id	sid	tid	token	lemma	pos
ejpam-5309	1	1	european	european	PROPN
ejpam-5309	1	2	journal	journal	PROPN
ejpam-5309	1	3	of	of	ADP
ejpam-5309	1	4	pure	pure	ADJ
ejpam-5309	1	5	and	and	CCONJ
ejpam-5309	1	6	applied	apply	VERB
ejpam-5309	1	7	mathematics	mathematic	NOUN
ejpam-5309	1	8	vol	vol	NOUN
ejpam-5309	1	9	.	.	PROPN
ejpam-5309	2	1	17	17	NUM
ejpam-5309	2	2	,	,	PUNCT
ejpam-5309	2	3	no	no	INTJ
ejpam-5309	2	4	.	.	NOUN
ejpam-5309	2	5	3	3	NUM
ejpam-5309	2	6	,	,	PUNCT
ejpam-5309	2	7	2024	2024	NUM
ejpam-5309	2	8	,	,	PUNCT
ejpam-5309	2	9	1417	1417	NUM
ejpam-5309	2	10	-	-	SYM
ejpam-5309	2	11	1428	1428	NUM
ejpam-5309	2	12	issn	issn	PROPN
ejpam-5309	2	13	1307	1307	NUM
ejpam-5309	2	14	-	-	SYM
ejpam-5309	2	15	5543	5543	NUM
ejpam-5309	2	16	–	–	PUNCT
ejpam-5309	2	17	ejpam.com	ejpam.com	X
ejpam-5309	2	18	published	publish	VERB
ejpam-5309	2	19	by	by	ADP
ejpam-5309	2	20	new	new	PROPN
ejpam-5309	2	21	york	york	PROPN
ejpam-5309	2	22	business	business	PROPN
ejpam-5309	2	23	global	global	PROPN
ejpam-5309	2	24	the	the	DET
ejpam-5309	2	25	connections	connection	NOUN
ejpam-5309	2	26	of	of	ADP
ejpam-5309	2	27	strongest	strong	ADJ
ejpam-5309	2	28	fuzzy	fuzzy	ADJ
ejpam-5309	2	29	γ	γ	NOUN
ejpam-5309	2	30	-	-	NOUN
ejpam-5309	2	31	ideals	ideal	NOUN
ejpam-5309	2	32	on	on	ADP
ejpam-5309	2	33	ternary	ternary	ADJ
ejpam-5309	2	34	γ	γ	X
ejpam-5309	2	35	-	-	PUNCT
ejpam-5309	2	36	semigroups	semigroup	NOUN
ejpam-5309	2	37	warud	warud	NOUN
ejpam-5309	2	38	nakkhasen1,∗	nakkhasen1,∗	PROPN
ejpam-5309	2	39	,	,	PUNCT
ejpam-5309	2	40	onnalin	onnalin	PROPN
ejpam-5309	2	41	yangnok1	yangnok1	PROPN
ejpam-5309	2	42	,	,	PUNCT
ejpam-5309	2	43	kewarin	kewarin	PROPN
ejpam-5309	2	44	chaidet1	chaidet1	PROPN
ejpam-5309	2	45	,	,	PUNCT
ejpam-5309	2	46	wichayaporn	wichayaporn	ADJ
ejpam-5309	2	47	jantanan2	jantanan2	PROPN
ejpam-5309	2	48	1	1	NUM
ejpam-5309	2	49	department	department	NOUN
ejpam-5309	2	50	of	of	ADP
ejpam-5309	2	51	mathematics	mathematic	NOUN
ejpam-5309	2	52	,	,	PUNCT
ejpam-5309	2	53	faculty	faculty	NOUN
ejpam-5309	2	54	of	of	ADP
ejpam-5309	2	55	science	science	NOUN
ejpam-5309	2	56	,	,	PUNCT
ejpam-5309	2	57	mahasarakham	mahasarakham	PROPN
ejpam-5309	2	58	university	university	PROPN
ejpam-5309	2	59	,	,	PUNCT
ejpam-5309	2	60	maha	maha	PROPN
ejpam-5309	2	61	sarakham	sarakham	PROPN
ejpam-5309	2	62	44150	44150	NUM
ejpam-5309	2	63	,	,	PUNCT
ejpam-5309	2	64	thailand	thailand	PROPN
ejpam-5309	2	65	2	2	NUM
ejpam-5309	2	66	department	department	NOUN
ejpam-5309	2	67	of	of	ADP
ejpam-5309	2	68	mathematics	mathematic	NOUN
ejpam-5309	2	69	,	,	PUNCT
ejpam-5309	2	70	faculty	faculty	NOUN
ejpam-5309	2	71	of	of	ADP
ejpam-5309	2	72	science	science	NOUN
ejpam-5309	2	73	,	,	PUNCT
ejpam-5309	2	74	buriram	buriram	NOUN
ejpam-5309	2	75	rajabhat	rajabhat	PROPN
ejpam-5309	2	76	university	university	NOUN
ejpam-5309	2	77	,	,	PUNCT
ejpam-5309	2	78	buriram	buriram	NOUN
ejpam-5309	2	79	31000	31000	NUM
ejpam-5309	2	80	,	,	PUNCT
ejpam-5309	2	81	thailand	thailand	PROPN
ejpam-5309	2	82	abstract	abstract	NOUN
ejpam-5309	2	83	.	.	PUNCT
ejpam-5309	3	1	the	the	DET
ejpam-5309	3	2	fuzzy	fuzzy	ADJ
ejpam-5309	3	3	relation	relation	NOUN
ejpam-5309	3	4	rµ	rµ	VERB
ejpam-5309	3	5	on	on	ADP
ejpam-5309	3	6	µ	µ	NUM
ejpam-5309	3	7	,	,	PUNCT
ejpam-5309	3	8	where	where	SCONJ
ejpam-5309	3	9	µ	µ	NOUN
ejpam-5309	3	10	is	be	AUX
ejpam-5309	3	11	a	a	DET
ejpam-5309	3	12	fuzzy	fuzzy	ADJ
ejpam-5309	3	13	set	set	NOUN
ejpam-5309	3	14	of	of	ADP
ejpam-5309	3	15	a	a	DET
ejpam-5309	3	16	set	set	NOUN
ejpam-5309	3	17	x	x	NOUN
ejpam-5309	3	18	,	,	PUNCT
ejpam-5309	3	19	is	be	AUX
ejpam-5309	3	20	called	call	VERB
ejpam-5309	3	21	a	a	DET
ejpam-5309	3	22	strongest	strong	ADJ
ejpam-5309	3	23	fuzzy	fuzzy	ADJ
ejpam-5309	3	24	relation	relation	NOUN
ejpam-5309	3	25	on	on	ADP
ejpam-5309	3	26	x	x	PUNCT
ejpam-5309	3	27	if	if	SCONJ
ejpam-5309	3	28	rµ(x	rµ(x	NOUN
ejpam-5309	3	29	,	,	PUNCT
ejpam-5309	3	30	y	y	NOUN
ejpam-5309	3	31	)	)	PUNCT
ejpam-5309	3	32	=	=	SYM
ejpam-5309	4	1	min{µ(x	min{µ(x	NOUN
ejpam-5309	4	2	)	)	PUNCT
ejpam-5309	4	3	,	,	PUNCT
ejpam-5309	4	4	µ(y	µ(y	PROPN
ejpam-5309	4	5	)	)	PUNCT
ejpam-5309	4	6	}	}	PUNCT
ejpam-5309	4	7	,	,	PUNCT
ejpam-5309	4	8	for	for	ADP
ejpam-5309	4	9	all	all	DET
ejpam-5309	4	10	x	x	NOUN
ejpam-5309	4	11	,	,	PUNCT
ejpam-5309	4	12	y	y	PROPN
ejpam-5309	4	13	∈	∈	PROPN
ejpam-5309	4	14	x.	x.	NOUN
ejpam-5309	5	1	the	the	DET
ejpam-5309	5	2	notion	notion	NOUN
ejpam-5309	5	3	of	of	ADP
ejpam-5309	5	4	strongest	strong	ADJ
ejpam-5309	5	5	fuzzy	fuzzy	ADJ
ejpam-5309	5	6	relations	relation	NOUN
ejpam-5309	5	7	will	will	AUX
ejpam-5309	5	8	be	be	AUX
ejpam-5309	5	9	applied	apply	VERB
ejpam-5309	5	10	in	in	ADP
ejpam-5309	5	11	our	our	PRON
ejpam-5309	5	12	investigation	investigation	NOUN
ejpam-5309	5	13	on	on	ADP
ejpam-5309	5	14	ternary	ternary	ADJ
ejpam-5309	5	15	γ	γ	NOUN
ejpam-5309	5	16	-	-	PUNCT
ejpam-5309	5	17	semigroups	semigroup	NOUN
ejpam-5309	5	18	.	.	PUNCT
ejpam-5309	6	1	in	in	ADP
ejpam-5309	6	2	order	order	NOUN
ejpam-5309	6	3	to	to	PART
ejpam-5309	6	4	achieve	achieve	VERB
ejpam-5309	6	5	this	this	PRON
ejpam-5309	6	6	,	,	PUNCT
ejpam-5309	6	7	we	we	PRON
ejpam-5309	6	8	will	will	AUX
ejpam-5309	6	9	define	define	VERB
ejpam-5309	6	10	the	the	DET
ejpam-5309	6	11	concepts	concept	NOUN
ejpam-5309	6	12	of	of	ADP
ejpam-5309	6	13	strongest	strong	ADJ
ejpam-5309	6	14	fuzzy	fuzzy	ADJ
ejpam-5309	6	15	ternary	ternary	ADJ
ejpam-5309	6	16	γ	γ	NOUN
ejpam-5309	6	17	-	-	NOUN
ejpam-5309	6	18	subsemigroups	subsemigroup	NOUN
ejpam-5309	6	19	,	,	PUNCT
ejpam-5309	6	20	strongest	strong	ADJ
ejpam-5309	6	21	fuzzy	fuzzy	ADJ
ejpam-5309	6	22	γ	γ	NOUN
ejpam-5309	6	23	-	-	PUNCT
ejpam-5309	6	24	ideals	ideal	NOUN
ejpam-5309	6	25	(	(	PUNCT
ejpam-5309	6	26	resp	resp	NOUN
ejpam-5309	6	27	.	.	PUNCT
ejpam-5309	7	1	left	leave	VERB
ejpam-5309	7	2	,	,	PUNCT
ejpam-5309	7	3	right	right	ADJ
ejpam-5309	7	4	,	,	PUNCT
ejpam-5309	7	5	and	and	CCONJ
ejpam-5309	7	6	lateral	lateral	ADJ
ejpam-5309	7	7	)	)	PUNCT
ejpam-5309	7	8	,	,	PUNCT
ejpam-5309	7	9	and	and	CCONJ
ejpam-5309	7	10	strongest	strong	ADJ
ejpam-5309	7	11	fuzzy	fuzzy	ADJ
ejpam-5309	7	12	bi	bi	ADJ
ejpam-5309	7	13	-	-	ADJ
ejpam-5309	7	14	γ	γ	NOUN
ejpam-5309	7	15	-	-	PUNCT
ejpam-5309	7	16	ideals	ideal	NOUN
ejpam-5309	7	17	on	on	ADP
ejpam-5309	7	18	ternary	ternary	ADJ
ejpam-5309	7	19	γ	γ	NOUN
ejpam-5309	7	20	-	-	PUNCT
ejpam-5309	7	21	semigroups	semigroup	NOUN
ejpam-5309	7	22	.	.	PUNCT
ejpam-5309	8	1	then	then	ADV
ejpam-5309	8	2	,	,	PUNCT
ejpam-5309	8	3	we	we	PRON
ejpam-5309	8	4	study	study	VERB
ejpam-5309	8	5	the	the	DET
ejpam-5309	8	6	connections	connection	NOUN
ejpam-5309	8	7	and	and	CCONJ
ejpam-5309	8	8	characterizations	characterization	NOUN
ejpam-5309	8	9	of	of	ADP
ejpam-5309	8	10	these	these	DET
ejpam-5309	8	11	concepts	concept	NOUN
ejpam-5309	8	12	in	in	ADP
ejpam-5309	8	13	ternary	ternary	ADJ
ejpam-5309	8	14	γ	γ	NOUN
ejpam-5309	8	15	-	-	PUNCT
ejpam-5309	8	16	semigroups	semigroup	NOUN
ejpam-5309	8	17	.	.	PUNCT
ejpam-5309	9	1	2020	2020	NUM
ejpam-5309	9	2	mathematics	mathematic	NOUN
ejpam-5309	9	3	subject	subject	NOUN
ejpam-5309	9	4	classifications	classification	NOUN
ejpam-5309	9	5	:	:	PUNCT
ejpam-5309	9	6	20m75	20m75	NUM
ejpam-5309	9	7	,	,	PUNCT
ejpam-5309	9	8	08a72	08a72	NOUN
ejpam-5309	9	9	key	key	ADJ
ejpam-5309	9	10	words	word	NOUN
ejpam-5309	9	11	and	and	CCONJ
ejpam-5309	9	12	phrases	phrase	NOUN
ejpam-5309	9	13	:	:	PUNCT
ejpam-5309	9	14	strongest	strong	ADJ
ejpam-5309	9	15	fuzzy	fuzzy	ADJ
ejpam-5309	9	16	relation	relation	NOUN
ejpam-5309	9	17	,	,	PUNCT
ejpam-5309	9	18	strongest	strong	ADJ
ejpam-5309	9	19	fuzzy	fuzzy	ADJ
ejpam-5309	9	20	γ	γ	X
ejpam-5309	9	21	-	-	PUNCT
ejpam-5309	9	22	ideal	ideal	ADJ
ejpam-5309	9	23	,	,	PUNCT
ejpam-5309	9	24	γ	γ	NOUN
ejpam-5309	9	25	-	-	PUNCT
ejpam-5309	9	26	ideal	ideal	ADJ
ejpam-5309	9	27	,	,	PUNCT
ejpam-5309	9	28	ternary	ternary	ADJ
ejpam-5309	9	29	γ	γ	X
ejpam-5309	9	30	-	-	PUNCT
ejpam-5309	9	31	semigroup	semigroup	ADJ
ejpam-5309	9	32	1	1	NUM
ejpam-5309	9	33	.	.	PUNCT
ejpam-5309	9	34	introduction	introduction	NOUN
ejpam-5309	9	35	the	the	DET
ejpam-5309	9	36	notion	notion	NOUN
ejpam-5309	9	37	of	of	ADP
ejpam-5309	9	38	ternary	ternary	ADJ
ejpam-5309	9	39	γ	γ	NOUN
ejpam-5309	9	40	-	-	PUNCT
ejpam-5309	9	41	semigroups	semigroup	NOUN
ejpam-5309	9	42	was	be	AUX
ejpam-5309	9	43	introduced	introduce	VERB
ejpam-5309	9	44	by	by	ADP
ejpam-5309	9	45	madhusudhana	madhusudhana	PROPN
ejpam-5309	9	46	rao	rao	PROPN
ejpam-5309	9	47	et	et	PROPN
ejpam-5309	9	48	al	al	PROPN
ejpam-5309	9	49	.	.	PUNCT
ejpam-5309	10	1	[	[	X
ejpam-5309	10	2	6	6	NUM
ejpam-5309	10	3	]	]	PUNCT
ejpam-5309	10	4	in	in	ADP
ejpam-5309	10	5	2015	2015	NUM
ejpam-5309	10	6	.	.	PUNCT
ejpam-5309	11	1	the	the	DET
ejpam-5309	11	2	ternary	ternary	ADJ
ejpam-5309	11	3	γ	γ	X
ejpam-5309	11	4	-	-	PUNCT
ejpam-5309	11	5	semigroups	semigroup	NOUN
ejpam-5309	11	6	were	be	AUX
ejpam-5309	11	7	generalized	generalize	VERB
ejpam-5309	11	8	the	the	DET
ejpam-5309	11	9	concepts	concept	NOUN
ejpam-5309	11	10	of	of	ADP
ejpam-5309	11	11	semigroups	semigroup	NOUN
ejpam-5309	11	12	,	,	PUNCT
ejpam-5309	11	13	γsemigroups	γsemigroup	NOUN
ejpam-5309	11	14	and	and	CCONJ
ejpam-5309	11	15	ternary	ternary	ADJ
ejpam-5309	11	16	semigroups	semigroup	NOUN
ejpam-5309	11	17	.	.	PUNCT
ejpam-5309	12	1	they	they	PRON
ejpam-5309	12	2	characterized	characterize	VERB
ejpam-5309	12	3	and	and	CCONJ
ejpam-5309	12	4	examined	examine	VERB
ejpam-5309	12	5	about	about	ADP
