,	PUNCT
bracis-28360	307	21	kaluszka	kaluszka	PROPN
bracis-28360	307	22	,	,	PUNCT
bracis-28360	307	23	m.	m.	NOUN
bracis-28360	307	24	:	:	PUNCT
bracis-28360	307	25	on	on	ADP
bracis-28360	307	26	the	the	DET
bracis-28360	307	27	extended	extend	VERB
bracis-28360	307	28	choquet	choquet	NOUN
bracis-28360	307	29	-	-	PUNCT
bracis-28360	307	30	sugeno	sugeno	NOUN
bracis-28360	307	31	-	-	PUNCT
bracis-28360	307	32	like	like	ADJ
bracis-28360	307	33	operator	operator	NOUN
bracis-28360	307	34	.	.	PUNCT
bracis-28360	308	1	int	int	NOUN
bracis-28360	308	2	.	.	PUNCT
bracis-28360	309	1	j.	j.	PROPN
bracis-28360	309	2	approx	approx	PROPN
bracis-28360	309	3	.	.	PUNCT
bracis-28360	310	1	reason	reason	NOUN
bracis-28360	310	2	.	.	PUNCT
bracis-28360	311	1	154	154	NUM
bracis-28360	311	2	,	,	PUNCT
bracis-28360	311	3	48–55	48–55	NUM
bracis-28360	311	4	(	(	PUNCT
bracis-28360	311	5	2023	2023	NUM
bracis-28360	311	6	)	)	PUNCT
bracis-28360	311	7	article	article	NOUN
bracis-28360	311	8	  	  	SPACE
bracis-28360	311	9	mathscinet	mathscinet	NOUN
bracis-28360	311	10	  	  	SPACE
bracis-28360	311	11	math	math	NOUN
bracis-28360	311	12	  	  	SPACE
bracis-28360	311	13	google	google	PROPN
bracis-28360	311	14	scholar	scholar	NOUN
bracis-28360	311	15	  	  	SPACE
bracis-28360	311	16	bustince	bustince	NOUN
bracis-28360	311	17	,	,	PUNCT
bracis-28360	311	18	h.	h.	PROPN
bracis-28360	311	19	,	,	PUNCT
bracis-28360	311	20	fernandez	fernandez	PROPN
bracis-28360	311	21	,	,	PUNCT
bracis-28360	311	22	j.	j.	PROPN
bracis-28360	311	23	,	,	PUNCT
bracis-28360	311	24	kolesárová	kolesárová	PROPN
bracis-28360	311	25	,	,	PUNCT
bracis-28360	311	26	a.	a.	NOUN
bracis-28360	311	27	,	,	PUNCT
bracis-28360	311	28	mesiar	mesiar	PROPN
bracis-28360	311	29	,	,	PUNCT
bracis-28360	311	30	r.	r.	PROPN
bracis-28360	311	31	:	:	PUNCT
bracis-28360	311	32	directional	directional	ADJ
bracis-28360	311	33	monotonicity	monotonicity	NOUN
bracis-28360	311	34	of	of	ADP
bracis-28360	311	35	fusion	fusion	NOUN
bracis-28360	311	36	functions	function	NOUN
bracis-28360	311	37	.	.	PUNCT
bracis-28360	312	1	eur	eur	PROPN
bracis-28360	312	2	.	.	PUNCT
bracis-28360	313	1	j.	j.	PROPN
bracis-28360	313	2	oper	oper	PROPN
bracis-28360	313	3	.	.	PUNCT
bracis-28360	313	4	res	re	NOUN
bracis-28360	313	5	.	.	PUNCT
bracis-28360	313	6	244(1	244(1	NUM
bracis-28360	313	7	)	)	PUNCT
bracis-28360	313	8	,	,	PUNCT
bracis-28360	313	9	300–308	300–308	NUM
bracis-28360	313	10	(	(	PUNCT
bracis-28360	313	11	2015	2015	NUM
bracis-28360	313	12	)	)	PUNCT
bracis-28360	313	13	article	article	NOUN
bracis-28360	313	14	  	  	SPACE
bracis-28360	313	15	mathscinet	mathscinet	NOUN
bracis-28360	313	16	  	  	SPACE
bracis-28360	313	17	math	math	NOUN
bracis-28360	313	18	  	  	SPACE
bracis-28360	313	19	google	google	PROPN
bracis-28360	313	20	scholar	scholar	NOUN
bracis-28360	313	21	  	  	SPACE
bracis-28360	313	22	bustince	bustince	NOUN
bracis-28360	313	23	,	,	PUNCT
bracis-28360	313	24	h.	h.	PROPN
bracis-28360	313	25	,	,	PUNCT
bracis-28360	313	26	fernandez	fernandez	PROPN
bracis-28360	313	27	,	,	PUNCT
bracis-28360	313	28	j.	j.	PROPN
bracis-28360	313	29	,	,	PUNCT
bracis-28360	313	30	mesiar	mesiar	PROPN
bracis-28360	313	31	,	,	PUNCT
bracis-28360	313	32	r.	r.	PROPN
bracis-28360	313	33	,	,	PUNCT
bracis-28360	313	34	montero	montero	PROPN
bracis-28360	313	35	,	,	PUNCT
bracis-28360	313	36	j.	j.	PROPN
bracis-28360	313	37	,	,	PUNCT
bracis-28360	313	38	orduna	orduna	PROPN
bracis-28360	313	39	,	,	PUNCT
bracis-28360	313	40	r.	r.	PROPN
bracis-28360	313	41	:	:	PUNCT
bracis-28360	313	42	overlap	overlap	NOUN
bracis-28360	313	43	functions	function	NOUN
bracis-28360	313	44	.	.	PUNCT
bracis-28360	314	1	nonlinear	nonlinear	ADJ
bracis-28360	314	2	anal	anal	PROPN
bracis-28360	314	3	.	.	PUNCT
bracis-28360	315	1	theory	theory	NOUN
bracis-28360	315	2	methods	method	NOUN
bracis-28360	315	3	app	app	VERB
bracis-28360	315	4	.	.	PUNCT
bracis-28360	316	1	72(3–4	72(3–4	NOUN
bracis-28360	316	2	)	)	PUNCT
bracis-28360	316	3	,	,	PUNCT
bracis-28360	316	4	1488–1499	1488–1499	NUM
bracis-28360	316	5	(	(	PUNCT
bracis-28360	316	6	2010	2010	NUM
bracis-28360	316	7	)	)	PUNCT
bracis-28360	316	8	article	article	NOUN
bracis-28360	316	9	  	  	SPACE
bracis-28360	316	10	mathscinet	mathscinet	NOUN
bracis-28360	316	11	  	  	SPACE
bracis-28360	316	12	math	math	NOUN
bracis-28360	316	13	  	  	SPACE
bracis-28360	316	14	google	google	PROPN
bracis-28360	316	15	scholar	scholar	NOUN
bracis-28360	316	16	  	  	SPACE
bracis-28360	316	17	bustince	bustince	NOUN
bracis-28360	316	18	,	,	PUNCT
bracis-28360	316	19	h.	h.	PROPN
bracis-28360	316	20	,	,	PUNCT
bracis-28360	316	21	jurio	jurio	PROPN
bracis-28360	316	22	,	,	PUNCT
bracis-28360	316	23	a.	a.	NOUN
bracis-28360	316	24	,	,	PUNCT
bracis-28360	316	25	pradera	pradera	NOUN
bracis-28360	316	26	,	,	PUNCT
bracis-28360	316	27	a.	a.	NOUN
bracis-28360	316	28	,	,	PUNCT
bracis-28360	316	29	mesiar	mesiar	PROPN
bracis-28360	316	30	,	,	PUNCT
bracis-28360	316	31	r.	r.	PROPN
bracis-28360	316	32	,	,	PUNCT
bracis-28360	316	33	beliakov	beliakov	PROPN
bracis-28360	316	34	,	,	PUNCT
bracis-28360	316	35	g.	g.	PROPN
bracis-28360	316	36	:	:	PUNCT
bracis-28360	316	37	generalization	generalization	NOUN
bracis-28360	316	38	of	of	ADP
bracis-28360	316	39	the	the	DET
bracis-28360	316	40	weighted	weighted	ADJ
bracis-28360	316	41	voting	voting	NOUN
bracis-28360	316	42	method	method	NOUN
bracis-28360	316	43	using	use	VERB
bracis-28360	316	44	penalty	penalty	NOUN
bracis-28360	316	45	functions	function	NOUN
bracis-28360	316	46	constructed	construct	VERB
bracis-28360	316	47	via	via	ADP
bracis-28360	316	48	faithful	faithful	ADJ
bracis-28360	316	49	restricted	restrict	VERB
bracis-28360	316	50	dissimilarity	dissimilarity	NOUN
bracis-28360	316	51	functions	function	NOUN
bracis-28360	316	52	.	.	PUNCT
bracis-28360	317	1	eur	eur	PROPN
bracis-28360	317	2	.	.	PUNCT
bracis-28360	318	1	j.	j.	PROPN
bracis-28360	318	2	oper	oper	PROPN
bracis-28360	318	3	.	.	PUNCT
bracis-28360	319	1	res	re	NOUN
bracis-28360	319	2	.	.	PUNCT
bracis-28360	320	1	225(3	225(3	NUM
bracis-28360	320	2	)	)	PUNCT
bracis-28360	320	3	,	,	PUNCT
bracis-28360	320	4	472–478	472–478	NUM
bracis-28360	320	5	(	(	PUNCT
bracis-28360	320	6	2013	2013	NUM
bracis-28360	320	7	)	)	PUNCT
bracis-28360	320	8	article	article	NOUN
bracis-28360	320	9	  	  	SPACE
bracis-28360	320	10	mathscinet	mathscinet	NOUN
bracis-28360	320	11	  	  	SPACE
bracis-28360	320	12	math	math	NOUN
bracis-28360	320	13	  	  	SPACE
bracis-28360	320	14	google	google	PROPN
bracis-28360	320	15	scholar	scholar	NOUN
bracis-28360	320	16	  	  	SPACE
bracis-28360	320	17	bustince	bustince	NOUN
bracis-28360	320	18	,	,	PUNCT
bracis-28360	320	19	h.	h.	PROPN
bracis-28360	320	20	,	,	PUNCT
bracis-28360	320	21	et	et	PROPN
bracis-28360	320	22	al	al	PROPN
bracis-28360	320	23	.	.	PUNCT
bracis-28360	320	24	:	:	PUNCT
bracis-28360	321	1	d	d	X
bracis-28360	321	2	-	-	PUNCT
bracis-28360	321	3	choquet	choquet	NOUN
bracis-28360	321	4	integrals	integral	NOUN
bracis-28360	321	5	:	:	PUNCT
bracis-28360	321	6	choquet	choquet	NOUN
bracis-28360	321	7	integrals	integral	NOUN
bracis-28360	321	8	based	base	VERB
bracis-28360	321	9	on	on	ADP
bracis-28360	321	10	dissimilarities	dissimilarity	NOUN
bracis-28360	321	11	.	.	PUNCT
bracis-28360	322	1	fuzzy	fuzzy	ADJ
bracis-28360	322	2	sets	set	VERB
bracis-28360	322	3	syst	syst	PROPN
bracis-28360	322	4	.	.	PUNCT
bracis-28360	323	1	(	(	PUNCT
bracis-28360	323	2	2020	2020	NUM
bracis-28360	323	3	)	)	PUNCT
bracis-28360	323	4	google	google	NOUN
bracis-28360	323	5	scholar	scholar	NOUN
bracis-28360	323	6	  	  	SPACE
bracis-28360	323	7	bustince	bustince	NOUN
bracis-28360	323	8	,	,	PUNCT
bracis-28360	323	9	h.	h.	PROPN
bracis-28360	323	10	,	,	PUNCT
bracis-28360	323	11	et	et	PROPN
bracis-28360	323	12	al	al	PROPN
bracis-28360	323	13	.	.	PROPN
bracis-28360	323	14	:	:	PUNCT
bracis-28360	323	15	ordered	order	VERB
bracis-28360	323	16	directionally	directionally	ADV
bracis-28360	323	17	monotone	monotone	ADJ
bracis-28360	323	18	functions	function	NOUN
bracis-28360	323	19	:	:	PUNCT