ejpam-5309	12	6	several	several	ADJ
ejpam-5309	12	7	some	some	DET
ejpam-5309	12	8	elements	element	NOUN
ejpam-5309	12	9	of	of	ADP
ejpam-5309	12	10	ternary	ternary	ADJ
ejpam-5309	12	11	γ	γ	NOUN
ejpam-5309	12	12	-	-	PUNCT
ejpam-5309	12	13	semigroups	semigroup	NOUN
ejpam-5309	12	14	.	.	PUNCT
ejpam-5309	13	1	then	then	ADV
ejpam-5309	13	2	vasantha	vasantha	NOUN
ejpam-5309	13	3	and	and	CCONJ
ejpam-5309	13	4	madhusudhana	madhusudhana	PROPN
ejpam-5309	13	5	rao	rao	NOUN
ejpam-5309	14	1	[	[	X
ejpam-5309	14	2	8	8	NUM
ejpam-5309	14	3	]	]	PUNCT
ejpam-5309	14	4	developed	develop	VERB
ejpam-5309	14	5	and	and	CCONJ
ejpam-5309	14	6	characterized	characterize	VERB
ejpam-5309	14	7	the	the	DET
ejpam-5309	14	8	terms	term	NOUN
ejpam-5309	14	9	completely	completely	ADV
ejpam-5309	14	10	semiprime	semiprime	VERB
ejpam-5309	14	11	ternary	ternary	ADJ
ejpam-5309	14	12	γ	γ	X
ejpam-5309	14	13	-	-	ADJ
ejpam-5309	14	14	ideal	ideal	ADJ
ejpam-5309	14	15	and	and	CCONJ
ejpam-5309	14	16	semiprime	semiprime	NOUN
ejpam-5309	14	17	ternary	ternary	PROPN
ejpam-5309	14	18	γ	γ	X
ejpam-5309	14	19	-	-	NOUN
ejpam-5309	14	20	ideal	ideal	NOUN
ejpam-5309	14	21	in	in	ADP
ejpam-5309	14	22	ternary	ternary	ADJ
ejpam-5309	14	23	γ	γ	X
ejpam-5309	14	24	-	-	PUNCT
ejpam-5309	14	25	semigroups	semigroup	NOUN
ejpam-5309	14	26	.	.	PUNCT
ejpam-5309	15	1	after	after	ADP
ejpam-5309	15	2	that	that	PRON
ejpam-5309	15	3	,	,	PUNCT
ejpam-5309	15	4	vasantha	vasantha	NOUN
ejpam-5309	15	5	et	et	PROPN
ejpam-5309	15	6	al	al	PROPN
ejpam-5309	15	7	.	.	PUNCT
ejpam-5309	16	1	[	[	X
ejpam-5309	16	2	11	11	NUM
ejpam-5309	16	3	]	]	PUNCT
ejpam-5309	16	4	introduced	introduce	VERB
ejpam-5309	16	5	the	the	DET
ejpam-5309	16	6	concepts	concept	NOUN
ejpam-5309	16	7	of	of	ADP
ejpam-5309	16	8	trio	trio	NOUN
ejpam-5309	16	9	l	l	NOUN
ejpam-5309	16	10	-	-	NOUN
ejpam-5309	16	11	trio	trio	ADJ
ejpam-5309	16	12	tγ	tγ	NOUN
ejpam-5309	16	13	-	-	PUNCT
ejpam-5309	16	14	ideals	ideal	NOUN
ejpam-5309	16	15	,	,	PUNCT
ejpam-5309	16	16	la	la	ADJ
ejpam-5309	16	17	-	-	NOUN
ejpam-5309	16	18	trio	trio	ADJ
ejpam-5309	16	19	tγ	tγ	NOUN
ejpam-5309	16	20	-	-	PUNCT
ejpam-5309	16	21	ideals	ideal	NOUN
ejpam-5309	16	22	,	,	PUNCT
ejpam-5309	16	23	r	r	NOUN
ejpam-5309	16	24	-	-	PUNCT
ejpam-5309	16	25	trio	trio	ADJ
ejpam-5309	16	26	tγ	tγ	NOUN
ejpam-5309	16	27	-	-	PUNCT
ejpam-5309	16	28	ideals	ideal	NOUN
ejpam-5309	16	29	,	,	PUNCT
ejpam-5309	16	30	and	and	CCONJ
ejpam-5309	16	31	trio	trio	ADJ
ejpam-5309	16	32	tγ	tγ	NOUN
ejpam-5309	16	33	-	-	PUNCT
ejpam-5309	16	34	ideals	ideal	NOUN
ejpam-5309	16	35	in	in	ADP
ejpam-5309	16	36	trio	trio	ADJ
ejpam-5309	16	37	ternary	ternary	ADJ
ejpam-5309	16	38	γ	γ	NOUN
ejpam-5309	16	39	-	-	PUNCT
ejpam-5309	16	40	semigroups	semigroup	NOUN
ejpam-5309	16	41	.	.	PUNCT
ejpam-5309	17	1	afterwards	afterwards	ADV
ejpam-5309	17	2	,	,	PUNCT
ejpam-5309	17	3	ali	ali	PROPN
ejpam-5309	17	4	et	et	PROPN
ejpam-5309	17	5	al	al	PROPN
ejpam-5309	17	6	.	.	PUNCT
ejpam-5309	18	1	[	[	X
ejpam-5309	18	2	1	1	X
ejpam-5309	18	3	]	]	PUNCT
ejpam-5309	18	4	introduced	introduce	VERB
ejpam-5309	18	5	and	and	CCONJ
ejpam-5309	18	6	discussed	discuss	VERB
ejpam-5309	18	7	some	some	DET
ejpam-5309	18	8	properties	property	NOUN
ejpam-5309	18	9	of	of	ADP
ejpam-5309	18	10	po	po	NOUN
ejpam-5309	18	11	-	-	ADJ
ejpam-5309	18	12	bi	bi	ADJ
ejpam-5309	18	13	quasi	quasi	PROPN
ejpam-5309	18	14	-	-	ADJ
ejpam-5309	18	15	γ	γ	NOUN
ejpam-5309	18	16	-	-	PUNCT
ejpam-5309	18	17	ideals	ideal	NOUN
ejpam-5309	18	18	,	,	PUNCT
ejpam-5309	18	19	po	po	NOUN
ejpam-5309	18	20	-	-	PUNCT
ejpam-5309	18	21	bi	bi	ADJ
ejpam-5309	18	22	-	-	ADJ
ejpam-5309	18	23	γ	γ	NOUN
ejpam-5309	18	24	-	-	PUNCT
ejpam-5309	18	25	ideals	ideal	NOUN
ejpam-5309	18	26	,	,	PUNCT
ejpam-5309	18	27	and	and	CCONJ
ejpam-5309	18	28	generalized	generalize	VERB
ejpam-5309	18	29	po	po	NOUN
ejpam-5309	18	30	-	-	ADJ
ejpam-5309	18	31	bi	bi	ADJ
ejpam-5309	18	32	quasi	quasi	PROPN
ejpam-5309	18	33	-	-	ADJ
ejpam-5309	18	34	γ	γ	NOUN
ejpam-5309	18	35	-	-	PUNCT
ejpam-5309	18	36	ideals	ideal	NOUN
ejpam-5309	18	37	in	in	ADP
ejpam-5309	18	38	po	po	NOUN
ejpam-5309	18	39	-	-	ADJ
ejpam-5309	18	40	bi	bi	ADJ
ejpam-5309	18	41	-	-	ADJ
ejpam-5309	18	42	ternary	ternary	ADJ
ejpam-5309	18	43	γ	γ	NOUN
ejpam-5309	18	44	-	-	PUNCT
ejpam-5309	18	45	semigroups	semigroup	NOUN
ejpam-5309	18	46	.	.	PUNCT
ejpam-5309	19	1	for	for	ADP
ejpam-5309	19	2	other	other	ADJ
ejpam-5309	19	3	research	research	NOUN
ejpam-5309	19	4	related	relate	VERB
ejpam-5309	19	5	to	to	AUX
ejpam-5309	19	6	ternary	ternary	VERB
ejpam-5309	19	7	γ	γ	NOUN
ejpam-5309	19	8	-	-	PUNCT
ejpam-5309	19	9	semigroups	semigroup	NOUN
ejpam-5309	19	10	,	,	PUNCT
ejpam-5309	19	11	additional	additional	ADJ
ejpam-5309	19	12	studies	study	NOUN
ejpam-5309	19	13	can	can	AUX
ejpam-5309	19	14	be	be	AUX
ejpam-5309	19	15	done	do	VERB
ejpam-5309	19	16	in	in	ADP
ejpam-5309	19	17	general	general	ADJ
ejpam-5309	19	18	(	(	PUNCT
ejpam-5309	19	19	e.g.	e.g.	ADV
ejpam-5309	19	20	,	,	PUNCT
ejpam-5309	19	21	[	[	X
ejpam-5309	19	22	7	7	NUM
ejpam-5309	19	23	,	,	PUNCT
ejpam-5309	19	24	9	9	NUM
ejpam-5309	19	25	,	,	PUNCT
ejpam-5309	19	26	10	10	NUM
ejpam-5309	19	27	]	]	NUM
ejpam-5309	19	28	)	)	PUNCT
ejpam-5309	19	29	.	.	PUNCT
ejpam-5309	20	1	∗corresponding	∗corresponde	VERB
ejpam-5309	20	2	author	author	NOUN
ejpam-5309	20	3	.	.	PUNCT
ejpam-5309	21	1	doi	doi	NOUN
ejpam-5309	21	2	:	:	PUNCT
ejpam-5309	21	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5309	https://doi.org/10.29020/nybg.ejpam.v17i3.5309	NOUN
ejpam-5309	21	4	email	email	NOUN
ejpam-5309	21	5	addresses	address	VERB
ejpam-5309	21	6	:	:	PUNCT
ejpam-5309	22	1	warud.n@msu.ac.th	warud.n@msu.ac.th	PRON
ejpam-5309	22	2	(	(	PUNCT
ejpam-5309	22	3	w.	w.	PROPN
ejpam-5309	22	4	nakkhasen	nakkhasen	PROPN
ejpam-5309	22	5	)	)	PUNCT
ejpam-5309	22	6	,	,	PUNCT
ejpam-5309	22	7	63010213011@msu.ac.th	63010213011@msu.ac.th	NUM
ejpam-5309	22	8	(	(	PUNCT
ejpam-5309	22	9	o.	o.	PROPN
ejpam-5309	22	10	yangnok	yangnok	PROPN
ejpam-5309	22	11	)	)	PUNCT
ejpam-5309	22	12	,	,	PUNCT
ejpam-5309	22	13	63010213018@msu.ac.th	63010213018@msu.ac.th	NUM
ejpam-5309	22	14	(	(	PUNCT
ejpam-5309	22	15	k.	k.	PROPN
ejpam-5309	22	16	chaidet	chaidet	PROPN
ejpam-5309	22	17	)	)	PUNCT
ejpam-5309	22	18	,	,	PUNCT
ejpam-5309	22	19	wichayaporn.jan@bru.ac.th	wichayaporn.jan@bru.ac.th	PROPN
ejpam-5309	22	20	(	(	PUNCT
ejpam-5309	22	21	w.	w.	PROPN
ejpam-5309	22	22	jantanan	jantanan	PROPN
ejpam-5309	22	23	)	)	PUNCT
ejpam-5309	22	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5309	22	25	1417	1417	NUM
ejpam-5309	22	26	©	©	ADP
ejpam-5309	22	27	2024	2024	NUM
ejpam-5309	22	28	ejpam	ejpam	NOUN
ejpam-5309	22	29	all	all	DET
ejpam-5309	22	30	rights	right	NOUN
ejpam-5309	22	31	reserved	reserve	VERB
ejpam-5309	22	32	.	.	PUNCT
ejpam-5309	23	1	w.	w.	PROPN
ejpam-5309	23	2	nakkhasen	nakkhasen	PROPN
ejpam-5309	23	3	et	et	PROPN
ejpam-5309	23	4	al	al	PROPN
ejpam-5309	23	5	.	.	PUNCT
ejpam-5309	23	6	/	/	SYM
ejpam-5309	23	7	eur	eur	PROPN
ejpam-5309	23	8	.	.	PUNCT
ejpam-5309	24	1	j.	j.	PROPN
ejpam-5309	24	2	pure	pure	PROPN
ejpam-5309	24	3	appl	appl	PROPN
ejpam-5309	24	4	.	.	PROPN
ejpam-5309	24	5	math	math	PROPN
ejpam-5309	24	6	,	,	PUNCT
ejpam-5309	24	7	17	17	NUM
ejpam-5309	24	8	(	(	PUNCT
ejpam-5309	24	9	3	3	NUM
ejpam-5309	24	10	)	)	PUNCT
ejpam-5309	24	11	(	(	PUNCT
ejpam-5309	24	12	2024	2024	NUM
ejpam-5309	24	13	)	)	PUNCT
ejpam-5309	24	14	,	,	PUNCT
ejpam-5309	24	15	1417	1417	NUM
ejpam-5309	24	16	-	-	SYM
ejpam-5309	24	17	1428	1428	NUM
ejpam-5309	24	18	1418	1418	NUM
ejpam-5309	24	19	fuzzy	fuzzy	ADJ
ejpam-5309	24	20	subsets	subset	NOUN
ejpam-5309	24	21	or	or	CCONJ
ejpam-5309	24	22	fuzzy	fuzzy	ADJ
ejpam-5309	24	23	sets	set	NOUN
ejpam-5309	24	24	are	be	AUX
ejpam-5309	24	25	defined	define	VERB
ejpam-5309	24	26	by	by	ADP
ejpam-5309	24	27	zadeh	zadeh	PROPN
ejpam-5309	25	1	[	[	X
ejpam-5309	25	2	13	13	NUM
ejpam-5309	25	3	]	]	PUNCT
ejpam-5309	25	4	as	as	ADP
ejpam-5309	25	5	a	a	DET
ejpam-5309	25	6	function	function	NOUN
ejpam-5309	25	7	from	from	ADP
ejpam-5309	25	8	a	a	DET
ejpam-5309	25	9	nonempty	nonempty	ADV
ejpam-5309	25	10	set	set	VERB
ejpam-5309	25	11	x	x	INTJ
ejpam-5309	25	12	to	to	ADP
ejpam-5309	25	13	the	the	DET
ejpam-5309	25	14	unit	unit	NOUN
ejpam-5309	25	15	interval	interval	NOUN
ejpam-5309	25	16	[	[	X
ejpam-5309	25	17	0	0	NUM
ejpam-5309	25	18	,	,	PUNCT
ejpam-5309	25	19	1	1	NUM
ejpam-5309	25	20	]	]	PUNCT
ejpam-5309	25	21	.	.	PUNCT
ejpam-5309	26	1	this	this	DET
ejpam-5309	26	2	idea	idea	NOUN
ejpam-5309	26	3	is	be	AUX
ejpam-5309	26	4	a	a	DET
ejpam-5309	26	5	mathematical	mathematical	ADJ
ejpam-5309	26	6	extension	extension	NOUN
ejpam-5309	26	7	of	of	ADP
ejpam-5309	26	8	the	the	DET
ejpam-5309	26	9	classical	classical	ADJ
ejpam-5309	26	10	sets	set	NOUN
ejpam-5309	26	11	in	in	ADP
ejpam-5309	26	12	mathematics	mathematic	NOUN
ejpam-5309	26	13	.	.	PUNCT
ejpam-5309	27	1	then	then	ADV
ejpam-5309	27	2	,	,	PUNCT
ejpam-5309	27	3	in	in	ADP
ejpam-5309	27	4	1985	1985	NUM
ejpam-5309	27	5	,	,	PUNCT
ejpam-5309	27	6	bhattacharya	bhattacharya	NOUN
ejpam-5309	27	7	and	and	CCONJ
ejpam-5309	27	8	mukherjee	mukherjee	PROPN
ejpam-5309	28	1	[	[	X
ejpam-5309	28	2	3	3	NUM
ejpam-5309	28	3	]	]	PUNCT
ejpam-5309	28	4	proved	prove	VERB
ejpam-5309	28	5	that	that	SCONJ
ejpam-5309	28	6	a	a	DET
ejpam-5309	28	7	strongest	strong	ADJ
ejpam-5309	28	8	fuzzy	fuzzy	ADJ
ejpam-5309	28	9	relation	relation	NOUN
ejpam-5309	28	10	µσ	µσ	NOUN
ejpam-5309	28	11	on	on	ADP