bracis-28360	323	20	justification	justification	NOUN
bracis-28360	323	21	and	and	CCONJ
bracis-28360	323	22	application	application	NOUN
bracis-28360	323	23	.	.	PUNCT
bracis-28360	324	1	ieee	ieee	PROPN
bracis-28360	324	2	trans	trans	PROPN
bracis-28360	324	3	.	.	PUNCT
bracis-28360	324	4	fuzzy	fuzzy	ADJ
bracis-28360	324	5	syst	syst	PROPN
bracis-28360	324	6	.	.	PUNCT
bracis-28360	324	7	26(4	26(4	NUM
bracis-28360	324	8	)	)	PUNCT
bracis-28360	324	9	,	,	PUNCT
bracis-28360	324	10	2237–2250	2237–2250	NUM
bracis-28360	324	11	(	(	PUNCT
bracis-28360	324	12	2018	2018	NUM
bracis-28360	324	13	)	)	PUNCT
bracis-28360	324	14	article	article	NOUN
bracis-28360	324	15	  	  	SPACE
bracis-28360	324	16	google	google	PROPN
bracis-28360	324	17	scholar	scholar	NOUN
bracis-28360	324	18	  	  	SPACE
bracis-28360	324	19	choquet	choquet	NOUN
bracis-28360	324	20	,	,	PUNCT
bracis-28360	324	21	g.	g.	NOUN
bracis-28360	324	22	:	:	PUNCT
bracis-28360	324	23	theory	theory	NOUN
bracis-28360	324	24	of	of	ADP
bracis-28360	324	25	capacities	capacity	NOUN
bracis-28360	324	26	.	.	PUNCT
bracis-28360	325	1	institut	institut	PROPN
bracis-28360	325	2	fourier	fourier	NOUN
bracis-28360	325	3	5	5	NUM
bracis-28360	325	4	,	,	PUNCT
bracis-28360	325	5	131–295	131–295	NUM
bracis-28360	325	6	(	(	PUNCT
bracis-28360	325	7	1953–1954	1953–1954	NUM
bracis-28360	325	8	)	)	PUNCT
bracis-28360	325	9	google	google	NOUN
bracis-28360	325	10	scholar	scholar	NOUN
bracis-28360	325	11	  	  	SPACE
bracis-28360	325	12	cordón	cordón	NOUN
bracis-28360	325	13	,	,	PUNCT
bracis-28360	325	14	o.	o.	PROPN
bracis-28360	325	15	,	,	PUNCT
bracis-28360	325	16	del	del	PROPN
bracis-28360	325	17	jesus	jesus	PROPN
bracis-28360	325	18	,	,	PUNCT
bracis-28360	325	19	m.j	m.j	PROPN
bracis-28360	325	20	.	.	PROPN
bracis-28360	325	21	,	,	PUNCT
bracis-28360	325	22	herrera	herrera	PROPN
bracis-28360	325	23	,	,	PUNCT
bracis-28360	325	24	f.	f.	PROPN
bracis-28360	325	25	:	:	PUNCT
bracis-28360	325	26	a	a	DET
bracis-28360	325	27	proposal	proposal	NOUN
bracis-28360	325	28	on	on	ADP
bracis-28360	325	29	reasoning	reasoning	NOUN
bracis-28360	325	30	methods	method	NOUN
bracis-28360	325	31	in	in	ADP
bracis-28360	325	32	fuzzy	fuzzy	ADJ
bracis-28360	325	33	rule	rule	NOUN
bracis-28360	325	34	-	-	PUNCT
bracis-28360	325	35	based	base	VERB
bracis-28360	325	36	classification	classification	NOUN
bracis-28360	325	37	systems	system	NOUN
bracis-28360	325	38	.	.	PUNCT
bracis-28360	326	1	int	int	NOUN
bracis-28360	326	2	.	.	PUNCT
bracis-28360	327	1	j.	j.	PROPN
bracis-28360	327	2	approx	approx	PROPN
bracis-28360	327	3	.	.	PUNCT
bracis-28360	328	1	reason	reason	NOUN
bracis-28360	328	2	.	.	PUNCT
bracis-28360	329	1	20(1	20(1	NUM
bracis-28360	329	2	)	)	PUNCT
bracis-28360	329	3	,	,	PUNCT
bracis-28360	329	4	21–45	21–45	NUM
bracis-28360	329	5	(	(	PUNCT
bracis-28360	329	6	1999	1999	NUM
bracis-28360	329	7	)	)	PUNCT
bracis-28360	329	8	article	article	NOUN
bracis-28360	329	9	  	  	SPACE
bracis-28360	329	10	google	google	PROPN
bracis-28360	329	11	scholar	scholar	NOUN
bracis-28360	329	12	  	  	SPACE
bracis-28360	329	13	cordon	cordon	ADJ
bracis-28360	329	14	,	,	PUNCT
bracis-28360	329	15	o.	o.	PROPN
bracis-28360	329	16	,	,	PUNCT
bracis-28360	329	17	del	del	PROPN
bracis-28360	329	18	jesus	jesus	PROPN
bracis-28360	329	19	,	,	PUNCT
bracis-28360	329	20	m.j	m.j	PROPN
bracis-28360	329	21	.	.	PROPN
bracis-28360	329	22	,	,	PUNCT
bracis-28360	329	23	herrera	herrera	PROPN
bracis-28360	329	24	,	,	PUNCT
bracis-28360	329	25	f.	f.	PROPN
bracis-28360	329	26	:	:	PUNCT
bracis-28360	329	27	analyzing	analyze	VERB
bracis-28360	329	28	the	the	DET
bracis-28360	329	29	reasoning	reasoning	NOUN
bracis-28360	329	30	mechanisms	mechanism	NOUN
bracis-28360	329	31	in	in	ADP
bracis-28360	329	32	fuzzy	fuzzy	ADJ
bracis-28360	329	33	rule	rule	NOUN
bracis-28360	329	34	based	base	VERB
bracis-28360	329	35	classification	classification	NOUN
bracis-28360	329	36	systems	system	NOUN
bracis-28360	329	37	.	.	PUNCT
bracis-28360	330	1	math	math	NOUN
bracis-28360	330	2	.	.	PUNCT
bracis-28360	331	1	soft	soft	ADJ
bracis-28360	331	2	comput	comput	NOUN
bracis-28360	331	3	.	.	PUNCT
bracis-28360	332	1	5(2–3	5(2–3	NUM
bracis-28360	332	2	)	)	PUNCT
bracis-28360	332	3	,	,	PUNCT
bracis-28360	332	4	321–332	321–332	NUM
bracis-28360	332	5	(	(	PUNCT
bracis-28360	332	6	1998	1998	NUM
bracis-28360	332	7	)	)	PUNCT
bracis-28360	332	8	google	google	PROPN
bracis-28360	332	9	scholar	scholar	NOUN
bracis-28360	332	10	  	  	SPACE
bracis-28360	332	11	dimuro	dimuro	NOUN
bracis-28360	332	12	,	,	PUNCT
bracis-28360	332	13	g.p	g.p	PROPN
bracis-28360	332	14	.	.	PROPN
bracis-28360	332	15	,	,	PUNCT
bracis-28360	332	16	et	et	PROPN
bracis-28360	332	17	al	al	PROPN
bracis-28360	332	18	.	.	PROPN
bracis-28360	332	19	:	:	PUNCT
bracis-28360	333	1	the	the	DET
bracis-28360	333	2	state	state	NOUN
bracis-28360	333	3	-	-	PUNCT
bracis-28360	333	4	of	of	ADP
bracis-28360	333	5	-	-	PUNCT
bracis-28360	333	6	art	art	NOUN
bracis-28360	333	7	of	of	ADP
bracis-28360	333	8	the	the	DET
bracis-28360	333	9	generalizations	generalization	NOUN
bracis-28360	333	10	of	of	ADP
bracis-28360	333	11	the	the	DET
bracis-28360	333	12	choquet	choquet	NOUN
bracis-28360	333	13	integral	integral	ADJ
bracis-28360	333	14	:	:	PUNCT
bracis-28360	333	15	from	from	ADP
bracis-28360	333	16	aggregation	aggregation	NOUN
bracis-28360	333	17	and	and	CCONJ
bracis-28360	333	18	pre	pre	NOUN
bracis-28360	333	19	-	-	NOUN
bracis-28360	333	20	aggregation	aggregation	NOUN
bracis-28360	333	21	to	to	PART
bracis-28360	333	22	ordered	order	VERB
bracis-28360	333	23	directionally	directionally	ADV
bracis-28360	333	24	monotone	monotone	ADJ
bracis-28360	333	25	functions	function	NOUN
bracis-28360	333	26	.	.	PUNCT
bracis-28360	334	1	inf	inf	PROPN
bracis-28360	334	2	.	.	PUNCT
bracis-28360	334	3	fusion	fusion	PROPN
bracis-28360	334	4	57	57	NUM
bracis-28360	334	5	,	,	PUNCT
bracis-28360	334	6	27–43	27–43	NUM
bracis-28360	334	7	(	(	PUNCT
bracis-28360	334	8	2020	2020	NUM
bracis-28360	334	9	)	)	PUNCT
bracis-28360	334	10	article	article	NOUN
bracis-28360	334	11	  	  	SPACE
bracis-28360	334	12	google	google	PROPN
bracis-28360	334	13	scholar	scholar	NOUN
bracis-28360	334	14	  	  	SPACE
bracis-28360	334	15	hodges	hodge	NOUN
bracis-28360	334	16	,	,	PUNCT
bracis-28360	334	17	j.l	j.l	PROPN
bracis-28360	334	18	.	.	PROPN
bracis-28360	334	19	,	,	PUNCT
bracis-28360	334	20	lehmann	lehmann	PROPN
bracis-28360	334	21	,	,	PUNCT
bracis-28360	334	22	e.l	e.l	PROPN
bracis-28360	334	23	.	.	PROPN
bracis-28360	334	24	:	:	PUNCT
bracis-28360	334	25	ranks	rank	VERB
bracis-28360	334	26	methods	method	NOUN
bracis-28360	334	27	for	for	ADP
bracis-28360	334	28	combination	combination	NOUN
bracis-28360	334	29	of	of	ADP
bracis-28360	334	30	independent	independent	ADJ
bracis-28360	334	31	experiments	experiment	NOUN
bracis-28360	334	32	in	in	ADP
bracis-28360	334	33	analysis	analysis	NOUN
bracis-28360	334	34	of	of	ADP
bracis-28360	334	35	variance	variance	NOUN
bracis-28360	334	36	.	.	PUNCT
bracis-28360	335	1	ann	ann	PROPN
bracis-28360	335	2	.	.	PUNCT
bracis-28360	335	3	math	math	PROPN
bracis-28360	335	4	.	.	PUNCT
bracis-28360	336	1	stat	stat	PROPN
bracis-28360	336	2	.	.	PUNCT
bracis-28360	337	1	33	33	NUM
bracis-28360	337	2	,	,	PUNCT
bracis-28360	337	3	482–497	482–497	NUM
bracis-28360	337	4	(	(	PUNCT
bracis-28360	337	5	1962	1962	NUM
bracis-28360	337	6	)	)	PUNCT
bracis-28360	337	7	article	article	NOUN
bracis-28360	337	8	  	  	SPACE
bracis-28360	337	9	mathscinet	mathscinet	NOUN
bracis-28360	337	10	  	  	SPACE
bracis-28360	337	11	math	math	NOUN
bracis-28360	337	12	  	  	SPACE
bracis-28360	337	13	google	google	PROPN
bracis-28360	337	14	scholar	scholar	NOUN
bracis-28360	337	15	  	  	SPACE
bracis-28360	337	16	holm	holm	NOUN
bracis-28360	337	17	,	,	PUNCT
bracis-28360	337	18	s.	s.	PROPN
bracis-28360	337	19	:	:	PUNCT
bracis-28360	337	20	a	a	DET
bracis-28360	337	21	simple	simple	ADJ
bracis-28360	337	22	sequentially	sequentially	ADV
bracis-28360	337	23	rejective	rejective	ADJ
bracis-28360	337	24	multiple	multiple	ADJ
bracis-28360	337	25	test	test	NOUN
bracis-28360	337	26	procedure	procedure	NOUN
bracis-28360	337	27	.	.	PUNCT
bracis-28360	338	1	scand	scand	PROPN
bracis-28360	338	2	.	.	PUNCT
bracis-28360	339	1	j.	j.	PROPN
bracis-28360	339	2	stat	stat	PROPN
bracis-28360	339	3	.	.	PUNCT
bracis-28360	340	1	6	6	NUM
bracis-28360	340	2	,	,	PUNCT
bracis-28360	340	3	65–70	65–70	NUM
bracis-28360	340	4	(	(	PUNCT
bracis-28360	340	5	1979	1979	NUM
bracis-28360	340	6	)	)	PUNCT
bracis-28360	340	7	mathscinet	mathscinet	NOUN
bracis-28360	340	8	  	  	SPACE
bracis-28360	340	9	math	math	NOUN
bracis-28360	340	10	  	  	SPACE
bracis-28360	340	11	google	google	PROPN
bracis-28360	340	12	scholar	scholar	NOUN
bracis-28360	340	13	  	  	SPACE
bracis-28360	340	14	ishibuchi	ishibuchi	NOUN
bracis-28360	340	15	,	,	PUNCT
bracis-28360	340	16	h.	h.	PROPN
bracis-28360	340	17	,	,	PUNCT
bracis-28360	340	18	nakashima	nakashima	PROPN
bracis-28360	340	19	,	,	PUNCT
bracis-28360	340	20	t.	t.	PROPN
bracis-28360	340	21	:	:	PUNCT
bracis-28360	340	22	effect	effect	NOUN
bracis-28360	340	23	of	of	ADP
bracis-28360	340	24	rule	rule	NOUN
bracis-28360	340	25	weights	weight	NOUN
bracis-28360	340	26	in	in	ADP
bracis-28360	340	27	fuzzy	fuzzy	ADJ
bracis-28360	340	28	rule	rule	NOUN
bracis-28360	340	29	-	-	PUNCT
bracis-28360	340	30	based	base	VERB
bracis-28360	340	31	classification	classification	NOUN
bracis-28360	340	32	systems	system	NOUN
bracis-28360	340	33	.	.	PUNCT
bracis-28360	341	1	fuzzy	fuzzy	ADJ
bracis-28360	341	2	syst	syst	PROPN
bracis-28360	341	3	.	.	PUNCT
bracis-28360	342	1	ieee	ieee	PROPN
bracis-28360	342	2	trans	trans	PROPN
bracis-28360	342	3	.	.	PUNCT
bracis-28360	343	1	9(4	9(4	NUM
bracis-28360	343	2	)	)	PUNCT
bracis-28360	343	3	,	,	PUNCT
bracis-28360	343	4	506–515	506–515	NUM
bracis-28360	343	5	(	(	PUNCT
bracis-28360	343	6	2001	2001	NUM
bracis-28360	343	7	)	)	PUNCT
bracis-28360	343	8	article	article	NOUN
bracis-28360	343	9	  	  	SPACE
bracis-28360	343	10	google	google	PROPN
bracis-28360	343	11	scholar	scholar	NOUN
bracis-28360	343	12	  	  	SPACE
bracis-28360	343	13	ishibuchi	ishibuchi	NOUN
bracis-28360	343	14	,	,	PUNCT
bracis-28360	343	15	h.	h.	PROPN
bracis-28360	343	16	,	,	PUNCT
bracis-28360	343	17	nakashima	nakashima	PROPN
bracis-28360	343	18	,	,	PUNCT
bracis-28360	343	19	t.	t.	PROPN
bracis-28360	343	20	,	,	PUNCT
bracis-28360	343	21	nii	nii	PROPN
bracis-28360	343	22	,	,	PUNCT
bracis-28360	343	23	m.	m.	NOUN
bracis-28360	343	24	:	:	PUNCT
bracis-28360	343	25	classification	classification	NOUN
bracis-28360	343	26	and	and	CCONJ
bracis-28360	343	27	modeling	modeling	NOUN
bracis-28360	343	28	with	with	ADP
bracis-28360	343	29	linguistic	linguistic	ADJ
bracis-28360	343	30	information	information	NOUN
bracis-28360	343	31	granules	granule	NOUN
bracis-28360	343	32	,	,	PUNCT
bracis-28360	343	33	advanced	advanced	ADJ
bracis-28360	343	34	approaches	approach	NOUN
bracis-28360	343	35	to	to	ADP
bracis-28360	343	36	linguistic	linguistic	ADJ
bracis-28360	343	37	data	datum	NOUN
bracis-28360	343	38	mining	mining	NOUN
bracis-28360	343	39	.	.	PUNCT
bracis-28360	344	1	advanced	advanced	ADJ
bracis-28360	344	2	information	information	NOUN
bracis-28360	344	3	processing	processing	NOUN
bracis-28360	344	4	.	.	PUNCT
bracis-28360	345	1	springer	springer	NOUN
bracis-28360	345	2	,	,	PUNCT
bracis-28360	345	3	berlin	berlin	PROPN
bracis-28360	345	4	,	,	PUNCT
bracis-28360	345	5	heidelberg	heidelberg	PROPN
bracis-28360	345	6	(	(	PUNCT
bracis-28360	345	7	2005	2005	NUM
bracis-28360	345	8	)	)	PUNCT
bracis-28360	345	9	.	.	PUNCT
bracis-28360	346	1	https://doi.org/10.1007/b138232	https://doi.org/10.1007/b138232	PROPN
bracis-28360	346	2	ko	ko	PROPN
bracis-28360	346	3	,	,	PUNCT
bracis-28360	346	4	l.	l.	PROPN
bracis-28360	346	5	,	,	PUNCT
bracis-28360	346	6	et	et	PROPN
bracis-28360	346	7	al	al	PROPN
bracis-28360	346	8	.	.	PROPN
bracis-28360	346	9	:	:	PUNCT
bracis-28360	346	10	multimodal	multimodal	ADJ
bracis-28360	346	11	fuzzy	fuzzy	ADJ
bracis-28360	346	12	fusion	fusion	NOUN
bracis-28360	346	13	for	for	ADP
bracis-28360	346	14	enhancing	enhance	VERB
bracis-28360	346	15	the	the	DET
bracis-28360	346	16	motor	motor	NOUN
bracis-28360	346	17	-	-	PUNCT
bracis-28360	346	18	imagery	imagery	NOUN
bracis-28360	346	19	-	-	PUNCT
bracis-28360	346	20	based	base	VERB
bracis-28360	346	21	brain	brain	NOUN
bracis-28360	346	22	computer	computer	NOUN
bracis-28360	346	23	interface	interface	NOUN
bracis-28360	346	24	.	.	PUNCT
bracis-28360	347	1	ieee	ieee	NOUN
bracis-28360	347	2	comput	comput	PROPN
bracis-28360	347	3	.	.	PUNCT
bracis-28360	348	1	intell	intell	PROPN
bracis-28360	348	2	.	.	PUNCT
bracis-28360	349	1	mag	mag	INTJ
bracis-28360	349	2	.	.	PUNCT
bracis-28360	350	1	14(1	14(1	NUM
bracis-28360	350	2	)	)	PUNCT
bracis-28360	350	3	,	,	PUNCT
bracis-28360	350	4	96–106	96–106	NUM
bracis-28360	350	5	(	(	PUNCT
bracis-28360	350	6	2019	2019	NUM
bracis-28360	350	7	)	)	PUNCT
bracis-28360	350	8	article	article	NOUN
bracis-28360	350	9	  	  	SPACE
bracis-28360	350	10	google	google	PROPN
bracis-28360	350	11	scholar	scholar	NOUN
bracis-28360	350	12	  	  	SPACE
bracis-28360	350	13	lucca	lucca	PROPN
bracis-28360	350	14	,	,	PUNCT
bracis-28360	350	15	g.	g.	PROPN
bracis-28360	350	16	,	,	PUNCT
bracis-28360	350	17	dimuro	dimuro	PROPN
bracis-28360	350	18	,	,	PUNCT
bracis-28360	350	19	g.p	g.p	PROPN
bracis-28360	350	20	.	.	PROPN
bracis-28360	350	21	,	,	PUNCT
bracis-28360	350	22	fernandez	fernandez	PROPN
bracis-28360	350	23	,	,	PUNCT
bracis-28360	350	24	j.	j.	PROPN
bracis-28360	350	25	,	,	PUNCT
bracis-28360	350	26	bustince	bustince	NOUN
bracis-28360	350	27	,	,	PUNCT
bracis-28360	350	28	h.	h.	NOUN
bracis-28360	350	29	,	,	PUNCT
bracis-28360	350	30	bedregal	bedregal	PROPN
bracis-28360	350	31	,	,	PUNCT
bracis-28360	350	32	b.	b.	PROPN
bracis-28360	350	33	,	,	PUNCT
bracis-28360	350	34	sanz	sanz	PROPN
bracis-28360	350	35	,	,	PUNCT
bracis-28360	350	36	j.a	j.a	PROPN
bracis-28360	350	37	.	.	PROPN
bracis-28360	350	38	:	:	PUNCT
bracis-28360	351	1	improving	improve	VERB
bracis-28360	351	2	the	the	DET
bracis-28360	351	3	performance	performance	NOUN
bracis-28360	351	4	of	of	ADP
bracis-28360	351	5	fuzzy	fuzzy	ADJ
bracis-28360	351	6	rule	rule	NOUN
bracis-28360	351	7	-	-	PUNCT
bracis-28360	351	8	based	base	VERB
bracis-28360	351	9	classification	classification	NOUN
bracis-28360	351	10	systems	system	NOUN
bracis-28360	351	11	based	base	VERB
bracis-28360	351	12	on	on	ADP
bracis-28360	351	13	a	a	DET
bracis-28360	351	14	nonaveraging	nonaveraging	ADJ
bracis-28360	351	15	generalization	generalization	NOUN
bracis-28360	351	16	of	of	ADP
bracis-28360	351	17	cc	cc	NOUN
bracis-28360	351	18	-	-	PUNCT
bracis-28360	351	19	integrals	integral	NOUN
bracis-28360	351	20	named	name	VERB
bracis-28360	351	21	\(c_{f_1f_2}\)-integrals	\(c_{f_1f_2}\)-integral	NOUN
bracis-28360	351	22	.	.	PUNCT
bracis-28360	352	1	ieee	ieee	PROPN
bracis-28360	352	2	trans	trans	PROPN
bracis-28360	352	3	.	.	PUNCT
bracis-28360	352	4	fuzzy	fuzzy	ADJ
bracis-28360	352	5	syst	syst	PROPN
bracis-28360	352	6	.	.	PUNCT
bracis-28360	352	7	27(1	27(1	NUM
bracis-28360	352	8	)	)	PUNCT
bracis-28360	352	9	,	,	PUNCT
bracis-28360	352	10	124–134	124–134	NUM
bracis-28360	352	11	(	(	PUNCT
bracis-28360	352	12	2019	2019	NUM
bracis-28360	352	13	)	)	PUNCT
bracis-28360	352	14	article	article	NOUN
bracis-28360	352	15	  	  	SPACE
bracis-28360	352	16	google	google	PROPN
bracis-28360	352	17	scholar	scholar	NOUN
bracis-28360	352	18	  	  	SPACE
bracis-28360	352	19	lucca	lucca	PROPN
bracis-28360	352	20	,	,	PUNCT
bracis-28360	352	21	g.	g.	PROPN
bracis-28360	352	22	,	,	PUNCT
bracis-28360	352	23	sanz	sanz	PROPN
bracis-28360	352	24	,	,	PUNCT
bracis-28360	352	25	j.	j.	PROPN
bracis-28360	352	26	,	,	PUNCT
bracis-28360	352	27	pereira	pereira	PROPN
bracis-28360	352	28	dimuro	dimuro	PROPN
bracis-28360	352	29	,	,	PUNCT
bracis-28360	352	30	g.	g.	PROPN
bracis-28360	352	31	,	,	PUNCT
bracis-28360	352	32	bedregal	bedregal	PROPN
bracis-28360	352	33	,	,	PUNCT
bracis-28360	352	34	b.	b.	PROPN
bracis-28360	352	35	,	,	PUNCT
bracis-28360	352	36	mesiar	mesiar	PROPN