ejpam-5309	28	12	a	a	DET
ejpam-5309	28	13	group	group	NOUN
ejpam-5309	28	14	s	s	PART
ejpam-5309	28	15	is	be	AUX
ejpam-5309	28	16	a	a	DET
ejpam-5309	28	17	fuzzy	fuzzy	ADJ
ejpam-5309	28	18	subgroup	subgroup	NOUN
ejpam-5309	28	19	if	if	SCONJ
ejpam-5309	28	20	and	and	CCONJ
ejpam-5309	28	21	only	only	ADV
ejpam-5309	28	22	if	if	SCONJ
ejpam-5309	28	23	σ	σ	PROPN
ejpam-5309	28	24	is	be	AUX
ejpam-5309	28	25	a	a	DET
ejpam-5309	28	26	fuzzy	fuzzy	ADJ
ejpam-5309	28	27	subgroup	subgroup	NOUN
ejpam-5309	28	28	.	.	PUNCT
ejpam-5309	29	1	this	this	DET
ejpam-5309	29	2	concept	concept	NOUN
ejpam-5309	29	3	of	of	ADP
ejpam-5309	29	4	strongest	strong	ADJ
ejpam-5309	29	5	fuzzy	fuzzy	ADJ
ejpam-5309	29	6	relations	relation	NOUN
ejpam-5309	29	7	has	have	AUX
ejpam-5309	29	8	been	be	AUX
ejpam-5309	29	9	studied	study	VERB
ejpam-5309	29	10	continuously	continuously	ADV
ejpam-5309	29	11	.	.	PUNCT
ejpam-5309	30	1	mostafa	mostafa	PROPN
ejpam-5309	30	2	et	et	PROPN
ejpam-5309	30	3	al	al	PROPN
ejpam-5309	30	4	.	.	PUNCT
ejpam-5309	31	1	[	[	X
ejpam-5309	31	2	5	5	NUM
ejpam-5309	31	3	]	]	PUNCT
ejpam-5309	31	4	presented	present	VERB
ejpam-5309	31	5	some	some	DET
ejpam-5309	31	6	properties	property	NOUN
ejpam-5309	31	7	of	of	ADP
ejpam-5309	31	8	ku	ku	NOUN
ejpam-5309	31	9	-	-	PUNCT
ejpam-5309	31	10	ideals	ideal	NOUN
ejpam-5309	31	11	in	in	ADP
ejpam-5309	31	12	terms	term	NOUN
ejpam-5309	31	13	of	of	ADP
ejpam-5309	31	14	strongest	strong	ADJ
ejpam-5309	31	15	fuzzy	fuzzy	ADJ
ejpam-5309	31	16	relations	relation	NOUN
ejpam-5309	31	17	in	in	ADP
ejpam-5309	31	18	kualgebras	kualgebra	NOUN
ejpam-5309	31	19	.	.	PUNCT
ejpam-5309	32	1	subsequently	subsequently	ADV
ejpam-5309	32	2	,	,	PUNCT
ejpam-5309	32	3	the	the	DET
ejpam-5309	32	4	concept	concept	NOUN
ejpam-5309	32	5	of	of	ADP
ejpam-5309	32	6	strongest	strong	ADJ
ejpam-5309	32	7	fuzzy	fuzzy	ADJ
ejpam-5309	32	8	relations	relation	NOUN
ejpam-5309	32	9	in	in	ADP
ejpam-5309	32	10	the	the	DET
ejpam-5309	32	11	cartesian	cartesian	ADJ
ejpam-5309	32	12	product	product	NOUN
ejpam-5309	32	13	of	of	ADP
ejpam-5309	32	14	b	b	NOUN
ejpam-5309	32	15	-	-	PUNCT
ejpam-5309	32	16	algebras	algebras	PROPN
ejpam-5309	32	17	was	be	AUX
ejpam-5309	32	18	investigated	investigate	VERB
ejpam-5309	32	19	by	by	ADP
ejpam-5309	32	20	yamini	yamini	NOUN
ejpam-5309	32	21	and	and	CCONJ
ejpam-5309	32	22	kailasavalli	kailasavalli	NOUN
ejpam-5309	33	1	[	[	X
ejpam-5309	33	2	12	12	NUM
ejpam-5309	33	3	]	]	PUNCT
ejpam-5309	33	4	in	in	ADP
ejpam-5309	33	5	2014	2014	NUM
ejpam-5309	33	6	.	.	PUNCT
ejpam-5309	34	1	following	follow	VERB
ejpam-5309	34	2	that	that	PRON
ejpam-5309	34	3	,	,	PUNCT
ejpam-5309	34	4	bhargavi	bhargavi	VERB
ejpam-5309	34	5	et	et	PROPN
ejpam-5309	34	6	al	al	PROPN
ejpam-5309	34	7	.	.	PUNCT
ejpam-5309	35	1	[	[	X
ejpam-5309	35	2	2	2	X
ejpam-5309	35	3	]	]	PUNCT
ejpam-5309	35	4	gave	give	VERB
ejpam-5309	35	5	and	and	CCONJ
ejpam-5309	35	6	analyzed	analyze	VERB
ejpam-5309	35	7	the	the	DET
ejpam-5309	35	8	concept	concept	NOUN
ejpam-5309	35	9	of	of	ADP
ejpam-5309	35	10	the	the	DET
ejpam-5309	35	11	cartesian	cartesian	ADJ
ejpam-5309	35	12	product	product	NOUN
ejpam-5309	35	13	of	of	ADP
ejpam-5309	35	14	fuzzy	fuzzy	ADJ
ejpam-5309	35	15	sets	set	NOUN
ejpam-5309	35	16	in	in	ADP
ejpam-5309	35	17	ternary	ternary	ADJ
ejpam-5309	35	18	γ	γ	NOUN
ejpam-5309	35	19	-	-	PUNCT
ejpam-5309	35	20	semigroups	semigroup	NOUN
ejpam-5309	35	21	.	.	PUNCT
ejpam-5309	36	1	in	in	ADP
ejpam-5309	36	2	addition	addition	NOUN
ejpam-5309	36	3	,	,	PUNCT
ejpam-5309	36	4	they	they	PRON
ejpam-5309	36	5	characterized	characterize	VERB
ejpam-5309	36	6	different	different	ADJ
ejpam-5309	36	7	types	type	NOUN
ejpam-5309	36	8	of	of	ADP
ejpam-5309	36	9	fuzzy	fuzzy	ADJ
ejpam-5309	36	10	γ	γ	NOUN
ejpam-5309	36	11	-	-	NOUN
ejpam-5309	36	12	ideals	ideal	NOUN
ejpam-5309	36	13	in	in	ADP
ejpam-5309	36	14	terms	term	NOUN
ejpam-5309	36	15	of	of	ADP
ejpam-5309	36	16	their	their	PRON
ejpam-5309	36	17	cartesian	cartesian	ADJ
ejpam-5309	36	18	product	product	NOUN
ejpam-5309	36	19	of	of	ADP
ejpam-5309	36	20	ternary	ternary	ADJ
ejpam-5309	36	21	γ	γ	NOUN
ejpam-5309	36	22	-	-	PUNCT
ejpam-5309	36	23	semigroups	semigroup	NOUN
ejpam-5309	36	24	.	.	PUNCT
ejpam-5309	37	1	recently	recently	ADV
ejpam-5309	37	2	,	,	PUNCT
ejpam-5309	37	3	derseh	derseh	PROPN
ejpam-5309	37	4	et	et	PROPN
ejpam-5309	37	5	al	al	PROPN
ejpam-5309	37	6	.	.	PUNCT
ejpam-5309	38	1	[	[	X
ejpam-5309	38	2	4	4	X
ejpam-5309	38	3	]	]	PUNCT
ejpam-5309	38	4	considered	consider	VERB
ejpam-5309	38	5	some	some	DET
ejpam-5309	38	6	properties	property	NOUN
ejpam-5309	38	7	of	of	ADP
ejpam-5309	38	8	strongest	strong	ADJ
ejpam-5309	38	9	intuitionistic	intuitionistic	ADJ
ejpam-5309	38	10	fuzzy	fuzzy	ADJ
ejpam-5309	38	11	pms	pm	NOUN
ejpam-5309	38	12	-	-	PUNCT
ejpam-5309	38	13	relations	relation	NOUN
ejpam-5309	38	14	on	on	ADP
ejpam-5309	38	15	pms	pm	NOUN
ejpam-5309	38	16	-	-	PUNCT
ejpam-5309	38	17	algebras	algebras	PROPN
ejpam-5309	38	18	in	in	ADP
ejpam-5309	38	19	2023	2023	NUM
ejpam-5309	38	20	.	.	PUNCT
ejpam-5309	39	1	the	the	DET
ejpam-5309	39	2	purpose	purpose	NOUN
ejpam-5309	39	3	of	of	ADP
ejpam-5309	39	4	this	this	DET
ejpam-5309	39	5	article	article	NOUN
ejpam-5309	39	6	is	be	AUX
ejpam-5309	39	7	applying	apply	VERB
ejpam-5309	39	8	the	the	DET
ejpam-5309	39	9	fuzzy	fuzzy	ADJ
ejpam-5309	39	10	relation	relation	NOUN
ejpam-5309	39	11	to	to	PART
ejpam-5309	39	12	define	define	VERB
ejpam-5309	39	13	the	the	DET
ejpam-5309	39	14	concepts	concept	NOUN
ejpam-5309	39	15	of	of	ADP
ejpam-5309	39	16	strongest	strong	ADJ
ejpam-5309	39	17	fuzzy	fuzzy	ADJ
ejpam-5309	39	18	γ	γ	NOUN
ejpam-5309	39	19	-	-	PUNCT
ejpam-5309	39	20	subsemigroups	subsemigroup	NOUN
ejpam-5309	39	21	,	,	PUNCT
ejpam-5309	39	22	strongest	strong	ADJ
ejpam-5309	39	23	fuzzy	fuzzy	ADJ
ejpam-5309	39	24	(	(	PUNCT
ejpam-5309	39	25	resp	resp	NOUN
ejpam-5309	39	26	.	.	PUNCT
ejpam-5309	40	1	left	leave	VERB
ejpam-5309	40	2	,	,	PUNCT
ejpam-5309	40	3	right	right	ADJ
ejpam-5309	40	4	,	,	PUNCT
ejpam-5309	40	5	lateral	lateral	ADJ
ejpam-5309	40	6	)	)	PUNCT
ejpam-5309	40	7	γ	γ	NOUN
ejpam-5309	40	8	-	-	NOUN
ejpam-5309	40	9	ideals	ideal	NOUN
ejpam-5309	40	10	,	,	PUNCT
ejpam-5309	40	11	and	and	CCONJ
ejpam-5309	40	12	strongest	strong	ADJ
ejpam-5309	40	13	fuzzy	fuzzy	ADJ
ejpam-5309	40	14	bi	bi	ADJ
ejpam-5309	40	15	-	-	ADJ
ejpam-5309	40	16	γ	γ	NOUN
ejpam-5309	40	17	-	-	PUNCT
ejpam-5309	40	18	ideals	ideal	NOUN
ejpam-5309	40	19	of	of	ADP
ejpam-5309	40	20	ternary	ternary	ADJ
ejpam-5309	40	21	γ	γ	NOUN
ejpam-5309	40	22	-	-	PUNCT
ejpam-5309	40	23	semigroups	semigroup	NOUN
ejpam-5309	40	24	.	.	PUNCT
ejpam-5309	41	1	later	later	ADV
ejpam-5309	41	2	on	on	ADV
ejpam-5309	41	3	,	,	PUNCT
ejpam-5309	41	4	we	we	PRON
ejpam-5309	41	5	consider	consider	VERB
ejpam-5309	41	6	the	the	DET
ejpam-5309	41	7	connections	connection	NOUN
ejpam-5309	41	8	of	of	ADP
ejpam-5309	41	9	strongest	strong	ADJ
ejpam-5309	41	10	fuzzy	fuzzy	ADJ
ejpam-5309	41	11	γ	γ	NOUN
ejpam-5309	41	12	-	-	PUNCT
ejpam-5309	41	13	subsemigroups	subsemigroup	NOUN
ejpam-5309	41	14	,	,	PUNCT
ejpam-5309	41	15	strongest	strong	ADJ
ejpam-5309	41	16	fuzzy	fuzzy	ADJ
ejpam-5309	41	17	(	(	PUNCT
ejpam-5309	41	18	resp	resp	NOUN
ejpam-5309	41	19	.	.	PUNCT
ejpam-5309	42	1	left	leave	VERB
ejpam-5309	42	2	,	,	PUNCT
ejpam-5309	42	3	right	right	ADJ
ejpam-5309	42	4	,	,	PUNCT
ejpam-5309	42	5	lateral	lateral	ADJ
ejpam-5309	42	6	)	)	PUNCT
ejpam-5309	42	7	γ	γ	NOUN
ejpam-5309	42	8	-	-	NOUN
ejpam-5309	42	9	ideals	ideal	NOUN
ejpam-5309	42	10	,	,	PUNCT
ejpam-5309	42	11	and	and	CCONJ
ejpam-5309	42	12	strongest	strong	ADJ
ejpam-5309	42	13	fuzzy	fuzzy	ADJ
ejpam-5309	42	14	bi	bi	ADJ
ejpam-5309	42	15	-	-	ADJ
ejpam-5309	42	16	γ	γ	NOUN
ejpam-5309	42	17	-	-	PUNCT
ejpam-5309	42	18	ideals	ideal	NOUN
ejpam-5309	42	19	on	on	ADP
ejpam-5309	42	20	ternary	ternary	ADJ
ejpam-5309	42	21	γ	γ	NOUN
ejpam-5309	42	22	-	-	PUNCT
ejpam-5309	42	23	semigroups	semigroup	NOUN
ejpam-5309	42	24	.	.	PUNCT
ejpam-5309	43	1	2	2	X
ejpam-5309	43	2	.	.	NUM
ejpam-5309	43	3	preliminaries	preliminary	NOUN
ejpam-5309	43	4	in	in	ADP
ejpam-5309	43	5	this	this	DET
ejpam-5309	43	6	section	section	NOUN
ejpam-5309	43	7	,	,	PUNCT
ejpam-5309	43	8	we	we	PRON
ejpam-5309	43	9	will	will	AUX
ejpam-5309	43	10	review	review	VERB
ejpam-5309	43	11	important	important	ADJ
ejpam-5309	43	12	basic	basic	ADJ
ejpam-5309	43	13	concepts	concept	NOUN
ejpam-5309	43	14	for	for	ADP
ejpam-5309	43	15	use	use	NOUN
ejpam-5309	43	16	in	in	ADP
ejpam-5309	43	17	the	the	DET
ejpam-5309	43	18	next	next	ADJ
ejpam-5309	43	19	section	section	NOUN
ejpam-5309	43	20	.	.	PUNCT
ejpam-5309	44	1	a	a	DET
ejpam-5309	44	2	fuzzy	fuzzy	ADJ
ejpam-5309	44	3	set	set	NOUN
ejpam-5309	44	4	[	[	X
ejpam-5309	44	5	13	13	NUM
ejpam-5309	44	6	]	]	SYM
ejpam-5309	44	7	µ	µ	NOUN
ejpam-5309	44	8	of	of	ADP
ejpam-5309	44	9	a	a	DET
ejpam-5309	44	10	nonempty	nonempty	ADV
ejpam-5309	44	11	set	set	VERB
ejpam-5309	44	12	x	x	PUNCT
ejpam-5309	44	13	is	be	AUX
ejpam-5309	44	14	a	a	DET
ejpam-5309	44	15	mapping	mapping	NOUN
ejpam-5309	44	16	form	form	NOUN
ejpam-5309	44	17	the	the	DET
ejpam-5309	44	18	set	set	NOUN
ejpam-5309	44	19	x	x	PUNCT
ejpam-5309	44	20	into	into	ADP
ejpam-5309	44	21	[	[	NOUN
ejpam-5309	44	22	0	0	NUM
ejpam-5309	44	23	,	,	PUNCT
ejpam-5309	44	24	1	1	NUM
ejpam-5309	44	25	]	]	PUNCT
ejpam-5309	44	26	.	.	PUNCT
ejpam-5309	45	1	the	the	DET
ejpam-5309	45	2	fuzzy	fuzzy	ADJ
ejpam-5309	45	3	relation	relation	NOUN