bracis-28360	352	37	,	,	PUNCT
bracis-28360	352	38	r.	r.	PROPN
bracis-28360	352	39	,	,	PUNCT
bracis-28360	352	40	kolesárová	kolesárová	PROPN
bracis-28360	352	41	,	,	PUNCT
bracis-28360	352	42	a.	a.	NOUN
bracis-28360	352	43	,	,	PUNCT
bracis-28360	352	44	bustince	bustince	NOUN
bracis-28360	352	45	sola	sola	PROPN
bracis-28360	352	46	,	,	PUNCT
bracis-28360	352	47	h.	h.	PROPN
bracis-28360	352	48	:	:	PUNCT
bracis-28360	352	49	pre	pre	ADJ
bracis-28360	352	50	-	-	ADJ
bracis-28360	352	51	aggregation	aggregation	NOUN
bracis-28360	352	52	functions	function	NOUN
bracis-28360	352	53	:	:	PUNCT
bracis-28360	352	54	construction	construction	NOUN
bracis-28360	352	55	and	and	CCONJ
bracis-28360	352	56	an	an	DET
bracis-28360	352	57	application	application	NOUN
bracis-28360	352	58	.	.	PUNCT
bracis-28360	353	1	ieee	ieee	PROPN
bracis-28360	353	2	trans	trans	PROPN
bracis-28360	353	3	.	.	PUNCT
bracis-28360	353	4	fuzzy	fuzzy	ADJ
bracis-28360	353	5	syst	syst	PROPN
bracis-28360	353	6	.	.	PUNCT
bracis-28360	354	1	24(2	24(2	NUM
bracis-28360	354	2	)	)	PUNCT
bracis-28360	354	3	,	,	PUNCT
bracis-28360	354	4	260–272	260–272	NUM
bracis-28360	354	5	(	(	PUNCT
bracis-28360	354	6	2016	2016	NUM
bracis-28360	354	7	)	)	PUNCT
bracis-28360	354	8	article	article	NOUN
bracis-28360	354	9	  	  	SPACE
bracis-28360	354	10	math	math	NOUN
bracis-28360	354	11	  	  	SPACE
bracis-28360	354	12	google	google	PROPN
bracis-28360	354	13	scholar	scholar	NOUN
bracis-28360	354	14	  	  	SPACE
bracis-28360	354	15	lucca	lucca	PROPN
bracis-28360	354	16	,	,	PUNCT
bracis-28360	354	17	g.	g.	PROPN
bracis-28360	354	18	,	,	PUNCT
bracis-28360	354	19	sanz	sanz	PROPN
bracis-28360	354	20	,	,	PUNCT
bracis-28360	354	21	j.a	j.a	PROPN
bracis-28360	354	22	.	.	PROPN
bracis-28360	354	23	,	,	PUNCT
bracis-28360	354	24	dimuro	dimuro	PROPN
bracis-28360	354	25	,	,	PUNCT
bracis-28360	354	26	g.p	g.p	PROPN
bracis-28360	354	27	.	.	PROPN
bracis-28360	354	28	,	,	PUNCT
bracis-28360	354	29	borges	borges	PROPN
bracis-28360	354	30	,	,	PUNCT
bracis-28360	354	31	e.n	e.n	PROPN
bracis-28360	354	32	.	.	PROPN
bracis-28360	354	33	,	,	PUNCT
bracis-28360	354	34	santos	santos	PROPN
bracis-28360	354	35	,	,	PUNCT
bracis-28360	354	36	h.	h.	PROPN
bracis-28360	354	37	,	,	PUNCT
bracis-28360	354	38	bustince	bustince	NOUN
bracis-28360	354	39	,	,	PUNCT
bracis-28360	354	40	h.	h.	NOUN
bracis-28360	354	41	:	:	PUNCT
bracis-28360	354	42	analyzing	analyze	VERB
bracis-28360	354	43	the	the	DET
bracis-28360	354	44	performance	performance	NOUN
bracis-28360	354	45	of	of	ADP
bracis-28360	354	46	different	different	ADJ
bracis-28360	354	47	fuzzy	fuzzy	ADJ
bracis-28360	354	48	measures	measure	NOUN
bracis-28360	354	49	with	with	ADP
bracis-28360	354	50	generalizations	generalization	NOUN
bracis-28360	354	51	of	of	ADP
bracis-28360	354	52	the	the	DET
bracis-28360	354	53	choquet	choquet	NOUN
bracis-28360	354	54	integral	integral	ADJ
bracis-28360	354	55	in	in	ADP
bracis-28360	354	56	classification	classification	NOUN
bracis-28360	354	57	problems	problem	NOUN
bracis-28360	354	58	.	.	PUNCT
bracis-28360	355	1	in	in	ADP
bracis-28360	355	2	:	:	PUNCT
bracis-28360	355	3	2019	2019	NUM
bracis-28360	355	4	fuzz	fuzz	NOUN
bracis-28360	355	5	-	-	PUNCT
bracis-28360	355	6	ieee	ieee	NOUN
bracis-28360	355	7	,	,	PUNCT
bracis-28360	355	8	pp	pp	ADJ
bracis-28360	355	9	.	.	PUNCT
bracis-28360	356	1	1–6	1–6	NUM
bracis-28360	356	2	(	(	PUNCT
bracis-28360	356	3	2019	2019	NUM
bracis-28360	356	4	)	)	PUNCT
bracis-28360	356	5	google	google	PROPN
bracis-28360	356	6	scholar	scholar	NOUN
bracis-28360	356	7	  	  	SPACE
bracis-28360	356	8	lucca	lucca	PROPN
bracis-28360	356	9	,	,	PUNCT
bracis-28360	356	10	g.	g.	PROPN
bracis-28360	356	11	,	,	PUNCT
bracis-28360	356	12	et	et	PROPN
bracis-28360	356	13	al	al	PROPN
bracis-28360	356	14	.	.	PROPN
bracis-28360	356	15	:	:	PUNCT
bracis-28360	357	1	cc	cc	NOUN
bracis-28360	357	2	-	-	NOUN
bracis-28360	357	3	integrals	integral	NOUN
bracis-28360	357	4	:	:	PUNCT
bracis-28360	357	5	choquet	choquet	NOUN
bracis-28360	357	6	-	-	PUNCT
bracis-28360	357	7	like	like	ADJ
bracis-28360	357	8	copula	copula	NOUN
bracis-28360	357	9	-	-	PUNCT
bracis-28360	357	10	based	base	VERB
bracis-28360	357	11	aggregation	aggregation	NOUN
bracis-28360	357	12	functions	function	NOUN
bracis-28360	357	13	and	and	CCONJ
bracis-28360	357	14	its	its	PRON
bracis-28360	357	15	application	application	NOUN
bracis-28360	357	16	in	in	ADP
bracis-28360	357	17	fuzzy	fuzzy	ADJ
bracis-28360	357	18	rule	rule	NOUN
bracis-28360	357	19	-	-	PUNCT
bracis-28360	357	20	based	base	VERB
bracis-28360	357	21	classification	classification	NOUN
bracis-28360	357	22	systems	system	NOUN
bracis-28360	357	23	.	.	PUNCT
bracis-28360	358	1	kbs	kbs	PROPN
bracis-28360	358	2	119	119	NUM
bracis-28360	358	3	,	,	PUNCT
bracis-28360	358	4	32–43	32–43	NUM
bracis-28360	358	5	(	(	PUNCT
bracis-28360	358	6	2017	2017	NUM
bracis-28360	358	7	)	)	PUNCT
bracis-28360	358	8	google	google	PROPN
bracis-28360	358	9	scholar	scholar	NOUN
bracis-28360	358	10	  	  	SPACE
bracis-28360	358	11	lucca	lucca	PROPN
bracis-28360	358	12	,	,	PUNCT
bracis-28360	358	13	g.	g.	PROPN
bracis-28360	358	14	,	,	PUNCT
bracis-28360	358	15	sanz	sanz	PROPN
bracis-28360	358	16	,	,	PUNCT
bracis-28360	358	17	j.a	j.a	PROPN
bracis-28360	358	18	.	.	PROPN
bracis-28360	358	19	,	,	PUNCT
bracis-28360	358	20	dimuro	dimuro	PROPN
bracis-28360	358	21	,	,	PUNCT
bracis-28360	358	22	g.p	g.p	PROPN
bracis-28360	358	23	.	.	PROPN
bracis-28360	358	24	,	,	PUNCT
bracis-28360	358	25	bedregal	bedregal	PROPN
bracis-28360	358	26	,	,	PUNCT
bracis-28360	358	27	b.	b.	PROPN
bracis-28360	358	28	,	,	PUNCT
bracis-28360	358	29	bustince	bustince	NOUN
bracis-28360	358	30	,	,	PUNCT
bracis-28360	358	31	h.	h.	NOUN
bracis-28360	358	32	,	,	PUNCT
bracis-28360	358	33	mesiar	mesiar	PROPN
bracis-28360	358	34	,	,	PUNCT
bracis-28360	358	35	r.	r.	PROPN
bracis-28360	358	36	:	:	PUNCT
bracis-28360	358	37	cf	cf	NOUN
bracis-28360	358	38	-	-	PUNCT
bracis-28360	358	39	integrals	integral	NOUN
bracis-28360	358	40	:	:	PUNCT
bracis-28360	358	41	a	a	DET
bracis-28360	358	42	new	new	ADJ
bracis-28360	358	43	family	family	NOUN
bracis-28360	358	44	of	of	ADP
bracis-28360	358	45	pre	pre	ADJ
bracis-28360	358	46	-	-	ADJ
bracis-28360	358	47	aggregation	aggregation	ADJ
bracis-28360	358	48	functions	function	NOUN
bracis-28360	358	49	with	with	ADP
bracis-28360	358	50	application	application	NOUN
bracis-28360	358	51	to	to	ADP
bracis-28360	358	52	fuzzy	fuzzy	ADJ
bracis-28360	358	53	rule	rule	NOUN
bracis-28360	358	54	-	-	PUNCT
bracis-28360	358	55	based	base	VERB
bracis-28360	358	56	classification	classification	NOUN
bracis-28360	358	57	systems	system	NOUN
bracis-28360	358	58	.	.	PUNCT
bracis-28360	359	1	inf	inf	PROPN
bracis-28360	359	2	.	.	PUNCT
bracis-28360	360	1	sci	sci	PROPN
bracis-28360	360	2	.	.	PROPN
bracis-28360	361	1	435	435	NUM
bracis-28360	361	2	,	,	PUNCT
bracis-28360	361	3	94–110	94–110	PROPN
bracis-28360	361	4	(	(	PUNCT
bracis-28360	361	5	2018	2018	NUM
bracis-28360	361	6	)	)	PUNCT
bracis-28360	361	7	article	article	NOUN
bracis-28360	361	8	  	  	SPACE
bracis-28360	361	9	math	math	NOUN
bracis-28360	361	10	  	  	SPACE
bracis-28360	361	11	google	google	PROPN
bracis-28360	361	12	scholar	scholar	NOUN
bracis-28360	361	13	  	  	SPACE
bracis-28360	361	14	marco	marco	PROPN
bracis-28360	361	15	-	-	NOUN
bracis-28360	361	16	detchart	detchart	NOUN
bracis-28360	361	17	,	,	PUNCT
bracis-28360	361	18	c.	c.	PROPN
bracis-28360	361	19	,	,	PUNCT
bracis-28360	361	20	lucca	lucca	PROPN
bracis-28360	361	21	,	,	PUNCT
bracis-28360	361	22	g.	g.	PROPN
bracis-28360	361	23	,	,	PUNCT
bracis-28360	361	24	lopez	lopez	NOUN
bracis-28360	361	25	-	-	PUNCT
bracis-28360	361	26	molina	molina	PROPN
bracis-28360	361	27	,	,	PUNCT
bracis-28360	361	28	c.	c.	PROPN
bracis-28360	361	29	,	,	PUNCT
bracis-28360	361	30	de	de	PROPN
bracis-28360	361	31	miguel	miguel	PROPN
bracis-28360	361	32	,	,	PUNCT
bracis-28360	361	33	l.	l.	PROPN
bracis-28360	361	34	,	,	PUNCT
bracis-28360	361	35	pereira	pereira	PROPN
bracis-28360	361	36	dimuro	dimuro	PROPN
bracis-28360	361	37	,	,	PUNCT
bracis-28360	361	38	g.	g.	PROPN
bracis-28360	361	39	,	,	PUNCT
bracis-28360	361	40	bustince	bustince	NOUN
bracis-28360	361	41	,	,	PUNCT
bracis-28360	361	42	h.	h.	PROPN
bracis-28360	361	43	:	:	PUNCT
bracis-28360	361	44	neuro	neuro	PROPN
bracis-28360	361	45	-	-	PUNCT
bracis-28360	361	46	inspired	inspire	VERB
bracis-28360	361	47	edge	edge	NOUN
bracis-28360	361	48	feature	feature	NOUN
bracis-28360	361	49	fusion	fusion	NOUN
bracis-28360	361	50	using	use	VERB
bracis-28360	361	51	choquet	choquet	NOUN
bracis-28360	361	52	integrals	integral	NOUN
bracis-28360	361	53	.	.	PUNCT
bracis-28360	362	1	inf	inf	PROPN
bracis-28360	362	2	.	.	PUNCT
bracis-28360	363	1	sci	sci	PROPN
bracis-28360	363	2	.	.	PROPN
bracis-28360	364	1	581	581	NUM
bracis-28360	364	2	,	,	PUNCT
bracis-28360	364	3	740–754	740–754	NUM
bracis-28360	364	4	(	(	PUNCT
bracis-28360	364	5	2021	2021	NUM
bracis-28360	364	6	)	)	PUNCT
bracis-28360	364	7	article	article	NOUN
bracis-28360	364	8	  	  	SPACE
bracis-28360	364	9	google	google	PROPN
bracis-28360	364	10	scholar	scholar	NOUN
bracis-28360	364	11	  	  	SPACE
bracis-28360	364	12	mesiar	mesiar	NOUN
bracis-28360	364	13	,	,	PUNCT
bracis-28360	364	14	r.	r.	PROPN
bracis-28360	364	15	,	,	PUNCT
bracis-28360	364	16	kolesárová	kolesárová	PROPN
bracis-28360	364	17	,	,	PUNCT
bracis-28360	364	18	a.	a.	NOUN
bracis-28360	364	19	,	,	PUNCT
bracis-28360	364	20	bustince	bustince	NOUN
bracis-28360	364	21	,	,	PUNCT
bracis-28360	364	22	h.	h.	PROPN
bracis-28360	364	23	,	,	PUNCT
bracis-28360	364	24	dimuro	dimuro	PROPN
bracis-28360	364	25	,	,	PUNCT
bracis-28360	364	26	g.	g.	PROPN
bracis-28360	364	27	,	,	PUNCT
bracis-28360	364	28	bedregal	bedregal	PROPN
bracis-28360	364	29	,	,	PUNCT
bracis-28360	364	30	b.	b.	NOUN
bracis-28360	364	31	:	:	PUNCT
bracis-28360	365	1	fusion	fusion	NOUN
bracis-28360	365	2	functions	function	NOUN
bracis-28360	365	3	based	base	VERB
bracis-28360	365	4	discrete	discrete	ADJ
bracis-28360	365	5	choquet	choquet	NOUN
bracis-28360	365	6	-	-	PUNCT
bracis-28360	365	7	like	like	ADJ
bracis-28360	365	8	integrals	integral	NOUN
bracis-28360	365	9	.	.	PUNCT
bracis-28360	366	1	ejor	ejor	PROPN
bracis-28360	366	2	252(2	252(2	NUM
bracis-28360	366	3	)	)	PUNCT
bracis-28360	366	4	,	,	PUNCT
bracis-28360	366	5	601–609	601–609	NUM
bracis-28360	366	6	(	(	PUNCT
bracis-28360	366	7	2016	2016	NUM
bracis-28360	366	8	)	)	PUNCT
bracis-28360	366	9	article	article	NOUN
bracis-28360	366	10	  	  	SPACE
bracis-28360	366	11	mathscinet	mathscinet	NOUN
bracis-28360	366	12	  	  	SPACE
bracis-28360	366	13	math	math	NOUN
bracis-28360	366	14	  	  	SPACE
bracis-28360	366	15	google	google	PROPN
bracis-28360	366	16	scholar	scholar	NOUN
bracis-28360	366	17	  	  	SPACE
bracis-28360	366	18	sanz	sanz	PROPN
bracis-28360	366	19	,	,	PUNCT
bracis-28360	366	20	j.a	j.a	PROPN
bracis-28360	366	21	.	.	PROPN
bracis-28360	366	22	,	,	PUNCT
bracis-28360	366	23	bernardo	bernardo	PROPN
bracis-28360	366	24	,	,	PUNCT
bracis-28360	366	25	d.	d.	PROPN
bracis-28360	366	26	,	,	PUNCT
bracis-28360	366	27	herrera	herrera	PROPN
bracis-28360	366	28	,	,	PUNCT
bracis-28360	366	29	f.	f.	PROPN
bracis-28360	366	30	,	,	PUNCT
bracis-28360	366	31	bustince	bustince	NOUN
bracis-28360	366	32	,	,	PUNCT
bracis-28360	366	33	h.	h.	PROPN
bracis-28360	366	34	,	,	PUNCT
bracis-28360	366	35	hagras	hagras	PROPN
bracis-28360	366	36	,	,	PUNCT
bracis-28360	366	37	h.	h.	PROPN
bracis-28360	366	38	:	:	PUNCT
bracis-28360	366	39	a	a	DET
bracis-28360	366	40	compact	compact	ADJ
bracis-28360	366	41	evolutionary	evolutionary	ADJ
bracis-28360	366	42	interval	interval	NOUN
bracis-28360	366	43	-	-	PUNCT
bracis-28360	366	44	valued	value	VERB
bracis-28360	366	45	fuzzy	fuzzy	ADJ
bracis-28360	366	46	rule	rule	NOUN
bracis-28360	366	47	-	-	PUNCT
bracis-28360	366	48	based	base	VERB
bracis-28360	366	49	classification	classification	NOUN
bracis-28360	366	50	system	system	NOUN
bracis-28360	366	51	for	for	ADP
bracis-28360	366	52	the	the	DET
bracis-28360	366	53	modeling	modeling	NOUN
bracis-28360	366	54	and	and	CCONJ
bracis-28360	366	55	prediction	prediction	NOUN
bracis-28360	366	56	of	of	ADP
bracis-28360	366	57	real	real	ADJ
bracis-28360	366	58	-	-	PUNCT
bracis-28360	366	59	world	world	NOUN
bracis-28360	366	60	financial	financial	ADJ
bracis-28360	366	61	applications	application	NOUN
bracis-28360	366	62	with	with	ADP
bracis-28360	366	63	imbalanced	imbalanced	ADJ
bracis-28360	366	64	data	datum	NOUN
bracis-28360	366	65	.	.	PUNCT
bracis-28360	367	1	ieee	ieee	PROPN
bracis-28360	367	2	trans	trans	PROPN
bracis-28360	367	3	.	.	PUNCT
bracis-28360	367	4	fuzzy	fuzzy	ADJ
bracis-28360	367	5	syst	syst	PROPN
bracis-28360	367	6	.	.	PUNCT
bracis-28360	367	7	23(4	23(4	NUM
bracis-28360	367	8	)	)	PUNCT
bracis-28360	367	9	,	,	PUNCT
bracis-28360	367	10	973–990	973–990	NUM
bracis-28360	367	11	(	(	PUNCT
bracis-28360	367	12	2015	2015	NUM
bracis-28360	367	13	)	)	PUNCT
bracis-28360	367	14	article	article	NOUN
bracis-28360	367	15	  	  	SPACE
bracis-28360	367	16	google	google	PROPN
bracis-28360	367	17	scholar	scholar	NOUN
bracis-28360	367	18	  	  	SPACE
bracis-28360	367	19	wieczynski	wieczynski	NOUN
bracis-28360	367	20	,	,	PUNCT
bracis-28360	367	21	j.	j.	PROPN
bracis-28360	367	22	,	,	PUNCT
bracis-28360	367	23	et	et	PROPN
bracis-28360	367	24	al	al	PROPN
bracis-28360	367	25	.	.	PROPN
bracis-28360	367	26	:	:	PUNCT
bracis-28360	367	27	applying	apply	VERB
bracis-28360	367	28	d	d	PROPN
bracis-28360	367	29	-	-	PUNCT
bracis-28360	367	30	xchoquet	xchoquet	ADJ
bracis-28360	367	31	integrals	integral	NOUN
bracis-28360	367	32	in	in	ADP
bracis-28360	367	33	classification	classification	NOUN
bracis-28360	367	34	problems	problem	NOUN
bracis-28360	367	35	.	.	PUNCT
bracis-28360	368	1	in	in	ADP
bracis-28360	368	2	:	:	PUNCT
bracis-28360	368	3	2022	2022	NUM
bracis-28360	368	4	ieee	ieee	PROPN
bracis-28360	368	5	international	international	ADJ
bracis-28360	368	6	conference	conference	NOUN
bracis-28360	368	7	on	on	ADP
bracis-28360	368	8	fuzzy	fuzzy	ADJ
bracis-28360	368	9	systems	system	NOUN
bracis-28360	368	10	(	(	PUNCT
bracis-28360	368	11	fuzz	fuzz	NOUN
bracis-28360	368	12	-	-	PUNCT
bracis-28360	368	13	ieee	ieee	NOUN
bracis-28360	368	14	)	)	PUNCT
bracis-28360	368	15	,	,	PUNCT
bracis-28360	368	16	pp	pp	PROPN
bracis-28360	368	17	.	.	PUNCT
bracis-28360	369	1	1–7	1–7	NUM
bracis-28360	369	2	(	(	PUNCT
bracis-28360	369	3	2022	2022	NUM
bracis-28360	369	4	)	)	PUNCT
bracis-28360	369	5	google	google	PROPN
bracis-28360	369	6	scholar	scholar	NOUN
bracis-28360	369	7	  	  	SPACE
bracis-28360	369	8	wieczynski	wieczynski	NOUN
bracis-28360	369	9	,	,	PUNCT
bracis-28360	369	10	j.	j.	PROPN
bracis-28360	369	11	,	,	PUNCT
bracis-28360	369	12	et	et	PROPN
bracis-28360	369	13	al	al	PROPN
bracis-28360	369	14	.	.	PUNCT
bracis-28360	369	15	:	:	PUNCT
bracis-28360	369	16	\(dc_{f}\)-integrals	\(dc_{f}\)-integral	NOUN
bracis-28360	369	17	:	:	PUNCT
bracis-28360	369	18	generalizing	generalize	VERB
bracis-28360	369	19	c\(_{f}\)-integrals	c\(_{f}\)-integral	NOUN
bracis-28360	369	20	by	by	ADP
bracis-28360	369	21	means	mean	NOUN
bracis-28360	369	22	of	of	ADP
bracis-28360	369	23	restricted	restricted	ADJ
bracis-28360	369	24	dissimilarity	dissimilarity	NOUN
bracis-28360	369	25	functions	function	NOUN
bracis-28360	369	26	.	.	PUNCT
bracis-28360	370	1	ieee	ieee	PROPN
bracis-28360	370	2	tfs	tfs	PROPN
bracis-28360	370	3	31(1	31(1	NUM
bracis-28360	370	4	)	)	PUNCT
bracis-28360	370	5	,	,	PUNCT
bracis-28360	370	6	160–173	160–173	NUM
bracis-28360	370	7	(	(	PUNCT
bracis-28360	370	8	2023	2023	NUM
bracis-28360	370	9	)	)	PUNCT
bracis-28360	370	10	google	google	NOUN
bracis-28360	370	11	scholar	scholar	NOUN
bracis-28360	370	12	  	  	SPACE
bracis-28360	370	13	wieczynski	wieczynski	NOUN
bracis-28360	370	14	,	,	PUNCT
bracis-28360	370	15	j.c	j.c	PROPN
bracis-28360	370	16	.	.	PROPN
bracis-28360	370	17	,	,	PUNCT
bracis-28360	370	18	et	et	PROPN
bracis-28360	370	19	al	al	PROPN
bracis-28360	370	20	.	.	PUNCT
bracis-28360	370	21	:	:	PUNCT
bracis-28360	371	1	d	d	X
bracis-28360	371	2	-	-	PUNCT
bracis-28360	371	3	xc	xc	NOUN