ejpam-5309	45	4	[	[	X
ejpam-5309	45	5	3	3	NUM
ejpam-5309	45	6	]	]	X
ejpam-5309	45	7	r	r	NOUN
ejpam-5309	45	8	on	on	ADP
ejpam-5309	45	9	a	a	DET
ejpam-5309	45	10	nonempty	nonempty	ADJ
ejpam-5309	45	11	set	set	VERB
ejpam-5309	45	12	x	x	PUNCT
ejpam-5309	45	13	is	be	AUX
ejpam-5309	45	14	a	a	DET
ejpam-5309	45	15	fuzzy	fuzzy	ADJ
ejpam-5309	45	16	set	set	NOUN
ejpam-5309	45	17	r	r	NOUN
ejpam-5309	45	18	:	:	PUNCT
ejpam-5309	45	19	x	x	X
ejpam-5309	45	20	×x	×x	X
ejpam-5309	45	21	→	→	SYM
ejpam-5309	45	22	[	[	X
ejpam-5309	45	23	0	0	NUM
ejpam-5309	45	24	,	,	PUNCT
ejpam-5309	45	25	1	1	NUM
ejpam-5309	45	26	]	]	PUNCT
ejpam-5309	45	27	.	.	PUNCT
ejpam-5309	46	1	let	let	VERB
ejpam-5309	46	2	r	r	NOUN
ejpam-5309	46	3	be	be	AUX
ejpam-5309	46	4	any	any	DET
ejpam-5309	46	5	fuzzy	fuzzy	ADJ
ejpam-5309	46	6	relation	relation	NOUN
ejpam-5309	46	7	on	on	ADP
ejpam-5309	46	8	a	a	DET
ejpam-5309	46	9	nonempty	nonempty	ADV
ejpam-5309	46	10	set	set	VERB
ejpam-5309	46	11	x	x	NOUN
ejpam-5309	46	12	,	,	PUNCT
ejpam-5309	46	13	and	and	CCONJ
ejpam-5309	46	14	µ	µ	PRON
ejpam-5309	46	15	be	be	AUX
ejpam-5309	46	16	a	a	DET
ejpam-5309	46	17	fuzzy	fuzzy	ADJ
ejpam-5309	46	18	set	set	NOUN
ejpam-5309	46	19	of	of	ADP
ejpam-5309	46	20	x.	x.	NOUN
ejpam-5309	46	21	then	then	ADV
ejpam-5309	46	22	r	r	NOUN
ejpam-5309	46	23	is	be	AUX
ejpam-5309	46	24	said	say	VERB
ejpam-5309	46	25	to	to	PART
ejpam-5309	46	26	be	be	AUX
ejpam-5309	46	27	a	a	DET
ejpam-5309	46	28	fuzzy	fuzzy	ADJ
ejpam-5309	46	29	relation	relation	NOUN
ejpam-5309	46	30	on	on	ADP
ejpam-5309	46	31	µ	µ	PRON
ejpam-5309	46	32	[	[	X
ejpam-5309	46	33	3	3	NUM
ejpam-5309	46	34	]	]	PUNCT
ejpam-5309	46	35	if	if	SCONJ
ejpam-5309	46	36	r(x	r(x	PROPN
ejpam-5309	46	37	,	,	PUNCT
ejpam-5309	46	38	y	y	NOUN
ejpam-5309	46	39	)	)	PUNCT
ejpam-5309	46	40	≤	≤	NOUN
ejpam-5309	47	1	min{µ(x	min{µ(x	NOUN
ejpam-5309	47	2	)	)	PUNCT
ejpam-5309	47	3	,	,	PUNCT
ejpam-5309	47	4	µ(y	µ(y	PROPN
ejpam-5309	47	5	)	)	PUNCT
ejpam-5309	47	6	}	}	PUNCT
ejpam-5309	47	7	,	,	PUNCT
ejpam-5309	47	8	for	for	ADP
ejpam-5309	47	9	all	all	DET
ejpam-5309	47	10	x	x	NOUN
ejpam-5309	47	11	,	,	PUNCT
ejpam-5309	47	12	y	y	PROPN
ejpam-5309	47	13	∈	∈	PROPN
ejpam-5309	47	14	x.	x.	NOUN
ejpam-5309	47	15	definition	definition	NOUN
ejpam-5309	47	16	1	1	NUM
ejpam-5309	47	17	.	.	PUNCT
ejpam-5309	48	1	[	[	X
ejpam-5309	48	2	3	3	X
ejpam-5309	48	3	]	]	X
ejpam-5309	48	4	let	let	VERB
ejpam-5309	48	5	µ	µ	X
ejpam-5309	48	6	be	be	AUX
ejpam-5309	48	7	a	a	DET
ejpam-5309	48	8	fuzzy	fuzzy	ADJ
ejpam-5309	48	9	set	set	NOUN
ejpam-5309	48	10	of	of	ADP
ejpam-5309	48	11	a	a	DET
ejpam-5309	48	12	nonempty	nonempty	ADJ
ejpam-5309	48	13	x	x	NOUN
ejpam-5309	48	14	,	,	PUNCT
ejpam-5309	48	15	and	and	CCONJ
ejpam-5309	48	16	rµ	rµ	VERB
ejpam-5309	48	17	be	be	AUX
ejpam-5309	48	18	a	a	DET
ejpam-5309	48	19	fuzzy	fuzzy	ADJ
ejpam-5309	48	20	relation	relation	NOUN
ejpam-5309	48	21	on	on	ADP
ejpam-5309	48	22	µ.	µ.	NOUN
ejpam-5309	48	23	then	then	ADV
ejpam-5309	48	24	rµ	rµ	INTJ
ejpam-5309	48	25	is	be	AUX
ejpam-5309	48	26	called	call	VERB
ejpam-5309	48	27	a	a	DET
ejpam-5309	48	28	strongest	strong	ADJ
ejpam-5309	48	29	fuzzy	fuzzy	ADJ
ejpam-5309	48	30	relation	relation	NOUN
ejpam-5309	48	31	on	on	ADP
ejpam-5309	48	32	x	x	PUNCT
ejpam-5309	48	33	if	if	SCONJ
ejpam-5309	48	34	rµ(x	rµ(x	NOUN
ejpam-5309	48	35	,	,	PUNCT
ejpam-5309	48	36	y	y	NOUN
ejpam-5309	48	37	)	)	PUNCT
ejpam-5309	48	38	=	=	SYM
ejpam-5309	48	39	min{µ(x	min{µ(x	NOUN
ejpam-5309	48	40	)	)	PUNCT
ejpam-5309	48	41	,	,	PUNCT
ejpam-5309	48	42	µ(y	µ(y	PROPN
ejpam-5309	48	43	)	)	PUNCT
ejpam-5309	48	44	}	}	PUNCT
ejpam-5309	48	45	,	,	PUNCT
ejpam-5309	48	46	for	for	ADP
ejpam-5309	48	47	all	all	DET
ejpam-5309	48	48	x	x	NOUN
ejpam-5309	48	49	,	,	PUNCT
ejpam-5309	48	50	y	y	PROPN
ejpam-5309	48	51	∈	∈	PROPN
ejpam-5309	48	52	x.	x.	NOUN
ejpam-5309	48	53	for	for	ADP
ejpam-5309	48	54	any	any	DET
ejpam-5309	48	55	strongest	strong	ADJ
ejpam-5309	48	56	fuzzy	fuzzy	ADJ
ejpam-5309	48	57	relation	relation	NOUN
ejpam-5309	48	58	rµ	rµ	VERB
ejpam-5309	48	59	on	on	ADP
ejpam-5309	48	60	a	a	DET
ejpam-5309	48	61	nonempty	nonempty	ADV
ejpam-5309	48	62	set	set	VERB
ejpam-5309	48	63	x	x	NOUN
ejpam-5309	48	64	,	,	PUNCT
ejpam-5309	48	65	and	and	CCONJ
ejpam-5309	48	66	for	for	ADP
ejpam-5309	48	67	each	each	DET
ejpam-5309	48	68	t	t	NOUN
ejpam-5309	48	69	∈	∈	PROPN
ejpam-5309	49	1	[	[	X
ejpam-5309	49	2	0	0	NUM
ejpam-5309	49	3	,	,	PUNCT
ejpam-5309	49	4	1	1	NUM
ejpam-5309	49	5	]	]	PUNCT
ejpam-5309	49	6	,	,	PUNCT
ejpam-5309	49	7	we	we	PRON
ejpam-5309	49	8	denote	denote	VERB
ejpam-5309	49	9	by	by	ADP
ejpam-5309	49	10	(	(	PUNCT
ejpam-5309	49	11	rµ)t	rµ)t	VERB
ejpam-5309	49	12	the	the	DET
ejpam-5309	49	13	level	level	NOUN
ejpam-5309	49	14	subset	subset	NOUN
ejpam-5309	49	15	of	of	ADP
ejpam-5309	49	16	rµ	rµ	INTJ
ejpam-5309	49	17	where	where	SCONJ
ejpam-5309	49	18	(	(	PUNCT
ejpam-5309	49	19	rµ)t	rµ)t	NOUN
ejpam-5309	49	20	:	:	PUNCT
ejpam-5309	49	21	=	=	SYM
ejpam-5309	49	22	{	{	PUNCT
ejpam-5309	49	23	(	(	PUNCT
ejpam-5309	49	24	x	x	NOUN
ejpam-5309	49	25	,	,	PUNCT
ejpam-5309	49	26	y	y	NOUN
ejpam-5309	49	27	)	)	PUNCT
ejpam-5309	49	28	|	|	ADV
ejpam-5309	49	29	rµ(x	rµ(x	NOUN
ejpam-5309	49	30	,	,	PUNCT
ejpam-5309	49	31	y	y	PROPN
ejpam-5309	49	32	)	)	PUNCT
ejpam-5309	49	33	≥	≥	NOUN
ejpam-5309	49	34	t	t	PROPN
ejpam-5309	49	35	}	}	PUNCT
ejpam-5309	49	36	(	(	PUNCT
ejpam-5309	49	37	see	see	VERB
ejpam-5309	49	38	[	[	X
ejpam-5309	49	39	3	3	NUM
ejpam-5309	49	40	]	]	NUM
ejpam-5309	49	41	)	)	PUNCT
ejpam-5309	49	42	.	.	PUNCT
ejpam-5309	50	1	let	let	VERB
ejpam-5309	50	2	x	x	PRON
ejpam-5309	50	3	be	be	AUX
ejpam-5309	50	4	a	a	DET
ejpam-5309	50	5	nonempty	nonempty	ADJ
ejpam-5309	50	6	set	set	NOUN
ejpam-5309	50	7	,	,	PUNCT
ejpam-5309	50	8	and	and	CCONJ
ejpam-5309	50	9	µ	µ	X
ejpam-5309	50	10	be	be	AUX
ejpam-5309	50	11	a	a	DET
ejpam-5309	50	12	fuzzy	fuzzy	ADJ
ejpam-5309	50	13	set	set	NOUN
ejpam-5309	50	14	of	of	ADP
ejpam-5309	50	15	x.	x.	NOUN
ejpam-5309	50	16	for	for	ADP
ejpam-5309	50	17	any	any	DET
ejpam-5309	50	18	subset	subset	NOUN
ejpam-5309	50	19	a	a	PRON
ejpam-5309	50	20	of	of	ADP
ejpam-5309	50	21	x	x	PRON
ejpam-5309	50	22	,	,	PUNCT
ejpam-5309	50	23	the	the	DET
ejpam-5309	50	24	characteristic	characteristic	ADJ
ejpam-5309	50	25	function	function	NOUN
ejpam-5309	50	26	χa	χa	ADP
ejpam-5309	50	27	µ	µ	PROPN
ejpam-5309	50	28	of	of	ADP
ejpam-5309	50	29	a	a	PRON
ejpam-5309	50	30	is	be	AUX
ejpam-5309	50	31	a	a	DET
ejpam-5309	50	32	strongest	strong	ADJ
ejpam-5309	50	33	fuzzy	fuzzy	ADJ
ejpam-5309	50	34	relation	relation	NOUN
ejpam-5309	50	35	on	on	ADP
ejpam-5309	50	36	x	x	PUNCT
ejpam-5309	50	37	defined	define	VERB
ejpam-5309	50	38	by	by	ADP
ejpam-5309	50	39	for	for	ADP
ejpam-5309	50	40	every	every	DET
ejpam-5309	50	41	x	x	NOUN
ejpam-5309	50	42	,	,	PUNCT
ejpam-5309	50	43	y	y	PROPN
ejpam-5309	50	44	∈	∈	PROPN
ejpam-5309	50	45	x	x	X
ejpam-5309	50	46	,	,	PUNCT
ejpam-5309	50	47	χa	χa	PROPN
ejpam-5309	50	48	µ	µ	X
ejpam-5309	50	49	(	(	PUNCT
ejpam-5309	50	50	x	x	NOUN
ejpam-5309	50	51	,	,	PUNCT
ejpam-5309	50	52	y	y	PROPN
ejpam-5309	50	53	)	)	PUNCT
ejpam-5309	50	54	=	=	PRON
ejpam-5309	50	55	{	{	PUNCT
ejpam-5309	50	56	1	1	NUM
ejpam-5309	50	57	if	if	SCONJ
ejpam-5309	50	58	x	x	X
ejpam-5309	50	59	,	,	PUNCT
ejpam-5309	50	60	y	y	PROPN
ejpam-5309	50	61	∈	∈	PROPN
ejpam-5309	51	1	a	a	PRON
ejpam-5309	51	2	,	,	PUNCT
ejpam-5309	51	3	0	0	NUM
ejpam-5309	51	4	otherwise	otherwise	ADV
ejpam-5309	51	5	.	.	PUNCT
ejpam-5309	52	1	definition	definition	NOUN
ejpam-5309	52	2	2	2	NUM
ejpam-5309	52	3	.	.	PUNCT
ejpam-5309	53	1	(	(	PUNCT
ejpam-5309	53	2	cf	cf	NOUN
ejpam-5309	53	3	.	.	PUNCT
ejpam-5309	54	1	[	[	X
ejpam-5309	54	2	6	6	NUM
ejpam-5309	54	3	]	]	PUNCT
ejpam-5309	54	4	)	)	PUNCT
ejpam-5309	54	5	let	let	VERB
ejpam-5309	54	6	t	t	PROPN
ejpam-5309	54	7	and	and	CCONJ
ejpam-5309	54	8	γ	γ	PRON
ejpam-5309	54	9	be	be	AUX
ejpam-5309	54	10	two	two	NUM
ejpam-5309	54	11	nonempty	nonempty	ADJ
ejpam-5309	54	12	sets	set	NOUN
ejpam-5309	54	13	.	.	PUNCT
ejpam-5309	55	1	a	a	DET
ejpam-5309	55	2	ternary	ternary	ADJ
ejpam-5309	55	3	γ	γ	NOUN
ejpam-5309	55	4	-	-	PUNCT
ejpam-5309	55	5	semigroup	semigroup	NOUN
ejpam-5309	55	6	is	be	AUX
ejpam-5309	55	7	an	an	DET
ejpam-5309	55	8	algebraic	algebraic	ADJ
ejpam-5309	55	9	structure	structure	NOUN
ejpam-5309	55	10	(	(	PUNCT
ejpam-5309	55	11	t	t	PROPN
ejpam-5309	55	12	,	,	PUNCT
ejpam-5309	55	13	γ	γ	X
ejpam-5309	55	14	,	,	PUNCT
ejpam-5309	55	15	[	[	X
ejpam-5309	55	16	]	]	X
ejpam-5309	55	17	)	)	PUNCT
ejpam-5309	55	18	if	if	SCONJ
ejpam-5309	55	19	there	there	PRON
ejpam-5309	55	20	exist	exist	VERB
ejpam-5309	55	21	a	a	DET
ejpam-5309	55	22	mapping	mapping	NOUN
ejpam-5309	56	1	[	[	PUNCT
ejpam-5309	56	2	]	]	X
ejpam-5309	56	3	:	:	PUNCT
ejpam-5309	56	4	t	t	PROPN
ejpam-5309	56	5	×	×	NOUN
ejpam-5309	56	6	γ×	γ×	PROPN
ejpam-5309	56	7	t	t	NOUN
ejpam-5309	56	8	×	×	NOUN
ejpam-5309	56	9	γ×	γ×	PROPN
ejpam-5309	56	10	t	t	PROPN
ejpam-5309	56	11	→	→	SYM
ejpam-5309	56	12	t	t	PROPN
ejpam-5309	56	13	,	,	PUNCT
ejpam-5309	56	14	written	write	VERB
ejpam-5309	56	15	as	as	ADP
ejpam-5309	56	16	(	(	PUNCT
ejpam-5309	56	17	a	a	PRON
ejpam-5309	56	18	,	,	PUNCT
ejpam-5309	56	19	α	α	PROPN
ejpam-5309	56	20	,	,	PUNCT
ejpam-5309	56	21	b	b	PROPN
ejpam-5309	56	22	,	,	PUNCT
ejpam-5309	56	23	β	β	NOUN
ejpam-5309	56	24	,	,	PUNCT
ejpam-5309	56	25	c	c	NOUN
ejpam-5309	56	26	)	)	PUNCT
ejpam-5309	56	27	→	→	PUNCT
ejpam-5309	57	1	[	[	X
ejpam-5309	57	2	aαbβc	aαbβc	X
ejpam-5309	57	3	]	]	AUX
ejpam-5309	57	4	satisfying	satisfy	VERB
ejpam-5309	57	5	the	the	DET
ejpam-5309	57	6	associative	associative	ADJ
ejpam-5309	57	7	law	law	NOUN
ejpam-5309	57	8	:	:	PUNCT
ejpam-5309	58	1	[	[	X
ejpam-5309	58	2	[	[	X
ejpam-5309	58	3	aαbβc]γdδe	aαbβc]γdδe	X
ejpam-5309	58	4	]	]	X
ejpam-5309	58	5	=	=	PUNCT
ejpam-5309	59	1	[	[	X
ejpam-5309	59	2	aα[bβcγd]δe	aα[bβcγd]δe	X
ejpam-5309	59	3	]	]	X
ejpam-5309	59	4	=	=	PUNCT
ejpam-5309	60	1	[	[	X
ejpam-5309	60	2	aαbβ[cγdδe	aαbβ[cγdδe	X
ejpam-5309	60	3	]	]	X
ejpam-5309	60	4	]	]	X
ejpam-5309	60	5	,	,	PUNCT
ejpam-5309	60	6	w.	w.	PROPN
ejpam-5309	60	7	nakkhasen	nakkhasen	PROPN
ejpam-5309	60	8	et	et	PROPN
ejpam-5309	60	9	al	al	PROPN
ejpam-5309	60	10	.	.	PUNCT
ejpam-5309	60	11	/	/	SYM
ejpam-5309	60	12	eur	eur	PROPN
ejpam-5309	60	13	.	.	PUNCT
ejpam-5309	61	1	j.	j.	PROPN
ejpam-5309	61	2	pure	pure	PROPN
ejpam-5309	61	3	appl	appl	PROPN
ejpam-5309	61	4	.	.	PROPN
ejpam-5309	61	5	math	math	PROPN
ejpam-5309	61	6	,	,	PUNCT
ejpam-5309	61	7	17	17	NUM
ejpam-5309	61	8	(	(	PUNCT
ejpam-5309	61	9	3	3	NUM
ejpam-5309	61	10	)	)	PUNCT
ejpam-5309	61	11	(	(	PUNCT
ejpam-5309	61	12	2024	2024	NUM
ejpam-5309	61	13	)	)	PUNCT
ejpam-5309	61	14	,	,	PUNCT
ejpam-5309	61	15	1417	1417	NUM
ejpam-5309	61	16	-	-	SYM
ejpam-5309	61	17	1428	1428	NUM
ejpam-5309	61	18	1419	1419	NUM
ejpam-5309	61	19	for	for	ADP
ejpam-5309	61	20	all	all	DET
ejpam-5309	61	21	a	a	DET
ejpam-5309	61	22	,	,	PUNCT
ejpam-5309	61	23	b	b	NOUN
ejpam-5309	61	24	,	,	PUNCT
ejpam-5309	61	25	c	c	NOUN
ejpam-5309	61	26	,	,	PUNCT
ejpam-5309	61	27	d	d	NOUN
ejpam-5309	61	28	,	,	PUNCT
ejpam-5309	61	29	e	e	PROPN
ejpam-5309	61	30	∈	∈	PROPN
ejpam-5309	61	31	t	t	PROPN
ejpam-5309	61	32	and	and	CCONJ
ejpam-5309	61	33	α	α	NOUN
ejpam-5309	61	34	,	,	PUNCT
ejpam-5309	61	35	β	β	X
ejpam-5309	61	36	,	,	PUNCT
ejpam-5309	61	37	γ	γ	PROPN
ejpam-5309	61	38	,	,	PUNCT
ejpam-5309	61	39	δ	δ	PROPN
ejpam-5309	61	40	∈	∈	PROPN
ejpam-5309	61	41	γ	γ	X
ejpam-5309	61	42	.	.	PROPN
ejpam-5309	61	43	for	for	ADP
ejpam-5309	61	44	the	the	DET
ejpam-5309	61	45	sake	sake	NOUN
ejpam-5309	61	46	of	of	ADP
ejpam-5309	61	47	simplicity	simplicity	NOUN
ejpam-5309	62	1	,	,	PUNCT
ejpam-5309	62	2	we	we	PRON
ejpam-5309	62	3	will	will	AUX
ejpam-5309	62	4	write	write	VERB
ejpam-5309	62	5	aαbβc	aαbβc	PROPN
ejpam-5309	62	6	instead	instead	ADV
ejpam-5309	62	7	of	of	ADP
ejpam-5309	62	8	[	[	X
ejpam-5309	62	9	aαbβc	aαbβc	X
ejpam-5309	62	10	]	]	X
ejpam-5309	62	11	,	,	PUNCT
ejpam-5309	62	12	for	for	ADP
ejpam-5309	62	13	each	each	DET
ejpam-5309	62	14	a	a	DET
ejpam-5309	62	15	,	,	PUNCT
ejpam-5309	62	16	b	b	NOUN
ejpam-5309	62	17	,	,	PUNCT
ejpam-5309	62	18	c	c	PROPN
ejpam-5309	62	19	∈	∈	PROPN
ejpam-5309	62	20	t	t	PROPN
ejpam-5309	62	21	and	and	CCONJ
ejpam-5309	62	22	α	α	NOUN
ejpam-5309	62	23	,	,	PUNCT
ejpam-5309	62	24	β	β	PROPN
ejpam-5309	62	25	∈	∈	PROPN
ejpam-5309	62	26	γ	γ	X
ejpam-5309	62	27	.	.	PUNCT
ejpam-5309	63	1	let	let	VERB
ejpam-5309	63	2	a	a	DET
ejpam-5309	63	3	,	,	PUNCT
ejpam-5309	63	4	b	b	NOUN
ejpam-5309	63	5	and	and	CCONJ
ejpam-5309	63	6	c	c	PROPN
ejpam-5309	63	7	be	be	AUX
ejpam-5309	63	8	any	any	DET
ejpam-5309	63	9	nonempty	nonempty	ADJ
ejpam-5309	63	10	subsets	subset	NOUN
ejpam-5309	63	11	of	of	ADP
ejpam-5309	63	12	a	a	DET
ejpam-5309	63	13	ternary	ternary	ADJ
ejpam-5309	63	14	γ	γ	NOUN
ejpam-5309	63	15	-	-	PUNCT
ejpam-5309	63	16	semigroup	semigroup	PROPN
ejpam-5309	63	17	t	t	PROPN
ejpam-5309	63	18	.	.	PUNCT
ejpam-5309	64	1	we	we	PRON
ejpam-5309	64	2	denote	denote	VERB
ejpam-5309	64	3	the	the	DET
ejpam-5309	64	4	set	set	NOUN
ejpam-5309	64	5	aγbγc	aγbγc	NOUN
ejpam-5309	64	6	:	:	PUNCT
ejpam-5309	64	7	=	=	SYM
ejpam-5309	64	8	{	{	PUNCT
ejpam-5309	64	9	aαbβc	aαbβc	INTJ
ejpam-5309	64	10	|	|	ADV
ejpam-5309	64	11	a	a	DET
ejpam-5309	64	12	∈	∈	PROPN
ejpam-5309	64	13	a	a	PRON
ejpam-5309	64	14	,	,	PUNCT
ejpam-5309	64	15	b	b	PROPN
ejpam-5309	64	16	∈	∈	PROPN
ejpam-5309	64	17	b	b	PROPN
ejpam-5309	64	18	,	,	PUNCT
ejpam-5309	64	19	c	c	PROPN
ejpam-5309	64	20	∈	∈	PROPN
ejpam-5309	64	21	c	c	X
ejpam-5309	64	22	,	,	PUNCT
ejpam-5309	64	23	α	α	X
ejpam-5309	64	24	,	,	PUNCT
ejpam-5309	64	25	β	β	X
ejpam-5309	64	26	∈	∈	PROPN
ejpam-5309	64	27	γ	γ	X
ejpam-5309	64	28	}	}	PUNCT
ejpam-5309	64	29	.	.	PUNCT
ejpam-5309	65	1	we	we	PRON
ejpam-5309	65	2	now	now	ADV
ejpam-5309	65	3	review	review	VERB
ejpam-5309	65	4	the	the	DET
ejpam-5309	65	5	concepts	concept	NOUN
ejpam-5309	65	6	of	of	ADP
ejpam-5309	65	7	various	various	ADJ
ejpam-5309	65	8	kinds	kind	NOUN
ejpam-5309	65	9	of	of	ADP
ejpam-5309	65	10	γ	γ	NOUN
ejpam-5309	65	11	-	-	PUNCT
ejpam-5309	65	12	ideals	ideal	NOUN
ejpam-5309	65	13	and	and	CCONJ
ejpam-5309	65	14	fuzzy	fuzzy	ADJ
ejpam-5309	65	15	γ	γ	NOUN
ejpam-5309	65	16	-	-	NOUN
ejpam-5309	65	17	ideals	ideal	NOUN
ejpam-5309	65	18	in	in	ADP
ejpam-5309	65	19	ternary	ternary	ADJ
ejpam-5309	65	20	γ	γ	X
ejpam-5309	65	21	-	-	PUNCT
ejpam-5309	65	22	semigroups	semigroup	NOUN
ejpam-5309	65	23	that	that	PRON
ejpam-5309	65	24	appeared	appear	VERB
ejpam-5309	65	25	in	in	ADP
ejpam-5309	65	26	[	[	X
ejpam-5309	65	27	2	2	NUM
ejpam-5309	65	28	]	]	PUNCT
ejpam-5309	65	29	in	in	ADP
ejpam-5309	65	30	the	the	DET
ejpam-5309	65	31	following	following	ADJ
ejpam-5309	65	32	ways	way	NOUN
ejpam-5309	65	33	.	.	PUNCT
ejpam-5309	66	1	definition	definition	NOUN
ejpam-5309	66	2	3	3	NUM
ejpam-5309	66	3	.	.	PUNCT
ejpam-5309	67	1	[	[	X
ejpam-5309	67	2	2	2	X
ejpam-5309	67	3	]	]	PUNCT
ejpam-5309	67	4	let	let	VERB
ejpam-5309	67	5	a	a	DET
ejpam-5309	67	6	be	be	AUX
ejpam-5309	67	7	any	any	DET
ejpam-5309	67	8	nonempty	nonempty	NOUN
ejpam-5309	67	9	subset	subset	NOUN
ejpam-5309	67	10	of	of	ADP
ejpam-5309	67	11	a	a	DET
ejpam-5309	67	12	ternary	ternary	ADJ
ejpam-5309	67	13	γ	γ	NOUN
ejpam-5309	67	14	-	-	PUNCT
ejpam-5309	67	15	semigroup	semigroup	PROPN
ejpam-5309	67	16	t	t	PROPN
ejpam-5309	67	17	.	.	PUNCT
ejpam-5309	68	1	then	then	ADV
ejpam-5309	68	2	:	:	PUNCT
ejpam-5309	68	3	(	(	PUNCT
ejpam-5309	68	4	i	i	NOUN
ejpam-5309	68	5	)	)	PUNCT
ejpam-5309	68	6	a	a	PRON
ejpam-5309	68	7	is	be	AUX
ejpam-5309	68	8	called	call	VERB
ejpam-5309	68	9	a	a	DET
ejpam-5309	68	10	ternary	ternary	ADJ
ejpam-5309	68	11	γ	γ	NOUN
ejpam-5309	68	12	-	-	NOUN
ejpam-5309	68	13	subsemigroup	subsemigroup	NOUN
ejpam-5309	68	14	of	of	ADP
ejpam-5309	68	15	t	t	PROPN
ejpam-5309	68	16	if	if	SCONJ
ejpam-5309	68	17	aγaγa	aγaγa	NOUN
ejpam-5309	68	18	⊆	⊆	SYM
ejpam-5309	68	19	a	a	PRON
ejpam-5309	68	20	;	;	PUNCT
ejpam-5309	68	21	(	(	PUNCT
ejpam-5309	68	22	ii	ii	NOUN
ejpam-5309	68	23	)	)	PUNCT
ejpam-5309	68	24	a	a	PRON
ejpam-5309	68	25	is	be	AUX
ejpam-5309	68	26	called	call	VERB
ejpam-5309	68	27	a	a	DET
ejpam-5309	68	28	left	left	ADJ
ejpam-5309	68	29	(	(	PUNCT
ejpam-5309	68	30	resp	resp	NOUN
ejpam-5309	68	31	.	.	PUNCT
ejpam-5309	69	1	right	right	ADJ
ejpam-5309	69	2	,	,	PUNCT
ejpam-5309	69	3	lateral	lateral	ADJ
ejpam-5309	69	4	)	)	PUNCT
ejpam-5309	69	5	γ	γ	NOUN
ejpam-5309	69	6	-	-	NOUN
ejpam-5309	69	7	ideal	ideal	NOUN
ejpam-5309	69	8	of	of	ADP
ejpam-5309	69	9	t	t	PROPN
ejpam-5309	69	10	if	if	SCONJ
ejpam-5309	69	11	tγtγa	tγtγa	VERB
ejpam-5309	69	12	⊆	⊆	NUM
ejpam-5309	69	13	a	a	DET
ejpam-5309	69	14	(	(	PUNCT
ejpam-5309	69	15	resp	resp	NOUN
ejpam-5309	69	16	.	.	PUNCT
ejpam-5309	70	1	aγtγt	aγtγt	VERB
ejpam-5309	70	2	⊆	⊆	NUM
ejpam-5309	70	3	a	a	PRON
ejpam-5309	70	4	,	,	PUNCT
ejpam-5309	70	5	tγaγt	tγaγt	PROPN
ejpam-5309	70	6	⊆	⊆	NUM
ejpam-5309	70	7	a	a	PRON
ejpam-5309	70	8	)	)	PUNCT
ejpam-5309	70	9	;	;	PUNCT
ejpam-5309	70	10	(	(	PUNCT
ejpam-5309	70	11	iii	iii	X
ejpam-5309	70	12	)	)	PUNCT
ejpam-5309	70	13	a	a	PRON
ejpam-5309	70	14	is	be	AUX
ejpam-5309	70	15	called	call	VERB
ejpam-5309	70	16	a	a	DET
ejpam-5309	70	17	γ	γ	NOUN
ejpam-5309	70	18	-	-	NOUN
ejpam-5309	70	19	ideal	ideal	NOUN
ejpam-5309	70	20	of	of	ADP
ejpam-5309	70	21	t	t	PROPN
ejpam-5309	70	22	if	if	SCONJ
ejpam-5309	70	23	it	it	PRON
ejpam-5309	70	24	is	be	AUX
ejpam-5309	70	25	a	a	DET
ejpam-5309	70	26	left	left	NOUN
ejpam-5309	70	27	,	,	PUNCT
ejpam-5309	70	28	a	a	DET
ejpam-5309	70	29	right	right	NOUN
ejpam-5309	70	30	,	,	PUNCT
ejpam-5309	70	31	and	and	CCONJ
ejpam-5309	70	32	a	a	DET
ejpam-5309	70	33	lateral	lateral	ADJ
ejpam-5309	70	34	γ	γ	NOUN
ejpam-5309	70	35	-	-	NOUN
ejpam-5309	70	36	ideal	ideal	NOUN
ejpam-5309	70	37	of	of	ADP
ejpam-5309	70	38	t	t	PROPN
ejpam-5309	70	39	;	;	PUNCT
ejpam-5309	70	40	(	(	PUNCT
ejpam-5309	70	41	iv	iv	X
ejpam-5309	70	42	)	)	PUNCT
ejpam-5309	70	43	a	a	DET
ejpam-5309	70	44	ternary	ternary	ADJ
ejpam-5309	70	45	γ	γ	X
ejpam-5309	70	46	-	-	NOUN
ejpam-5309	70	47	subsemigroup	subsemigroup	NOUN
ejpam-5309	70	48	a	a	PRON
ejpam-5309	70	49	of	of	ADP
ejpam-5309	70	50	t	t	PROPN
ejpam-5309	70	51	is	be	AUX
ejpam-5309	70	52	called	call	VERB
ejpam-5309	70	53	a	a	DET
ejpam-5309	70	54	bi	bi	ADJ
ejpam-5309	70	55	-	-	ADJ
ejpam-5309	70	56	γ	γ	NOUN
ejpam-5309	70	57	-	-	NOUN
ejpam-5309	70	58	ideal	ideal	NOUN
ejpam-5309	70	59	of	of	ADP
ejpam-5309	70	60	t	t	PROPN
ejpam-5309	70	61	if	if	SCONJ
ejpam-5309	70	62	tγaγtγaγt	tγaγtγaγt	PROPN
ejpam-5309	70	63	⊆	⊆	NUM
ejpam-5309	70	64	a.	a.	NOUN
ejpam-5309	70	65	definition	definition	NOUN
ejpam-5309	70	66	4	4	NUM
ejpam-5309	70	67	.	.	PUNCT
ejpam-5309	71	1	[	[	X
ejpam-5309	71	2	2	2	X
ejpam-5309	71	3	]	]	PUNCT
ejpam-5309	71	4	let	let	VERB
ejpam-5309	71	5	µ	µ	X
ejpam-5309	71	6	be	be	AUX
ejpam-5309	71	7	any	any	DET
ejpam-5309	71	8	fuzzy	fuzzy	ADJ
ejpam-5309	71	9	set	set	NOUN
ejpam-5309	71	10	of	of	ADP
ejpam-5309	71	11	a	a	DET