bracis-28360	371	4	integrals	integral	NOUN
bracis-28360	371	5	:	:	PUNCT
bracis-28360	371	6	on	on	ADP
bracis-28360	371	7	the	the	DET
bracis-28360	371	8	generalization	generalization	NOUN
bracis-28360	371	9	of	of	ADP
bracis-28360	371	10	the	the	DET
bracis-28360	371	11	expanded	expand	VERB
bracis-28360	371	12	form	form	NOUN
bracis-28360	371	13	of	of	ADP
bracis-28360	371	14	the	the	DET
bracis-28360	371	15	choquet	choquet	NOUN
bracis-28360	371	16	integral	integral	ADJ
bracis-28360	371	17	by	by	ADP
bracis-28360	371	18	restricted	restrict	VERB
bracis-28360	371	19	dissimilarity	dissimilarity	NOUN
bracis-28360	371	20	functions	function	NOUN
bracis-28360	371	21	and	and	CCONJ
bracis-28360	371	22	their	their	PRON
bracis-28360	371	23	applications	application	NOUN
bracis-28360	371	24	.	.	PUNCT
bracis-28360	372	1	ieee	ieee	PROPN
bracis-28360	372	2	tfs	tfs	PROPN
bracis-28360	372	3	30(12	30(12	NUM
bracis-28360	372	4	)	)	PUNCT
bracis-28360	372	5	,	,	PUNCT
bracis-28360	372	6	5376–5389	5376–5389	NUM
bracis-28360	372	7	(	(	PUNCT
bracis-28360	372	8	2022	2022	NUM
bracis-28360	372	9	)	)	PUNCT
bracis-28360	372	10	google	google	NOUN
bracis-28360	372	11	scholar	scholar	NOUN
bracis-28360	372	12	  	  	SPACE
bracis-28360	372	13	download	download	NOUN
bracis-28360	372	14	references	reference	NOUN
bracis-28360	372	15	author	author	NOUN
bracis-28360	372	16	information	information	NOUN
bracis-28360	372	17	authors	author	NOUN
bracis-28360	372	18	and	and	CCONJ
bracis-28360	372	19	affiliations	affiliation	NOUN
bracis-28360	372	20	centro	centro	X
bracis-28360	372	21	de	de	X
bracis-28360	372	22	ciêcias	ciêcias	PROPN
bracis-28360	372	23	computacionais	computacionais	PROPN
bracis-28360	372	24	,	,	PUNCT
bracis-28360	372	25	univ	univ	PROPN
bracis-28360	372	26	.	.	PUNCT
bracis-28360	373	1	fed	fed	PROPN
bracis-28360	373	2	.	.	PUNCT
bracis-28360	374	1	do	do	VERB
bracis-28360	374	2	rio	rio	PROPN
bracis-28360	374	3	grande	grande	PROPN
bracis-28360	374	4	,	,	PUNCT
bracis-28360	374	5	porto	porto	PROPN
bracis-28360	374	6	alegre	alegre	PROPN
bracis-28360	374	7	,	,	PUNCT
bracis-28360	374	8	brazil	brazil	PROPN
bracis-28360	374	9	joelson	joelson	PROPN
bracis-28360	374	10	sartori	sartori	PROPN
bracis-28360	374	11	,	,	PUNCT
bracis-28360	374	12	 	 	SPACE
bracis-28360	374	13	giancarlo	giancarlo	PROPN
bracis-28360	374	14	lucca	lucca	PROPN
bracis-28360	374	15	,	,	PUNCT
bracis-28360	374	16	 	 	SPACE
bracis-28360	374	17	helida	helida	PROPN
bracis-28360	374	18	santos	santos	PROPN
bracis-28360	374	19	,	,	PUNCT
bracis-28360	374	20	 	 	SPACE
bracis-28360	374	21	eduardo	eduardo	PROPN
bracis-28360	374	22	borges	borges	PROPN
bracis-28360	374	23	 	 	SPACE
bracis-28360	374	24	&	&	CCONJ
bracis-28360	374	25	 	 	SPACE
bracis-28360	374	26	graçaliz	graçaliz	PROPN
bracis-28360	374	27	pereira	pereira	PROPN
bracis-28360	374	28	dimuro	dimuro	PROPN
bracis-28360	374	29	instituto	instituto	PROPN
bracis-28360	374	30	de	de	PROPN
bracis-28360	374	31	matemática	matemática	PROPN
bracis-28360	374	32	,	,	PUNCT
bracis-28360	374	33	estatística	estatística	PROPN
bracis-28360	374	34	e	e	PROPN
bracis-28360	374	35	física	física	PROPN
bracis-28360	374	36	,	,	PUNCT
bracis-28360	374	37	univ	univ	PROPN
bracis-28360	374	38	.	.	PUNCT
bracis-28360	375	1	fed	fed	PROPN
bracis-28360	375	2	.	.	PUNCT
bracis-28360	376	1	do	do	VERB
bracis-28360	376	2	rio	rio	PROPN
bracis-28360	376	3	grande	grande	PROPN
bracis-28360	376	4	,	,	PUNCT
bracis-28360	376	5	porto	porto	PROPN
bracis-28360	376	6	alegre	alegre	PROPN
bracis-28360	376	7	,	,	PUNCT
bracis-28360	376	8	brazil	brazil	PROPN
bracis-28360	376	9	tiago	tiago	PROPN
bracis-28360	376	10	asmus	asmus	PROPN
bracis-28360	376	11	departamento	departamento	PROPN
bracis-28360	376	12	de	de	PROPN
bracis-28360	376	13	informática	informática	PROPN
bracis-28360	376	14	e	e	PROPN
bracis-28360	376	15	matemática	matemática	PROPN
bracis-28360	376	16	aplicada	aplicada	PROPN
bracis-28360	376	17	,	,	PUNCT
bracis-28360	376	18	univ	univ	PROPN
bracis-28360	376	19	.	.	PUNCT
bracis-28360	377	1	fed	fed	PROPN
bracis-28360	377	2	.	.	PUNCT
bracis-28360	378	1	do	do	AUX
bracis-28360	378	2	rio	rio	PROPN
bracis-28360	378	3	grande	grande	PROPN
bracis-28360	378	4	do	do	VERB
bracis-28360	378	5	norte	norte	NOUN
bracis-28360	378	6	,	,	PUNCT
bracis-28360	378	7	natal	natal	NOUN
bracis-28360	378	8	,	,	PUNCT
bracis-28360	378	9	brazil	brazil	PROPN
bracis-28360	378	10	benjamin	benjamin	PROPN
bracis-28360	378	11	bedregal	bedregal	PROPN
bracis-28360	378	12	dept	dept	PROPN
bracis-28360	378	13	.	.	PUNCT
bracis-28360	379	1	estadistica	estadistica	PROPN
bracis-28360	379	2	,	,	PUNCT
bracis-28360	379	3	informa	informa	VERB
bracis-28360	379	4	.	.	PUNCT
bracis-28360	380	1	y	y	PROPN
bracis-28360	380	2	matem	matem	NOUN
bracis-28360	380	3	.	.	PUNCT
bracis-28360	380	4	,	,	PUNCT
bracis-28360	380	5	univ	univ	PROPN
bracis-28360	380	6	.	.	PUNCT
bracis-28360	381	1	publica	publica	PROPN
bracis-28360	381	2	de	de	PROPN
bracis-28360	381	3	navarra	navarra	PROPN
bracis-28360	381	4	,	,	PUNCT
bracis-28360	381	5	pamplona	pamplona	PROPN
bracis-28360	381	6	,	,	PUNCT
bracis-28360	381	7	spain	spain	PROPN
bracis-28360	381	8	humberto	humberto	PROPN
bracis-28360	381	9	bustince	bustince	NOUN
bracis-28360	381	10	authors	author	NOUN
bracis-28360	381	11	joelson	joelson	NOUN
bracis-28360	381	12	sartoriview	sartoriview	NOUN
bracis-28360	381	13	author	author	NOUN
bracis-28360	381	14	publications	publication	VERB
bracis-28360	381	15	search	search	NOUN
bracis-28360	381	16	author	author	NOUN
bracis-28360	381	17	on	on	ADP
bracis-28360	381	18	:	:	PUNCT
bracis-28360	381	19	pubmed	pubmed	PROPN
bracis-28360	381	20	 	 	SPACE
bracis-28360	381	21	google	google	PROPN
bracis-28360	381	22	scholar	scholar	PROPN
bracis-28360	381	23	giancarlo	giancarlo	PROPN
bracis-28360	381	24	luccaview	luccaview	PROPN
bracis-28360	381	25	author	author	NOUN
bracis-28360	381	26	publications	publication	NOUN
bracis-28360	381	27	search	search	NOUN
bracis-28360	381	28	author	author	NOUN
bracis-28360	381	29	on	on	ADP
bracis-28360	381	30	:	:	PUNCT
bracis-28360	381	31	pubmed	pubmed	PROPN
bracis-28360	381	32	 	 	SPACE
bracis-28360	381	33	google	google	PROPN
bracis-28360	381	34	scholar	scholar	PROPN
bracis-28360	381	35	tiago	tiago	PROPN
bracis-28360	381	36	asmusview	asmusview	PROPN
bracis-28360	381	37	author	author	NOUN
bracis-28360	381	38	publications	publication	NOUN
bracis-28360	381	39	search	search	NOUN
bracis-28360	381	40	author	author	NOUN
bracis-28360	381	41	on	on	ADP
bracis-28360	381	42	:	:	PUNCT
bracis-28360	381	43	pubmed	pubmed	PROPN
bracis-28360	381	44	 	 	SPACE
bracis-28360	381	45	google	google	PROPN
bracis-28360	381	46	scholar	scholar	NOUN
bracis-28360	381	47	helida	helida	PROPN
bracis-28360	381	48	santosview	santosview	NOUN
bracis-28360	381	49	author	author	NOUN
bracis-28360	381	50	publications	publication	NOUN
bracis-28360	381	51	search	search	NOUN
bracis-28360	381	52	author	author	NOUN
bracis-28360	381	53	on	on	ADP
bracis-28360	381	54	:	:	PUNCT
bracis-28360	381	55	pubmed	pubmed	PROPN
bracis-28360	381	56	 	 	SPACE
bracis-28360	381	57	google	google	PROPN
bracis-28360	381	58	scholar	scholar	PROPN
bracis-28360	381	59	eduardo	eduardo	PROPN
bracis-28360	381	60	borgesview	borgesview	PROPN
bracis-28360	381	61	author	author	NOUN
bracis-28360	381	62	publications	publication	NOUN
bracis-28360	381	63	search	search	NOUN
bracis-28360	381	64	author	author	NOUN
bracis-28360	381	65	on	on	ADP
bracis-28360	381	66	:	:	PUNCT
bracis-28360	381	67	pubmed	pubmed	PROPN
bracis-28360	381	68	 	 	SPACE
bracis-28360	381	69	google	google	PROPN
bracis-28360	381	70	scholar	scholar	PROPN
bracis-28360	381	71	benjamin	benjamin	PROPN
bracis-28360	381	72	bedregalview	bedregalview	PROPN
bracis-28360	381	73	author	author	NOUN
bracis-28360	381	74	publications	publication	NOUN
bracis-28360	381	75	search	search	NOUN
bracis-28360	381	76	author	author	NOUN
bracis-28360	381	77	on	on	ADP
bracis-28360	381	78	:	:	PUNCT
bracis-28360	381	79	pubmed	pubmed	PROPN
bracis-28360	381	80	 	 	SPACE