ejpam-5309	71	12	ternary	ternary	ADJ
ejpam-5309	71	13	γ	γ	NOUN
ejpam-5309	71	14	-	-	PUNCT
ejpam-5309	71	15	semigroup	semigroup	PROPN
ejpam-5309	71	16	t	t	PROPN
ejpam-5309	71	17	.	.	PUNCT
ejpam-5309	72	1	then	then	ADV
ejpam-5309	72	2	:	:	PUNCT
ejpam-5309	72	3	(	(	PUNCT
ejpam-5309	72	4	i	i	NOUN
ejpam-5309	72	5	)	)	PUNCT
ejpam-5309	72	6	µ	µ	PROPN
ejpam-5309	72	7	is	be	AUX
ejpam-5309	72	8	called	call	VERB
ejpam-5309	72	9	a	a	DET
ejpam-5309	72	10	fuzzy	fuzzy	ADJ
ejpam-5309	72	11	ternary	ternary	ADJ
ejpam-5309	72	12	γ	γ	X
ejpam-5309	72	13	-	-	NOUN
ejpam-5309	72	14	subsemigroup	subsemigroup	NOUN
ejpam-5309	72	15	of	of	ADP
ejpam-5309	72	16	t	t	PROPN
ejpam-5309	72	17	if	if	SCONJ
ejpam-5309	72	18	µ(aαbβc	µ(aαbβc	PROPN
ejpam-5309	72	19	)	)	PUNCT
ejpam-5309	72	20	≥	≥	NOUN
ejpam-5309	72	21	min{µ(a	min{µ(a	PROPN
ejpam-5309	72	22	)	)	PUNCT
ejpam-5309	72	23	,	,	PUNCT
ejpam-5309	72	24	µ(b	µ(b	PROPN
ejpam-5309	72	25	)	)	PUNCT
ejpam-5309	72	26	,	,	PUNCT
ejpam-5309	72	27	µ(c	µ(c	PROPN
ejpam-5309	72	28	)	)	PUNCT
ejpam-5309	72	29	}	}	PUNCT
ejpam-5309	72	30	,	,	PUNCT
ejpam-5309	72	31	for	for	ADP
ejpam-5309	72	32	all	all	DET
ejpam-5309	72	33	a	a	DET
ejpam-5309	72	34	,	,	PUNCT
ejpam-5309	72	35	b	b	NOUN
ejpam-5309	72	36	,	,	PUNCT
ejpam-5309	72	37	c	c	PROPN
ejpam-5309	72	38	∈	∈	PROPN
ejpam-5309	72	39	t	t	PROPN
ejpam-5309	72	40	and	and	CCONJ
ejpam-5309	72	41	α	α	NOUN
ejpam-5309	72	42	,	,	PUNCT
ejpam-5309	72	43	β	β	PROPN
ejpam-5309	72	44	∈	∈	PROPN
ejpam-5309	72	45	γ	γ	X
ejpam-5309	72	46	;	;	PUNCT
ejpam-5309	72	47	(	(	PUNCT
ejpam-5309	72	48	ii	ii	NOUN
ejpam-5309	72	49	)	)	PUNCT
ejpam-5309	72	50	µ	µ	PROPN
ejpam-5309	72	51	is	be	AUX
ejpam-5309	72	52	called	call	VERB
ejpam-5309	72	53	a	a	DET
ejpam-5309	72	54	fuzzy	fuzzy	ADJ
ejpam-5309	72	55	left	left	NOUN
ejpam-5309	72	56	(	(	PUNCT
ejpam-5309	72	57	resp	resp	NOUN
ejpam-5309	72	58	.	.	PUNCT
ejpam-5309	73	1	right	right	ADJ
ejpam-5309	73	2	,	,	PUNCT
ejpam-5309	73	3	lateral	lateral	ADJ
ejpam-5309	73	4	)	)	PUNCT
ejpam-5309	73	5	γ	γ	NOUN
ejpam-5309	73	6	-	-	NOUN
ejpam-5309	73	7	ideal	ideal	NOUN
ejpam-5309	73	8	of	of	ADP
ejpam-5309	73	9	t	t	PROPN
ejpam-5309	73	10	if	if	SCONJ
ejpam-5309	73	11	µ(aαbβc	µ(aαbβc	PROPN
ejpam-5309	73	12	)	)	PUNCT
ejpam-5309	73	13	≥	≥	NOUN
ejpam-5309	73	14	µ(c	µ(c	PROPN
ejpam-5309	73	15	)	)	PUNCT
ejpam-5309	73	16	(	(	PUNCT
ejpam-5309	73	17	resp	resp	NOUN
ejpam-5309	73	18	.	.	PUNCT
ejpam-5309	74	1	µ(aαbβc	µ(aαbβc	PROPN
ejpam-5309	74	2	)	)	PUNCT
ejpam-5309	74	3	≥	≥	NOUN
ejpam-5309	74	4	µ(a	µ(a	PROPN
ejpam-5309	74	5	)	)	PUNCT
ejpam-5309	74	6	,	,	PUNCT
ejpam-5309	74	7	µ(aαbβc	µ(aαbβc	PROPN
ejpam-5309	74	8	)	)	PUNCT
ejpam-5309	74	9	≥	≥	NOUN
ejpam-5309	74	10	µ(b	µ(b	NOUN
ejpam-5309	74	11	)	)	PUNCT
ejpam-5309	74	12	)	)	PUNCT
ejpam-5309	75	1	,	,	PUNCT
ejpam-5309	75	2	for	for	ADP
ejpam-5309	75	3	all	all	DET
ejpam-5309	75	4	a	a	DET
ejpam-5309	75	5	,	,	PUNCT
ejpam-5309	75	6	b	b	NOUN
ejpam-5309	75	7	,	,	PUNCT
ejpam-5309	75	8	c	c	PROPN
ejpam-5309	75	9	∈	∈	PROPN
ejpam-5309	75	10	t	t	PROPN
ejpam-5309	75	11	and	and	CCONJ
ejpam-5309	75	12	α	α	NOUN
ejpam-5309	75	13	,	,	PUNCT
ejpam-5309	75	14	β	β	PROPN
ejpam-5309	75	15	∈	∈	PROPN
ejpam-5309	75	16	γ	γ	X
ejpam-5309	75	17	;	;	PUNCT
ejpam-5309	75	18	(	(	PUNCT
ejpam-5309	75	19	iii	iii	X
ejpam-5309	75	20	)	)	PUNCT
ejpam-5309	75	21	µ	µ	PROPN
ejpam-5309	75	22	is	be	AUX
ejpam-5309	75	23	called	call	VERB
ejpam-5309	75	24	a	a	DET
ejpam-5309	75	25	fuzzy	fuzzy	ADJ
ejpam-5309	75	26	γ	γ	NOUN
ejpam-5309	75	27	-	-	NOUN
ejpam-5309	75	28	ideal	ideal	NOUN
ejpam-5309	75	29	of	of	ADP
ejpam-5309	75	30	t	t	PROPN
ejpam-5309	75	31	if	if	SCONJ
ejpam-5309	75	32	it	it	PRON
ejpam-5309	75	33	is	be	AUX
ejpam-5309	75	34	a	a	DET
ejpam-5309	75	35	fuzzy	fuzzy	ADJ
ejpam-5309	75	36	left	leave	VERB
ejpam-5309	75	37	γ	γ	NOUN
ejpam-5309	75	38	-	-	PUNCT
ejpam-5309	75	39	ideal	ideal	ADJ
ejpam-5309	75	40	,	,	PUNCT
ejpam-5309	75	41	a	a	DET
ejpam-5309	75	42	fuzzy	fuzzy	ADJ
ejpam-5309	75	43	right	right	ADJ
ejpam-5309	75	44	γ	γ	X
ejpam-5309	75	45	-	-	NOUN
ejpam-5309	75	46	ideal	ideal	ADJ
ejpam-5309	75	47	,	,	PUNCT
ejpam-5309	75	48	and	and	CCONJ
ejpam-5309	75	49	a	a	DET
ejpam-5309	75	50	fuzzy	fuzzy	ADJ
ejpam-5309	75	51	lateral	lateral	ADJ
ejpam-5309	75	52	γ	γ	NOUN
ejpam-5309	75	53	-	-	NOUN
ejpam-5309	75	54	ideal	ideal	NOUN
ejpam-5309	75	55	of	of	ADP
ejpam-5309	75	56	t	t	PROPN
ejpam-5309	75	57	;	;	PUNCT
ejpam-5309	75	58	(	(	PUNCT
ejpam-5309	75	59	iv	iv	X
ejpam-5309	75	60	)	)	PUNCT
ejpam-5309	75	61	a	a	DET
ejpam-5309	75	62	fuzzy	fuzzy	ADJ
ejpam-5309	75	63	ternary	ternary	ADJ
ejpam-5309	75	64	γ	γ	PROPN
ejpam-5309	75	65	-	-	PROPN
ejpam-5309	75	66	subsemigroup	subsemigroup	NOUN
ejpam-5309	75	67	µ	µ	PROPN
ejpam-5309	75	68	of	of	ADP
ejpam-5309	75	69	t	t	PROPN
ejpam-5309	75	70	is	be	AUX
ejpam-5309	75	71	called	call	VERB
ejpam-5309	75	72	a	a	DET
ejpam-5309	75	73	fuzzy	fuzzy	ADJ
ejpam-5309	75	74	bi	bi	ADJ
ejpam-5309	75	75	-	-	ADJ
ejpam-5309	75	76	γ	γ	NOUN
ejpam-5309	75	77	-	-	NOUN
ejpam-5309	75	78	ideal	ideal	NOUN
ejpam-5309	75	79	of	of	ADP
ejpam-5309	75	80	t	t	PROPN
ejpam-5309	75	81	if	if	SCONJ
ejpam-5309	75	82	µ(aαbβcγdδe	µ(aαbβcγdδe	ADV
ejpam-5309	75	83	)	)	PUNCT
ejpam-5309	75	84	≥	≥	NOUN
ejpam-5309	75	85	min{µ(a	min{µ(a	PROPN
ejpam-5309	75	86	)	)	PUNCT
ejpam-5309	75	87	,	,	PUNCT
ejpam-5309	75	88	µ(c	µ(c	PROPN
ejpam-5309	75	89	)	)	PUNCT
ejpam-5309	75	90	,	,	PUNCT
ejpam-5309	75	91	µ(e	µ(e	PROPN
ejpam-5309	75	92	)	)	PUNCT
ejpam-5309	75	93	}	}	PUNCT
ejpam-5309	75	94	,	,	PUNCT
ejpam-5309	75	95	for	for	ADP
ejpam-5309	75	96	all	all	DET
ejpam-5309	75	97	a	a	DET
ejpam-5309	75	98	,	,	PUNCT
ejpam-5309	75	99	b	b	NOUN
ejpam-5309	75	100	,	,	PUNCT
ejpam-5309	75	101	c	c	NOUN
ejpam-5309	75	102	,	,	PUNCT
ejpam-5309	75	103	d	d	NOUN
ejpam-5309	75	104	,	,	PUNCT
ejpam-5309	75	105	e	e	PROPN
ejpam-5309	75	106	∈	∈	PROPN
ejpam-5309	75	107	t	t	PROPN
ejpam-5309	75	108	and	and	CCONJ
ejpam-5309	75	109	α	α	NOUN
ejpam-5309	75	110	,	,	PUNCT
ejpam-5309	75	111	β	β	X
ejpam-5309	75	112	,	,	PUNCT
ejpam-5309	75	113	γ	γ	PROPN
ejpam-5309	75	114	,	,	PUNCT
ejpam-5309	75	115	δ	δ	PROPN
ejpam-5309	75	116	∈	∈	PROPN
ejpam-5309	75	117	γ	γ	PROPN
ejpam-5309	75	118	.	.	PUNCT
ejpam-5309	76	1	let	let	VERB
ejpam-5309	76	2	s	s	PRON
ejpam-5309	76	3	and	and	CCONJ
ejpam-5309	76	4	t	t	PROPN
ejpam-5309	76	5	be	be	AUX
ejpam-5309	76	6	ternary	ternary	ADJ
ejpam-5309	76	7	γ	γ	X
ejpam-5309	76	8	-	-	PUNCT
ejpam-5309	76	9	semigroups	semigroup	NOUN
ejpam-5309	76	10	with	with	ADP
ejpam-5309	76	11	respect	respect	NOUN
ejpam-5309	76	12	to	to	ADP
ejpam-5309	76	13	the	the	DET
ejpam-5309	76	14	same	same	ADJ
ejpam-5309	76	15	set	set	NOUN
ejpam-5309	76	16	γ	γ	PROPN
ejpam-5309	76	17	.	.	PUNCT
ejpam-5309	77	1	the	the	DET
ejpam-5309	77	2	mapping	mapping	NOUN
ejpam-5309	77	3	·	·	PUNCT
ejpam-5309	77	4	:	:	PUNCT
ejpam-5309	77	5	(	(	PUNCT
ejpam-5309	77	6	s	s	NOUN
ejpam-5309	77	7	×	×	PROPN
ejpam-5309	77	8	t	t	NOUN
ejpam-5309	77	9	)	)	PUNCT
ejpam-5309	77	10	×	×	NOUN
ejpam-5309	77	11	γ×	γ×	NOUN
ejpam-5309	78	1	(	(	PUNCT
ejpam-5309	78	2	s	s	NOUN
ejpam-5309	78	3	×	×	PROPN
ejpam-5309	78	4	t	t	NOUN
ejpam-5309	78	5	)	)	PUNCT
ejpam-5309	78	6	×	×	NOUN
ejpam-5309	78	7	γ×	γ×	NOUN
ejpam-5309	79	1	(	(	PUNCT
ejpam-5309	79	2	s	s	PROPN
ejpam-5309	79	3	×	×	PROPN
ejpam-5309	79	4	t	t	NOUN
ejpam-5309	79	5	)	)	PUNCT
ejpam-5309	79	6	→	→	SYM
ejpam-5309	79	7	s	s	X
ejpam-5309	79	8	×	×	PROPN
ejpam-5309	79	9	t	t	NOUN
ejpam-5309	79	10	is	be	AUX
ejpam-5309	79	11	defined	define	VERB
ejpam-5309	79	12	by	by	ADP
ejpam-5309	79	13	(	(	PUNCT
ejpam-5309	79	14	s1	s1	PROPN
ejpam-5309	79	15	,	,	PUNCT
ejpam-5309	79	16	t1)α(s2	t1)α(s2	PROPN
ejpam-5309	79	17	,	,	PUNCT
ejpam-5309	79	18	t2)β(s3	t2)β(s3	PROPN
ejpam-5309	79	19	,	,	PUNCT
ejpam-5309	79	20	t3	t3	PROPN
ejpam-5309	79	21	)	)	PUNCT
ejpam-5309	79	22	=	=	PUNCT
ejpam-5309	79	23	(	(	PUNCT
ejpam-5309	79	24	s1αs2βs3	s1αs2βs3	NUM
ejpam-5309	79	25	,	,	PUNCT
ejpam-5309	79	26	t1αt2βt3	t1αt2βt3	NOUN
ejpam-5309	79	27	)	)	PUNCT
ejpam-5309	79	28	,	,	PUNCT
ejpam-5309	79	29	for	for	ADP
ejpam-5309	79	30	all	all	DET
ejpam-5309	79	31	(	(	PUNCT
ejpam-5309	79	32	s1	s1	PROPN
ejpam-5309	79	33	,	,	PUNCT
ejpam-5309	79	34	t1	t1	NOUN
ejpam-5309	79	35	)	)	PUNCT
ejpam-5309	79	36	,	,	PUNCT
ejpam-5309	79	37	(	(	PUNCT
ejpam-5309	79	38	s2	s2	PROPN
ejpam-5309	79	39	,	,	PUNCT
ejpam-5309	79	40	t2	t2	NOUN
ejpam-5309	79	41	)	)	PUNCT
ejpam-5309	79	42	,	,	PUNCT
ejpam-5309	79	43	(	(	PUNCT
ejpam-5309	79	44	s3	s3	PROPN
ejpam-5309	79	45	,	,	PUNCT
ejpam-5309	79	46	t3	t3	PROPN
ejpam-5309	79	47	)	)	PUNCT
ejpam-5309	79	48	∈	∈	PROPN
ejpam-5309	79	49	s	s	PART
ejpam-5309	79	50	×	×	NOUN
ejpam-5309	79	51	t	t	NOUN
ejpam-5309	79	52	and	and	CCONJ
ejpam-5309	79	53	α	α	NOUN
ejpam-5309	79	54	,	,	PUNCT
ejpam-5309	79	55	β	β	PROPN
ejpam-5309	79	56	∈	∈	PROPN
ejpam-5309	79	57	γ	γ	X
ejpam-5309	79	58	.	.	PUNCT
ejpam-5309	80	1	then	then	ADV
ejpam-5309	80	2	s	s	AUX
ejpam-5309	80	3	×	×	PROPN
ejpam-5309	80	4	t	t	PROPN
ejpam-5309	80	5	forms	form	VERB
ejpam-5309	80	6	a	a	DET
ejpam-5309	80	7	ternary	ternary	ADJ
ejpam-5309	80	8	γsemigroup	γsemigroup	NOUN
ejpam-5309	80	9	(	(	PUNCT
ejpam-5309	80	10	see	see	VERB
ejpam-5309	80	11	[	[	X
ejpam-5309	80	12	2	2	NUM
ejpam-5309	80	13	]	]	NUM
ejpam-5309	80	14	)	)	PUNCT
ejpam-5309	80	15	.	.	PUNCT
ejpam-5309	81	1	3	3	X
ejpam-5309	81	2	.	.	X
ejpam-5309	81	3	strongest	strong	ADJ
ejpam-5309	81	4	fuzzy	fuzzy	ADJ
ejpam-5309	81	5	γ	γ	NOUN
ejpam-5309	81	6	-	-	NOUN
ejpam-5309	81	7	ideals	ideal	NOUN
ejpam-5309	81	8	on	on	ADP
ejpam-5309	81	9	ternary	ternary	ADJ
ejpam-5309	81	10	γ	γ	X
ejpam-5309	81	11	-	-	PUNCT
ejpam-5309	81	12	semigroups	semigroup	NOUN
ejpam-5309	81	13	in	in	ADP
ejpam-5309	81	14	this	this	DET
ejpam-5309	81	15	section	section	NOUN
ejpam-5309	81	16	,	,	PUNCT
ejpam-5309	81	17	we	we	PRON
ejpam-5309	81	18	introduce	introduce	VERB
ejpam-5309	81	19	the	the	DET
ejpam-5309	81	20	concepts	concept	NOUN
ejpam-5309	81	21	of	of	ADP
ejpam-5309	81	22	strongest	strong	ADJ
ejpam-5309	81	23	fuzzy	fuzzy	ADJ
ejpam-5309	81	24	ternary	ternary	ADJ
ejpam-5309	81	25	γ	γ	NOUN
ejpam-5309	81	26	-	-	NOUN
ejpam-5309	81	27	subsemigroups	subsemigroup	NOUN
ejpam-5309	81	28	,	,	PUNCT
ejpam-5309	81	29	strongest	strong	ADJ
ejpam-5309	81	30	fuzzy	fuzzy	ADJ
ejpam-5309	81	31	(	(	PUNCT
ejpam-5309	81	32	resp	resp	NOUN
ejpam-5309	81	33	.	.	PUNCT
ejpam-5309	82	1	left	leave	VERB
ejpam-5309	82	2	,	,	PUNCT
ejpam-5309	82	3	right	right	INTJ
ejpam-5309	82	4	,	,	PUNCT
ejpam-5309	82	5	and	and	CCONJ
ejpam-5309	82	6	lateral	lateral	ADJ
ejpam-5309	82	7	)	)	PUNCT
ejpam-5309	82	8	γ	γ	NOUN
ejpam-5309	82	9	-	-	NOUN
ejpam-5309	82	10	ideals	ideal	NOUN
ejpam-5309	82	11	,	,	PUNCT
ejpam-5309	82	12	and	and	CCONJ
ejpam-5309	82	13	strongest	strong	ADJ
ejpam-5309	82	14	fuzzy	fuzzy	ADJ
ejpam-5309	82	15	bi	bi	ADJ
ejpam-5309	82	16	-	-	ADJ
ejpam-5309	82	17	γ	γ	NOUN
ejpam-5309	82	18	-	-	PUNCT
ejpam-5309	82	19	ideals	ideal	NOUN
ejpam-5309	82	20	on	on	ADP
ejpam-5309	82	21	ternary	ternary	ADJ
ejpam-5309	82	22	γ	γ	NOUN
ejpam-5309	82	23	-	-	PUNCT
ejpam-5309	82	24	semigroups	semigroup	NOUN
ejpam-5309	82	25	.	.	PUNCT
ejpam-5309	83	1	then	then	ADV
ejpam-5309	83	2	we	we	PRON
ejpam-5309	83	3	study	study	VERB
ejpam-5309	83	4	the	the	DET
ejpam-5309	83	5	relationships	relationship	NOUN
ejpam-5309	83	6	and	and	CCONJ
ejpam-5309	83	7	characterizations	characterization	NOUN
ejpam-5309	83	8	of	of	ADP
ejpam-5309	83	9	these	these	DET
ejpam-5309	83	10	concepts	concept	NOUN
ejpam-5309	83	11	in	in	ADP
ejpam-5309	83	12	ternary	ternary	ADJ
ejpam-5309	83	13	γ	γ	NOUN
ejpam-5309	83	14	-	-	PUNCT
ejpam-5309	83	15	semigroups	semigroup	NOUN
ejpam-5309	83	16	.	.	PUNCT
ejpam-5309	84	1	w.	w.	PROPN
ejpam-5309	84	2	nakkhasen	nakkhasen	PROPN
ejpam-5309	84	3	et	et	PROPN
ejpam-5309	84	4	al	al	PROPN
ejpam-5309	84	5	.	.	PUNCT
ejpam-5309	84	6	/	/	SYM
ejpam-5309	84	7	eur	eur	PROPN
ejpam-5309	84	8	.	.	PUNCT
ejpam-5309	85	1	j.	j.	PROPN
ejpam-5309	85	2	pure	pure	PROPN
ejpam-5309	85	3	appl	appl	PROPN
ejpam-5309	85	4	.	.	PROPN
ejpam-5309	85	5	math	math	PROPN
ejpam-5309	85	6	,	,	PUNCT
ejpam-5309	85	7	17	17	NUM
ejpam-5309	85	8	(	(	PUNCT
ejpam-5309	85	9	3	3	NUM
ejpam-5309	85	10	)	)	PUNCT
ejpam-5309	85	11	(	(	PUNCT
ejpam-5309	85	12	2024	2024	NUM
ejpam-5309	85	13	)	)	PUNCT
ejpam-5309	85	14	,	,	PUNCT
ejpam-5309	85	15	1417	1417	NUM
ejpam-5309	85	16	-	-	SYM
ejpam-5309	85	17	1428	1428	NUM
ejpam-5309	85	18	1420	1420	NUM
ejpam-5309	85	19	definition	definition	NOUN
ejpam-5309	85	20	5	5	NUM
ejpam-5309	85	21	.	.	PUNCT
ejpam-5309	86	1	let	let	VERB
ejpam-5309	86	2	t	t	PROPN
ejpam-5309	86	3	be	be	AUX
ejpam-5309	86	4	a	a	DET
ejpam-5309	86	5	ternary	ternary	ADJ
ejpam-5309	86	6	γ	γ	NOUN
ejpam-5309	86	7	-	-	PUNCT
ejpam-5309	86	8	semigroup	semigroup	NOUN
ejpam-5309	86	9	,	,	PUNCT
ejpam-5309	86	10	µ	µ	X
ejpam-5309	86	11	be	be	AUX
ejpam-5309	86	12	a	a	DET
ejpam-5309	86	13	fuzzy	fuzzy	ADJ
ejpam-5309	86	14	set	set	NOUN
ejpam-5309	86	15	of	of	ADP
ejpam-5309	86	16	t	t	PROPN
ejpam-5309	86	17	,	,	PUNCT
ejpam-5309	86	18	and	and	CCONJ
ejpam-5309	86	19	rµ	rµ	INTJ
ejpam-5309	86	20	be	be	AUX
ejpam-5309	86	21	a	a	DET
ejpam-5309	86	22	strongest	strong	ADJ
ejpam-5309	86	23	fuzzy	fuzzy	ADJ
ejpam-5309	86	24	relation	relation	NOUN
ejpam-5309	86	25	on	on	ADP
ejpam-5309	86	26	t	t	PROPN
ejpam-5309	86	27	.	.	PUNCT
ejpam-5309	87	1	then	then	ADV
ejpam-5309	87	2	rµ	rµ	INTJ
ejpam-5309	87	3	is	be	AUX
ejpam-5309	87	4	called	call	VERB
ejpam-5309	87	5	a	a	DET
ejpam-5309	87	6	strongest	strong	ADJ
ejpam-5309	87	7	fuzzy	fuzzy	ADJ
ejpam-5309	87	8	ternary	ternary	ADJ
ejpam-5309	87	9	γ	γ	NOUN
ejpam-5309	87	10	-	-	NOUN
ejpam-5309	87	11	subsemigroup	subsemigroup	NOUN
ejpam-5309	87	12	on	on	ADP
ejpam-5309	87	13	t	t	PROPN
ejpam-5309	87	14	if	if	SCONJ
ejpam-5309	87	15	rµ(a1αb1βc1	rµ(a1αb1βc1	PROPN
ejpam-5309	87	16	,	,	PUNCT
ejpam-5309	87	17	a2αb2βc2	a2αb2βc2	NUM
ejpam-5309	87	18	)	)	PUNCT
ejpam-5309	87	19	≥	≥	PROPN
ejpam-5309	87	20	min{rµ(a1	min{rµ(a1	PROPN
ejpam-5309	87	21	,	,	PUNCT
ejpam-5309	87	22	a2	a2	PROPN
ejpam-5309	87	23	)	)	PUNCT
ejpam-5309	87	24	,	,	PUNCT
ejpam-5309	87	25	rµ(b1	rµ(b1	NOUN
ejpam-5309	87	26	,	,	PUNCT
ejpam-5309	87	27	b2	b2	NOUN
ejpam-5309	87	28	)	)	PUNCT
ejpam-5309	87	29	,	,	PUNCT
ejpam-5309	87	30	rµ(c1	rµ(c1	PROPN
ejpam-5309	87	31	,	,	PUNCT
ejpam-5309	87	32	c2	c2	PROPN
ejpam-5309	87	33	)	)	PUNCT
ejpam-5309	87	34	}	}	PUNCT
ejpam-5309	87	35	,	,	PUNCT
ejpam-5309	87	36	for	for	ADP
ejpam-5309	87	37	all	all	DET
ejpam-5309	87	38	a1	a1	NOUN
ejpam-5309	87	39	,	,	PUNCT
ejpam-5309	87	40	a2	a2	PROPN
ejpam-5309	87	41	,	,	PUNCT
ejpam-5309	87	42	b1	b1	NOUN
ejpam-5309	87	43	,	,	PUNCT
ejpam-5309	87	44	b2	b2	NOUN
ejpam-5309	87	45	,	,	PUNCT
ejpam-5309	87	46	c1	c1	NOUN
ejpam-5309	87	47	,	,	PUNCT
ejpam-5309	87	48	c2	c2	PROPN
ejpam-5309	87	49	∈	∈	PROPN
ejpam-5309	87	50	t	t	PROPN
ejpam-5309	87	51	and	and	CCONJ
ejpam-5309	87	52	α	α	NOUN
ejpam-5309	87	53	,	,	PUNCT
ejpam-5309	87	54	β	β	PROPN
ejpam-5309	87	55	∈	∈	PROPN
ejpam-5309	87	56	γ	γ	PROPN
ejpam-5309	87	57	.	.	PROPN
ejpam-5309	87	58	definition	definition	NOUN
ejpam-5309	87	59	6	6	NUM
ejpam-5309	87	60	.	.	PUNCT
ejpam-5309	88	1	let	let	VERB
ejpam-5309	88	2	t	t	PROPN
ejpam-5309	88	3	be	be	AUX
ejpam-5309	88	4	a	a	DET
ejpam-5309	88	5	ternary	ternary	ADJ
ejpam-5309	88	6	γ	γ	NOUN
ejpam-5309	88	7	-	-	PUNCT
ejpam-5309	88	8	semigroup	semigroup	NOUN
ejpam-5309	88	9	,	,	PUNCT
ejpam-5309	88	10	µ	µ	X
ejpam-5309	88	11	be	be	AUX
ejpam-5309	88	12	a	a	DET
ejpam-5309	88	13	fuzzy	fuzzy	ADJ
ejpam-5309	88	14	set	set	NOUN
ejpam-5309	88	15	of	of	ADP
ejpam-5309	88	16	t	t	PROPN
ejpam-5309	88	17	,	,	PUNCT
ejpam-5309	88	18	and	and	CCONJ
ejpam-5309	88	19	rµ	rµ	INTJ
ejpam-5309	88	20	be	be	AUX
ejpam-5309	88	21	a	a	DET
ejpam-5309	88	22	strongest	strong	ADJ
ejpam-5309	88	23	fuzzy	fuzzy	ADJ
ejpam-5309	88	24	relation	relation	NOUN
ejpam-5309	88	25	on	on	ADP
ejpam-5309	88	26	t	t	PROPN
ejpam-5309	88	27	.	.	PUNCT
ejpam-5309	89	1	then	then	ADV
ejpam-5309	89	2	rµ	rµ	INTJ
ejpam-5309	89	3	is	be	AUX
ejpam-5309	89	4	called	call	VERB
ejpam-5309	89	5	:	:	PUNCT
ejpam-5309	89	6	(	(	PUNCT
ejpam-5309	89	7	i	i	NOUN
ejpam-5309	89	8	)	)	PUNCT
ejpam-5309	89	9	a	a	DET
ejpam-5309	89	10	strongest	strong	ADJ
ejpam-5309	89	11	fuzzy	fuzzy	ADJ
ejpam-5309	89	12	left	leave	VERB
ejpam-5309	89	13	γ	γ	NOUN
ejpam-5309	89	14	-	-	NOUN
ejpam-5309	89	15	ideal	ideal	NOUN
ejpam-5309	89	16	on	on	ADP
ejpam-5309	89	17	t	t	PROPN
ejpam-5309	89	18	if	if	SCONJ
ejpam-5309	89	19	rµ(a1αb1βc1	rµ(a1αb1βc1	PROPN
ejpam-5309	89	20	,	,	PUNCT
ejpam-5309	89	21	a2αb2βc2	a2αb2βc2	NUM
ejpam-5309	89	22	)	)	PUNCT
ejpam-5309	89	23	≥	≥	PROPN
ejpam-5309	89	24	rµ(c1	rµ(c1	PROPN
ejpam-5309	89	25	,	,	PUNCT
ejpam-5309	89	26	c2	c2	PROPN
ejpam-5309	89	27	)	)	PUNCT
ejpam-5309	89	28	,	,	PUNCT
ejpam-5309	89	29	for	for	ADP
ejpam-5309	89	30	all	all	DET
ejpam-5309	89	31	a1	a1	NOUN
ejpam-5309	89	32	,	,	PUNCT
ejpam-5309	89	33	a2	a2	PROPN
ejpam-5309	89	34	,	,	PUNCT
ejpam-5309	89	35	b1	b1	NOUN
ejpam-5309	89	36	,	,	PUNCT
ejpam-5309	89	37	b2	b2	NOUN
ejpam-5309	89	38	,	,	PUNCT
ejpam-5309	89	39	c1	c1	NOUN
ejpam-5309	89	40	,	,	PUNCT
ejpam-5309	89	41	c2	c2	PROPN
ejpam-5309	89	42	∈	∈	PROPN
ejpam-5309	89	43	t	t	PROPN
ejpam-5309	89	44	and	and	CCONJ
ejpam-5309	89	45	α	α	NOUN
ejpam-5309	89	46	,	,	PUNCT
ejpam-5309	89	47	β	β	PROPN
ejpam-5309	89	48	∈	∈	PROPN
ejpam-5309	89	49	γ	γ	X
ejpam-5309	89	50	;	;	PUNCT
ejpam-5309	89	51	(	(	PUNCT
ejpam-5309	89	52	ii	ii	NOUN
ejpam-5309	89	53	)	)	PUNCT
ejpam-5309	89	54	a	a	DET
ejpam-5309	89	55	strongest	strong	ADJ
ejpam-5309	89	56	fuzzy	fuzzy	ADJ
ejpam-5309	89	57	right	right	ADJ
ejpam-5309	89	58	γ	γ	X
ejpam-5309	89	59	-	-	NOUN
ejpam-5309	89	60	ideal	ideal	NOUN
ejpam-5309	89	61	on	on	ADP
ejpam-5309	89	62	t	t	PROPN
ejpam-5309	89	63	if	if	SCONJ
ejpam-5309	89	64	rµ(a1αb1βc1	rµ(a1αb1βc1	PROPN
ejpam-5309	89	65	,	,	PUNCT
ejpam-5309	89	66	a2αb2βc2	a2αb2βc2	NUM
ejpam-5309	89	67	)	)	PUNCT
ejpam-5309	89	68	≥	≥	NOUN
ejpam-5309	89	69	rµ(a1	rµ(a1	NOUN
ejpam-5309	89	70	,	,	PUNCT
ejpam-5309	89	71	a2	a2	PROPN
ejpam-5309	89	72	)	)	PUNCT
ejpam-5309	89	73	,	,	PUNCT
ejpam-5309	89	74	for	for	ADP
ejpam-5309	89	75	all	all	DET
ejpam-5309	89	76	a1	a1	NOUN
ejpam-5309	89	77	,	,	PUNCT
ejpam-5309	89	78	a2	a2	PROPN
ejpam-5309	89	79	,	,	PUNCT
ejpam-5309	89	80	b1	b1	NOUN
ejpam-5309	89	81	,	,	PUNCT
ejpam-5309	89	82	b2	b2	NOUN
ejpam-5309	89	83	,	,	PUNCT
ejpam-5309	89	84	c1	c1	NOUN
ejpam-5309	89	85	,	,	PUNCT
ejpam-5309	89	86	c2	c2	PROPN
ejpam-5309	89	87	∈	∈	PROPN
ejpam-5309	89	88	t	t	PROPN
ejpam-5309	89	89	and	and	CCONJ
ejpam-5309	89	90	α	α	NOUN
ejpam-5309	89	91	,	,	PUNCT
ejpam-5309	89	92	β	β	PROPN
ejpam-5309	89	93	∈	∈	PROPN
ejpam-5309	89	94	γ	γ	X
ejpam-5309	89	95	;	;	PUNCT
ejpam-5309	89	96	(	(	PUNCT
ejpam-5309	89	97	iii	iii	X
ejpam-5309	89	98	)	)	PUNCT
ejpam-5309	89	99	a	a	DET
ejpam-5309	89	100	strongest	strong	ADJ
ejpam-5309	89	101	fuzzy	fuzzy	ADJ
ejpam-5309	89	102	lateral	lateral	ADJ
ejpam-5309	89	103	γ	γ	NOUN
ejpam-5309	89	104	-	-	NOUN