bracis-28360	381	81	google	google	PROPN
bracis-28360	381	82	scholar	scholar	PROPN
bracis-28360	381	83	humberto	humberto	PROPN
bracis-28360	381	84	bustinceview	bustinceview	NOUN
bracis-28360	381	85	author	author	NOUN
bracis-28360	381	86	publications	publication	VERB
bracis-28360	381	87	search	search	NOUN
bracis-28360	381	88	author	author	NOUN
bracis-28360	381	89	on	on	ADP
bracis-28360	381	90	:	:	PUNCT
bracis-28360	381	91	pubmed	pubmed	PROPN
bracis-28360	381	92	 	 	SPACE
bracis-28360	381	93	google	google	PROPN
bracis-28360	381	94	scholar	scholar	NOUN
bracis-28360	381	95	graçaliz	graçaliz	PROPN
bracis-28360	381	96	pereira	pereira	PROPN
bracis-28360	381	97	dimuroview	dimuroview	PROPN
bracis-28360	381	98	author	author	NOUN
bracis-28360	381	99	publications	publication	NOUN
bracis-28360	381	100	search	search	NOUN
bracis-28360	381	101	author	author	NOUN
bracis-28360	381	102	on	on	ADP
bracis-28360	381	103	:	:	PUNCT
bracis-28360	381	104	pubmed	pubmed	PROPN
bracis-28360	381	105	 	 	SPACE
bracis-28360	381	106	google	google	PROPN
bracis-28360	381	107	scholar	scholar	NOUN
bracis-28360	381	108	corresponding	correspond	VERB
bracis-28360	381	109	author	author	NOUN
bracis-28360	381	110	correspondence	correspondence	NOUN
bracis-28360	381	111	to	to	ADP
bracis-28360	381	112	giancarlo	giancarlo	PROPN
bracis-28360	381	113	lucca	lucca	PROPN
bracis-28360	381	114	.	.	PUNCT
bracis-28360	382	1	editor	editor	NOUN
bracis-28360	382	2	information	information	NOUN
bracis-28360	382	3	editors	editor	NOUN
bracis-28360	382	4	and	and	CCONJ
bracis-28360	382	5	affiliations	affiliation	NOUN
bracis-28360	382	6	federal	federal	PROPN
bracis-28360	382	7	university	university	PROPN
bracis-28360	382	8	of	of	ADP
bracis-28360	382	9	são	são	PROPN
bracis-28360	382	10	carlos	carlos	PROPN
bracis-28360	382	11	,	,	PUNCT
bracis-28360	382	12	são	são	PROPN
bracis-28360	382	13	carlos	carlos	PROPN
bracis-28360	382	14	,	,	PUNCT
bracis-28360	382	15	brazil	brazil	PROPN
bracis-28360	382	16	murilo	murilo	PROPN
bracis-28360	382	17	c.	c.	PROPN
bracis-28360	382	18	naldi	naldi	PROPN
bracis-28360	382	19	centro	centro	PROPN
bracis-28360	382	20	universitario	universitario	PROPN
bracis-28360	382	21	da	da	PROPN
bracis-28360	382	22	fei	fei	PROPN
bracis-28360	382	23	,	,	PUNCT
bracis-28360	382	24	são	são	PROPN
bracis-28360	382	25	bernardo	bernardo	PROPN
bracis-28360	382	26	do	do	AUX
bracis-28360	382	27	campo	campo	PROPN
bracis-28360	382	28	,	,	PUNCT
bracis-28360	382	29	brazil	brazil	PROPN
bracis-28360	382	30	reinaldo	reinaldo	PROPN
bracis-28360	382	31	a.	a.	PROPN
bracis-28360	382	32	c.	c.	PROPN
bracis-28360	382	33	bianchi	bianchi	PROPN
bracis-28360	382	34	rights	right	NOUN
bracis-28360	382	35	and	and	CCONJ
bracis-28360	382	36	permissions	permission	NOUN
bracis-28360	382	37	reprints	reprint	NOUN
bracis-28360	382	38	and	and	CCONJ
bracis-28360	382	39	permissions	permission	VERB
bracis-28360	382	40	copyright	copyright	NOUN
bracis-28360	382	41	information	information	NOUN
bracis-28360	382	42	©	©	ADP
bracis-28360	382	43	2023	2023	NUM
bracis-28360	382	44	the	the	DET
bracis-28360	382	45	author(s	author(s	NOUN
bracis-28360	382	46	)	)	PUNCT
bracis-28360	382	47	,	,	PUNCT
bracis-28360	382	48	under	under	ADP
bracis-28360	382	49	exclusive	exclusive	ADJ
bracis-28360	382	50	license	license	NOUN
bracis-28360	382	51	to	to	ADP
bracis-28360	382	52	springer	springer	NOUN
bracis-28360	382	53	nature	nature	PROPN
bracis-28360	382	54	switzerland	switzerland	PROPN
bracis-28360	382	55	ag	ag	PROPN
bracis-28360	382	56	about	about	ADP
bracis-28360	382	57	this	this	DET
bracis-28360	382	58	paper	paper	NOUN
bracis-28360	382	59	cite	cite	VERB
bracis-28360	382	60	this	this	DET
bracis-28360	382	61	paper	paper	NOUN
bracis-28360	382	62	sartori	sartori	NOUN
bracis-28360	382	63	,	,	PUNCT
bracis-28360	382	64	j.	j.	PROPN
bracis-28360	382	65	et	et	PROPN
bracis-28360	382	66	al	al	PROPN
bracis-28360	382	67	.	.	PROPN
bracis-28360	383	1	(	(	PUNCT
bracis-28360	383	2	2023	2023	NUM
bracis-28360	383	3	)	)	PUNCT
bracis-28360	383	4	.	.	PUNCT
bracis-28360	384	1	d	d	X
bracis-28360	384	2	-	-	PUNCT
bracis-28360	384	3	cc	cc	NOUN
bracis-28360	384	4	integrals	integral	NOUN
bracis-28360	384	5	:	:	PUNCT
bracis-28360	384	6	generalizing	generalize	VERB
bracis-28360	384	7	cc	cc	NOUN
bracis-28360	384	8	-	-	NOUN
bracis-28360	384	9	integrals	integral	NOUN
bracis-28360	384	10	by	by	ADP
bracis-28360	384	11	 	 	SPACE
bracis-28360	384	12	restricted	restrict	VERB
bracis-28360	384	13	dissimilarity	dissimilarity	NOUN
bracis-28360	384	14	functions	function	NOUN
bracis-28360	384	15	with	with	ADP
bracis-28360	384	16	 	 	SPACE
bracis-28360	384	17	applications	application	NOUN
bracis-28360	384	18	to	to	PART
bracis-28360	384	19	 	 	SPACE
bracis-28360	384	20	fuzzy	fuzzy	ADJ
bracis-28360	384	21	-	-	PUNCT
bracis-28360	384	22	rule	rule	NOUN
bracis-28360	384	23	based	base	VERB
bracis-28360	384	24	systems	system	NOUN
bracis-28360	384	25	.	.	PUNCT
bracis-28360	385	1	in	in	ADP
bracis-28360	385	2	:	:	PUNCT
bracis-28360	385	3	naldi	naldi	PROPN
bracis-28360	385	4	,	,	PUNCT
bracis-28360	385	5	m.c	m.c	PROPN
bracis-28360	385	6	.	.	PROPN
bracis-28360	385	7	,	,	PUNCT
bracis-28360	385	8	bianchi	bianchi	PROPN
bracis-28360	385	9	,	,	PUNCT
bracis-28360	385	10	r.a.c	r.a.c	ADP
bracis-28360	385	11	.	.	PUNCT
bracis-28360	385	12	(	(	PUNCT
bracis-28360	385	13	eds	ed	NOUN
bracis-28360	385	14	)	)	PUNCT
bracis-28360	385	15	intelligent	intelligent	ADJ
bracis-28360	385	16	systems	system	NOUN
bracis-28360	385	17	.	.	PUNCT
bracis-28360	386	1	bracis	bracis	PROPN
bracis-28360	386	2	2023	2023	NUM
bracis-28360	386	3	.	.	PUNCT
bracis-28360	387	1	lecture	lecture	NOUN
bracis-28360	387	2	notes	note	NOUN
bracis-28360	387	3	in	in	ADP
bracis-28360	387	4	computer	computer	NOUN
bracis-28360	387	5	science	science	NOUN
bracis-28360	387	6	(	(	PUNCT
bracis-28360	387	7	)	)	PUNCT
bracis-28360	387	8	,	,	PUNCT
bracis-28360	387	9	vol	vol	NOUN
bracis-28360	387	10	14195	14195	NUM
bracis-28360	387	11	.	.	PUNCT
bracis-28360	388	1	springer	springer	NOUN
bracis-28360	388	2	,	,	PUNCT
bracis-28360	388	3	cham	cham	PROPN
bracis-28360	388	4	.	.	PUNCT
bracis-28360	389	1	https://doi.org/10.1007/978-3-031-45368-7_16	https://doi.org/10.1007/978-3-031-45368-7_16	PUNCT
bracis-28360	389	2	download	download	NOUN
bracis-28360	389	3	citation	citation	NOUN
bracis-28360	389	4	.ris	.ris	PUNCT
bracis-28360	389	5	.enw	.enw	PROPN
bracis-28360	389	6	.bib	.bib	PUNCT
bracis-28360	390	1	doi	doi	PROPN
bracis-28360	390	2	:	:	PUNCT
bracis-28360	390	3	https://doi.org/10.1007/978-3-031-45368-7_16	https://doi.org/10.1007/978-3-031-45368-7_16	PUNCT
bracis-28360	390	4	published	publish	VERB
bracis-28360	390	5	:	:	PUNCT
bracis-28360	390	6	12	12	NUM
bracis-28360	390	7	october	october	PROPN
bracis-28360	390	8	2023	2023	NUM
bracis-28360	390	9	publisher	publisher	NOUN
bracis-28360	390	10	name	name	NOUN
bracis-28360	390	11	:	:	PUNCT
bracis-28360	390	12	springer	springer	NOUN
bracis-28360	390	13	,	,	PUNCT
bracis-28360	390	14	cham	cham	PROPN
bracis-28360	390	15	print	print	PROPN
bracis-28360	390	16	isbn	isbn	PROPN
bracis-28360	390	17	:	:	PUNCT
bracis-28360	390	18	978	978	NUM
bracis-28360	390	19	-	-	SYM
bracis-28360	390	20	3	3	NUM
bracis-28360	390	21	-	-	PUNCT
bracis-28360	390	22	031	031	NUM
bracis-28360	390	23	-	-	PUNCT
bracis-28360	390	24	45367	45367	NUM
bracis-28360	390	25	-	-	PUNCT
bracis-28360	390	26	0	0	NUM
bracis-28360	390	27	online	online	ADJ
bracis-28360	390	28	isbn	isbn	NOUN
bracis-28360	390	29	:	:	PUNCT
bracis-28360	390	30	978	978	NUM
bracis-28360	390	31	-	-	SYM
bracis-28360	390	32	3	3	NUM
bracis-28360	390	33	-	-	PUNCT
bracis-28360	390	34	031	031	NUM
bracis-28360	390	35	-	-	PUNCT
bracis-28360	390	36	45368	45368	NUM
bracis-28360	390	37	-	-	PUNCT
bracis-28360	390	38	7	7	NUM
bracis-28360	390	39	ebook	ebook	NOUN
bracis-28360	390	40	packages	package	NOUN
bracis-28360	390	41	:	:	PUNCT
bracis-28360	390	42	computer	computer	NOUN
bracis-28360	390	43	sciencecomputer	sciencecomputer	NOUN
bracis-28360	390	44	science	science	NOUN
bracis-28360	390	45	(	(	PUNCT
bracis-28360	390	46	r0	r0	NOUN
bracis-28360	390	47	)	)	PUNCT
bracis-28360	390	48	share	share	VERB
bracis-28360	390	49	this	this	DET
bracis-28360	390	50	paper	paper	NOUN
bracis-28360	390	51	anyone	anyone	PRON
bracis-28360	390	52	you	you	PRON
bracis-28360	390	53	share	share	VERB
bracis-28360	390	54	the	the	DET
bracis-28360	390	55	following	follow	VERB
bracis-28360	390	56	link	link	NOUN
bracis-28360	390	57	with	with	ADP
bracis-28360	390	58	will	will	AUX
bracis-28360	390	59	be	be	AUX
bracis-28360	390	60	able	able	ADJ
bracis-28360	390	61	to	to	PART
bracis-28360	390	62	read	read	VERB
bracis-28360	390	63	this	this	DET
bracis-28360	390	64	content	content	NOUN
bracis-28360	390	65	:	:	PUNCT
bracis-28360	390	66	get	get	VERB
bracis-28360	390	67	shareable	shareable	ADJ
bracis-28360	390	68	linksorry	linksorry	NOUN
bracis-28360	390	69	,	,	PUNCT
bracis-28360	390	70	a	a	DET
bracis-28360	390	71	shareable	shareable	ADJ
bracis-28360	390	72	link	link	NOUN
bracis-28360	390	73	is	be	AUX
bracis-28360	390	74	not	not	PART
bracis-28360	390	75	currently	currently	ADV
bracis-28360	390	76	available	available	ADJ
bracis-28360	390	77	for	for	ADP
bracis-28360	390	78	this	this	DET
bracis-28360	390	79	article	article	NOUN
bracis-28360	390	80	.	.	PUNCT
bracis-28360	391	1	copy	copy	VERB
bracis-28360	391	2	shareable	shareable	ADJ
bracis-28360	391	3	link	link	NOUN
bracis-28360	391	4	to	to	PART
bracis-28360	391	5	clipboard	clipboard	NOUN
bracis-28360	391	6	provided	provide	VERB
bracis-28360	391	7	by	by	ADP
bracis-28360	391	8	the	the	DET
bracis-28360	391	9	springer	springer	NOUN
bracis-28360	391	10	nature	nature	PROPN
bracis-28360	391	11	sharedit	sharedit	PROPN
bracis-28360	391	12	content	content	NOUN
bracis-28360	391	13	-	-	PUNCT
bracis-28360	391	14	sharing	share	VERB
bracis-28360	391	15	initiative	initiative	NOUN
bracis-28360	391	16	keywords	keyword	NOUN
bracis-28360	391	17	choquet	choquet	VERB
bracis-28360	391	18	integral	integral	ADJ
bracis-28360	391	19	cc	cc	NOUN
bracis-28360	391	20	-	-	ADJ
bracis-28360	391	21	integral	integral	ADJ
bracis-28360	391	22	x	x	ADJ
bracis-28360	391	23	-	-	ADJ
bracis-28360	391	24	dc	dc	ADJ
bracis-28360	391	25	-	-	PUNCT
bracis-28360	391	26	integral	integral	ADJ
bracis-28360	391	27	fuzzy	fuzzy	ADJ
bracis-28360	391	28	-	-	PUNCT
bracis-28360	391	29	rule	rule	NOUN
bracis-28360	391	30	based	base	VERB
bracis-28360	391	31	classifification	classifification	NOUN
bracis-28360	391	32	systems	system	NOUN
bracis-28360	391	33	publish	publish	VERB
bracis-28360	391	34	with	with	ADP
bracis-28360	391	35	us	us	PROPN
bracis-28360	391	36	policies	policy	NOUN
bracis-28360	391	37	and	and	CCONJ
bracis-28360	391	38	ethics	ethic	NOUN
bracis-28360	391	39	profiles	profile	NOUN
bracis-28360	391	40	joelson	joelson	NOUN
bracis-28360	391	41	sartori	sartori	PROPN
bracis-28360	391	42	view	view	PROPN
bracis-28360	391	43	author	author	NOUN
bracis-28360	391	44	profile	profile	PROPN
bracis-28360	391	45	giancarlo	giancarlo	PROPN
bracis-28360	391	46	lucca	lucca	PROPN
bracis-28360	391	47	view	view	PROPN
bracis-28360	391	48	author	author	NOUN
bracis-28360	391	49	profile	profile	PROPN
bracis-28360	391	50	helida	helida	PROPN
bracis-28360	391	51	santos	santos	PROPN
bracis-28360	391	52	view	view	PROPN
bracis-28360	391	53	author	author	NOUN
bracis-28360	391	54	profile	profile	NOUN
bracis-28360	391	55	search	search	NOUN
bracis-28360	391	56	search	search	NOUN
bracis-28360	391	57	by	by	ADP
bracis-28360	391	58	keyword	keyword	NOUN
bracis-28360	391	59	or	or	CCONJ
bracis-28360	391	60	author	author	NOUN
bracis-28360	391	61	search	search	NOUN
bracis-28360	391	62	navigation	navigation	NOUN
bracis-28360	391	63	find	find	VERB
bracis-28360	391	64	a	a	DET
bracis-28360	391	65	journal	journal	NOUN
bracis-28360	391	66	publish	publish	VERB
bracis-28360	391	67	with	with	ADP
bracis-28360	391	68	us	we	PRON
bracis-28360	391	69	track	track	VERB
bracis-28360	391	70	your	your	PRON
bracis-28360	391	71	research	research	NOUN
bracis-28360	391	72	discover	discover	VERB
bracis-28360	391	73	content	content	NOUN
bracis-28360	391	74	journals	journal	NOUN
bracis-28360	391	75	a	a	DET
bracis-28360	391	76	-	-	PUNCT
bracis-28360	391	77	z	z	NOUN
bracis-28360	391	78	books	book	NOUN
bracis-28360	391	79	a	a	DET
bracis-28360	391	80	-	-	PUNCT
bracis-28360	391	81	z	z	NOUN
bracis-28360	391	82	publish	publish	NOUN
bracis-28360	391	83	with	with	ADP
bracis-28360	391	84	us	us	PROPN
bracis-28360	391	85	journal	journal	PROPN
bracis-28360	391	86	finder	finder	PROPN
bracis-28360	391	87	publish	publish	VERB
bracis-28360	391	88	your	your	PRON
bracis-28360	391	89	research	research	NOUN
bracis-28360	391	90	language	language	NOUN
bracis-28360	391	91	editing	edit	VERB
bracis-28360	391	92	open	open	ADJ
bracis-28360	391	93	access	access	NOUN
bracis-28360	391	94	publishing	publishing	NOUN
bracis-28360	391	95	products	product	NOUN
bracis-28360	391	96	and	and	CCONJ
bracis-28360	391	97	services	service	NOUN
bracis-28360	391	98	our	our	PRON
bracis-28360	391	99	products	product	NOUN
bracis-28360	391	100	librarians	librarian	VERB
bracis-28360	391	101	societies	society	NOUN
bracis-28360	391	102	partners	partner	NOUN
bracis-28360	391	103	and	and	CCONJ
bracis-28360	391	104	advertisers	advertiser	NOUN
bracis-28360	391	105	our	our	PRON
bracis-28360	391	106	brands	brand	NOUN
bracis-28360	391	107	springer	springer	NOUN
bracis-28360	391	108	nature	nature	PROPN
bracis-28360	391	109	portfolio	portfolio	PROPN
bracis-28360	391	110	bmc	bmc	PROPN
bracis-28360	391	111	palgrave	palgrave	PROPN
bracis-28360	391	112	macmillan	macmillan	PROPN
bracis-28360	391	113	apress	apress	PROPN
bracis-28360	391	114	discover	discover	VERB
bracis-28360	391	115	your	your	PRON
bracis-28360	391	116	privacy	privacy	NOUN
bracis-28360	391	117	choices	choice	NOUN
bracis-28360	391	118	/	/	SYM
bracis-28360	391	119	manage	manage	NOUN
bracis-28360	391	120	cookies	cookie	NOUN
bracis-28360	391	121	your	your	PRON
bracis-28360	391	122	us	us	PROPN
bracis-28360	392	1	state	state	NOUN
bracis-28360	392	2	privacy	privacy	NOUN
bracis-28360	392	3	rights	right	NOUN
bracis-28360	392	4	accessibility	accessibility	NOUN
bracis-28360	392	5	statement	statement	NOUN
bracis-28360	392	6	terms	term	NOUN
bracis-28360	392	7	and	and	CCONJ
bracis-28360	392	8	conditions	condition	NOUN
bracis-28360	392	9	privacy	privacy	NOUN
bracis-28360	392	10	policy	policy	NOUN
bracis-28360	392	11	help	help	NOUN
bracis-28360	392	12	and	and	CCONJ
bracis-28360	392	13	support	support	VERB
bracis-28360	392	14	legal	legal	ADJ
bracis-28360	392	15	notice	notice	NOUN
bracis-28360	392	16	cancel	cancel	VERB
bracis-28360	392	17	contracts	contract	NOUN
bracis-28360	392	18	here	here	ADV
bracis-28360	392	19	129.74.145.123	129.74.145.123	NUM
bracis-28360	392	20	hesburgh	hesburgh	PROPN
bracis-28360	392	21	library	library	PROPN
bracis-28360	392	22	er	er	INTJ
bracis-28360	392	23	unit	unit	NOUN
bracis-28360	392	24	(	(	PUNCT
bracis-28360	392	25	3005732405	3005732405	NUM
bracis-28360	392	26	)	)	PUNCT
bracis-28360	392	27	northeast	northeast	ADJ
bracis-28360	392	28	research	research	NOUN
bracis-28360	392	29	libraries	library	NOUN
bracis-28360	392	30	(	(	PUNCT
bracis-28360	392	31	nerl	nerl	PROPN
bracis-28360	392	32	)	)	PUNCT
bracis-28360	392	33	(	(	PUNCT
bracis-28360	392	34	8200828607	8200828607	NUM
bracis-28360	392	35	)	)	PUNCT
bracis-28360	392	36	nerl	nerl	VERB
bracis-28360	392	37	ta	ta	X
bracis-28360	392	38	account	account	NOUN
bracis-28360	392	39	(	(	PUNCT
bracis-28360	392	40	3006206169	3006206169	NUM
bracis-28360	392	41	)	)	PUNCT
bracis-28360	392	42	university	university	NOUN
bracis-28360	392	43	of	of	ADP
bracis-28360	392	44	notre	notre	PROPN
bracis-28360	392	45	dame	dame	PROPN
bracis-28360	392	46	hesburgh	hesburgh	PROPN
bracis-28360	392	47	library	library	NOUN
bracis-28360	392	48	(	(	PUNCT
bracis-28360	392	49	3000184373	3000184373	NUM
bracis-28360	392	50	)	)	PUNCT
bracis-28360	393	1	©	©	ADP
bracis-28360	393	2	2025	2025	NUM
bracis-28360	393	3	springer	springer	NOUN
bracis-28360	393	4	nature	nature	NOUN