ejpam-5309	89	105	ideal	ideal	NOUN
ejpam-5309	89	106	on	on	ADP
ejpam-5309	89	107	t	t	PROPN
ejpam-5309	89	108	if	if	SCONJ
ejpam-5309	89	109	rµ(a1αb1βc1	rµ(a1αb1βc1	PROPN
ejpam-5309	89	110	,	,	PUNCT
ejpam-5309	89	111	a2αb2βc2	a2αb2βc2	NUM
ejpam-5309	89	112	)	)	PUNCT
ejpam-5309	89	113	≥	≥	NOUN
ejpam-5309	89	114	rµ(b1	rµ(b1	NOUN
ejpam-5309	89	115	,	,	PUNCT
ejpam-5309	89	116	b2	b2	NOUN
ejpam-5309	89	117	)	)	PUNCT
ejpam-5309	89	118	,	,	PUNCT
ejpam-5309	89	119	for	for	ADP
ejpam-5309	89	120	all	all	DET
ejpam-5309	89	121	a1	a1	NOUN
ejpam-5309	89	122	,	,	PUNCT
ejpam-5309	89	123	a2	a2	PROPN
ejpam-5309	89	124	,	,	PUNCT
ejpam-5309	89	125	b1	b1	NOUN
ejpam-5309	89	126	,	,	PUNCT
ejpam-5309	89	127	b2	b2	NOUN
ejpam-5309	89	128	,	,	PUNCT
ejpam-5309	89	129	c1	c1	NOUN
ejpam-5309	89	130	,	,	PUNCT
ejpam-5309	89	131	c2	c2	PROPN
ejpam-5309	89	132	∈	∈	PROPN
ejpam-5309	89	133	t	t	PROPN
ejpam-5309	89	134	and	and	CCONJ
ejpam-5309	89	135	α	α	NOUN
ejpam-5309	89	136	,	,	PUNCT
ejpam-5309	89	137	β	β	PROPN
ejpam-5309	89	138	∈	∈	PROPN
ejpam-5309	89	139	γ	γ	X
ejpam-5309	89	140	;	;	PUNCT
ejpam-5309	89	141	(	(	PUNCT
ejpam-5309	89	142	iv	iv	X
ejpam-5309	89	143	)	)	PUNCT
ejpam-5309	89	144	a	a	DET
ejpam-5309	89	145	strongest	strong	ADJ
ejpam-5309	89	146	fuzzy	fuzzy	ADJ
ejpam-5309	89	147	γ	γ	NOUN
ejpam-5309	89	148	-	-	NOUN
ejpam-5309	89	149	ideal	ideal	NOUN
ejpam-5309	89	150	on	on	ADP
ejpam-5309	89	151	t	t	PROPN
ejpam-5309	89	152	if	if	SCONJ
ejpam-5309	89	153	it	it	PRON
ejpam-5309	89	154	is	be	AUX
ejpam-5309	89	155	a	a	DET
ejpam-5309	89	156	strongest	strong	ADJ
ejpam-5309	89	157	fuzzy	fuzzy	ADJ
ejpam-5309	89	158	left	leave	VERB
ejpam-5309	89	159	γ	γ	NOUN
ejpam-5309	89	160	-	-	PUNCT
ejpam-5309	89	161	ideal	ideal	ADJ
ejpam-5309	89	162	,	,	PUNCT
ejpam-5309	89	163	a	a	DET
ejpam-5309	89	164	strongest	strong	ADJ
ejpam-5309	89	165	fuzzy	fuzzy	ADJ
ejpam-5309	89	166	right	right	ADJ
ejpam-5309	89	167	γ	γ	X
ejpam-5309	89	168	-	-	NOUN
ejpam-5309	89	169	ideal	ideal	ADJ
ejpam-5309	89	170	,	,	PUNCT
ejpam-5309	89	171	and	and	CCONJ
ejpam-5309	89	172	a	a	DET
ejpam-5309	89	173	strongest	strong	ADJ
ejpam-5309	89	174	fuzzy	fuzzy	ADJ
ejpam-5309	89	175	lateral	lateral	ADJ
ejpam-5309	89	176	γ	γ	NOUN
ejpam-5309	89	177	-	-	NOUN
ejpam-5309	89	178	ideal	ideal	NOUN
ejpam-5309	89	179	on	on	ADP
ejpam-5309	89	180	t	t	PROPN
ejpam-5309	89	181	.	.	PUNCT
ejpam-5309	90	1	definition	definition	NOUN
ejpam-5309	90	2	7	7	NUM
ejpam-5309	90	3	.	.	PUNCT
ejpam-5309	91	1	let	let	VERB
ejpam-5309	91	2	t	t	PROPN
ejpam-5309	91	3	be	be	AUX
ejpam-5309	91	4	a	a	DET
ejpam-5309	91	5	ternary	ternary	ADJ
ejpam-5309	91	6	γ	γ	NOUN
ejpam-5309	91	7	-	-	PUNCT
ejpam-5309	91	8	semigroup	semigroup	NOUN
ejpam-5309	91	9	,	,	PUNCT
ejpam-5309	91	10	µ	µ	X
ejpam-5309	91	11	be	be	AUX
ejpam-5309	91	12	a	a	DET
ejpam-5309	91	13	fuzzy	fuzzy	ADJ
ejpam-5309	91	14	set	set	NOUN
ejpam-5309	91	15	of	of	ADP
ejpam-5309	91	16	t	t	PROPN
ejpam-5309	91	17	,	,	PUNCT
ejpam-5309	91	18	and	and	CCONJ
ejpam-5309	91	19	rµ	rµ	INTJ
ejpam-5309	91	20	be	be	AUX
ejpam-5309	91	21	a	a	DET
ejpam-5309	91	22	strongest	strong	ADJ
ejpam-5309	91	23	fuzzy	fuzzy	ADJ
ejpam-5309	91	24	ternary	ternary	ADJ
ejpam-5309	91	25	γ	γ	NOUN
ejpam-5309	91	26	-	-	NOUN
ejpam-5309	91	27	subsemigroup	subsemigroup	NOUN
ejpam-5309	91	28	on	on	ADP
ejpam-5309	91	29	t	t	PROPN
ejpam-5309	91	30	.	.	PUNCT
ejpam-5309	92	1	then	then	ADV
ejpam-5309	92	2	rµ	rµ	INTJ
ejpam-5309	92	3	is	be	AUX
ejpam-5309	92	4	said	say	VERB
ejpam-5309	92	5	to	to	PART
ejpam-5309	92	6	be	be	AUX
ejpam-5309	92	7	a	a	DET
ejpam-5309	92	8	strongest	strong	ADJ
ejpam-5309	92	9	fuzzy	fuzzy	ADJ
ejpam-5309	92	10	bi	bi	ADJ
ejpam-5309	92	11	-	-	ADJ
ejpam-5309	92	12	γ	γ	NOUN
ejpam-5309	92	13	-	-	NOUN
ejpam-5309	92	14	ideal	ideal	NOUN
ejpam-5309	92	15	on	on	ADP
ejpam-5309	92	16	t	t	PROPN
ejpam-5309	92	17	if	if	SCONJ
ejpam-5309	92	18	rµ(a1αb1βc1γd1δe1	rµ(a1αb1βc1γd1δe1	ADV
ejpam-5309	92	19	,	,	PUNCT
ejpam-5309	92	20	a2αb2βc2γd2δe2	a2αb2βc2γd2δe2	NOUN
ejpam-5309	92	21	)	)	PUNCT
ejpam-5309	92	22	≥	≥	NOUN
ejpam-5309	92	23	min{rµ(a1	min{rµ(a1	PROPN
ejpam-5309	92	24	,	,	PUNCT
ejpam-5309	92	25	a2	a2	PROPN
ejpam-5309	92	26	)	)	PUNCT
ejpam-5309	92	27	,	,	PUNCT
ejpam-5309	92	28	rµ(c1	rµ(c1	PROPN
ejpam-5309	92	29	,	,	PUNCT
ejpam-5309	92	30	c2	c2	PROPN
ejpam-5309	92	31	)	)	PUNCT
ejpam-5309	92	32	,	,	PUNCT
ejpam-5309	92	33	rµ(e1	rµ(e1	NOUN
ejpam-5309	92	34	,	,	PUNCT
ejpam-5309	92	35	e2	e2	PROPN
ejpam-5309	92	36	)	)	PUNCT
ejpam-5309	92	37	}	}	PUNCT
ejpam-5309	92	38	,	,	PUNCT
ejpam-5309	92	39	for	for	ADP
ejpam-5309	92	40	all	all	DET
ejpam-5309	92	41	a1	a1	NOUN
ejpam-5309	92	42	,	,	PUNCT
ejpam-5309	92	43	a2	a2	PROPN
ejpam-5309	92	44	,	,	PUNCT
ejpam-5309	92	45	b1	b1	NOUN
ejpam-5309	92	46	,	,	PUNCT
ejpam-5309	92	47	b2	b2	NOUN
ejpam-5309	92	48	,	,	PUNCT
ejpam-5309	92	49	c1	c1	PROPN
ejpam-5309	92	50	,	,	PUNCT
ejpam-5309	92	51	c2	c2	PROPN
ejpam-5309	92	52	,	,	PUNCT
ejpam-5309	92	53	d1	d1	PROPN
ejpam-5309	92	54	,	,	PUNCT
ejpam-5309	92	55	d2	d2	PROPN
ejpam-5309	92	56	,	,	PUNCT
ejpam-5309	92	57	e1	e1	PROPN
ejpam-5309	92	58	,	,	PUNCT
ejpam-5309	92	59	e2	e2	PROPN
ejpam-5309	92	60	∈	∈	PROPN
ejpam-5309	92	61	t	t	PROPN
ejpam-5309	92	62	and	and	CCONJ
ejpam-5309	92	63	α	α	NOUN
ejpam-5309	92	64	,	,	PUNCT
ejpam-5309	92	65	β	β	X
ejpam-5309	92	66	,	,	PUNCT
ejpam-5309	92	67	γ	γ	PROPN
ejpam-5309	92	68	,	,	PUNCT
ejpam-5309	92	69	δ	δ	PROPN
ejpam-5309	92	70	∈	∈	PROPN
ejpam-5309	92	71	γ	γ	X
ejpam-5309	92	72	.	.	PUNCT
ejpam-5309	92	73	by	by	ADP
ejpam-5309	92	74	definition	definition	NOUN
ejpam-5309	92	75	7	7	NUM
ejpam-5309	92	76	,	,	PUNCT
ejpam-5309	92	77	it	it	PRON
ejpam-5309	92	78	is	be	AUX
ejpam-5309	92	79	clear	clear	ADJ
ejpam-5309	92	80	that	that	SCONJ
ejpam-5309	92	81	every	every	DET
ejpam-5309	92	82	strongest	strong	ADJ
ejpam-5309	92	83	fuzzy	fuzzy	ADJ
ejpam-5309	92	84	bi	bi	ADJ
ejpam-5309	92	85	-	-	ADJ
ejpam-5309	92	86	γ	γ	NOUN
ejpam-5309	92	87	-	-	NOUN
ejpam-5309	92	88	ideal	ideal	NOUN
ejpam-5309	92	89	on	on	ADP
ejpam-5309	92	90	a	a	DET
ejpam-5309	92	91	ternary	ternary	ADJ
ejpam-5309	92	92	γsemigroup	γsemigroup	NOUN
ejpam-5309	92	93	is	be	AUX
ejpam-5309	92	94	also	also	ADV
ejpam-5309	92	95	a	a	DET
ejpam-5309	92	96	strongest	strong	ADJ
ejpam-5309	92	97	fuzzy	fuzzy	ADJ
ejpam-5309	92	98	ternary	ternary	ADJ
ejpam-5309	92	99	γ	γ	NOUN
ejpam-5309	92	100	-	-	NOUN
ejpam-5309	92	101	subsemigroup	subsemigroup	NOUN
ejpam-5309	92	102	,	,	PUNCT
ejpam-5309	92	103	but	but	CCONJ
ejpam-5309	92	104	the	the	DET
ejpam-5309	92	105	converse	converse	NOUN
ejpam-5309	92	106	is	be	AUX
ejpam-5309	92	107	not	not	PART
ejpam-5309	92	108	always	always	ADV
ejpam-5309	92	109	true	true	ADJ
ejpam-5309	92	110	,	,	PUNCT
ejpam-5309	92	111	as	as	ADP
ejpam-5309	92	112	the	the	DET
ejpam-5309	92	113	following	follow	VERB
ejpam-5309	92	114	example	example	NOUN
ejpam-5309	92	115	.	.	PUNCT
ejpam-5309	93	1	example	example	NOUN
ejpam-5309	94	1	1	1	NUM
ejpam-5309	94	2	.	.	PUNCT
ejpam-5309	95	1	let	let	VERB
ejpam-5309	95	2	t	t	NOUN
ejpam-5309	95	3	=	=	PUNCT
ejpam-5309	95	4	{	{	PUNCT
ejpam-5309	95	5	a	a	PRON
ejpam-5309	95	6	,	,	PUNCT
ejpam-5309	95	7	b	b	NOUN
ejpam-5309	95	8	,	,	PUNCT
ejpam-5309	95	9	c	c	NOUN
ejpam-5309	95	10	}	}	PUNCT
ejpam-5309	95	11	and	and	CCONJ
ejpam-5309	95	12	γ	γ	X
ejpam-5309	95	13	=	=	PROPN
ejpam-5309	95	14	t	t	PROPN
ejpam-5309	95	15	.	.	PUNCT
ejpam-5309	96	1	define	define	VERB
ejpam-5309	96	2	the	the	DET
ejpam-5309	96	3	operation	operation	NOUN
ejpam-5309	96	4	·	·	PUNCT
ejpam-5309	96	5	on	on	ADP
ejpam-5309	96	6	t	t	PROPN
ejpam-5309	96	7	by	by	ADP
ejpam-5309	96	8	xαyβz	xαyβz	PROPN
ejpam-5309	97	1	=	=	SYM
ejpam-5309	97	2	(	(	PUNCT
ejpam-5309	97	3	x	x	X
ejpam-5309	97	4	∗	∗	PROPN
ejpam-5309	97	5	y	y	NOUN
ejpam-5309	97	6	)	)	PUNCT
ejpam-5309	97	7	∗	∗	NOUN
ejpam-5309	97	8	z	z	PROPN
ejpam-5309	97	9	,	,	PUNCT
ejpam-5309	97	10	for	for	ADP
ejpam-5309	97	11	all	all	DET
ejpam-5309	97	12	x	x	NOUN
ejpam-5309	97	13	,	,	PUNCT
ejpam-5309	97	14	y	y	PROPN
ejpam-5309	97	15	,	,	PUNCT
ejpam-5309	97	16	z	z	PROPN
ejpam-5309	97	17	∈	∈	PROPN
ejpam-5309	97	18	t	t	PROPN
ejpam-5309	97	19	and	and	CCONJ
ejpam-5309	97	20	α	α	NOUN
ejpam-5309	97	21	,	,	PUNCT
ejpam-5309	97	22	β	β	X
ejpam-5309	97	23	∈	∈	PROPN
ejpam-5309	97	24	γ	γ	X
ejpam-5309	97	25	where	where	SCONJ
ejpam-5309	97	26	the	the	DET
ejpam-5309	97	27	binary	binary	PROPN
ejpam-5309	97	28	operation	operation	NOUN
ejpam-5309	97	29	∗	∗	NOUN
ejpam-5309	97	30	on	on	ADP
ejpam-5309	97	31	t	t	PROPN
ejpam-5309	97	32	is	be	AUX
ejpam-5309	97	33	defined	define	VERB
ejpam-5309	97	34	by	by	ADP
ejpam-5309	97	35	the	the	DET
ejpam-5309	97	36	following	follow	VERB
ejpam-5309	97	37	table	table	NOUN
ejpam-5309	97	38	:	:	PUNCT
ejpam-5309	97	39	∗	∗	VERB
ejpam-5309	97	40	a	a	DET
ejpam-5309	97	41	b	b	NOUN
ejpam-5309	97	42	c	c	NOUN
ejpam-5309	97	43	a	a	DET
ejpam-5309	97	44	a	a	DET
ejpam-5309	97	45	a	a	DET
ejpam-5309	97	46	a	a	DET
ejpam-5309	97	47	b	b	NOUN
ejpam-5309	97	48	a	a	DET
ejpam-5309	97	49	b	b	PROPN
ejpam-5309	97	50	b	b	PROPN
ejpam-5309	97	51	c	c	PROPN
ejpam-5309	97	52	a	a	DET
ejpam-5309	97	53	c	c	NOUN
ejpam-5309	97	54	c	c	NOUN
ejpam-5309	97	55	then	then	ADV
ejpam-5309	97	56	,	,	PUNCT
ejpam-5309	97	57	t	t	PROPN
ejpam-5309	97	58	is	be	AUX
ejpam-5309	97	59	a	a	DET
ejpam-5309	97	60	ternary	ternary	ADJ
ejpam-5309	97	61	γ	γ	NOUN
ejpam-5309	97	62	-	-	PUNCT
ejpam-5309	97	63	semigroup	semigroup	NOUN
ejpam-5309	97	64	[	[	X
ejpam-5309	97	65	6	6	NUM
ejpam-5309	97	66	]	]	PUNCT
ejpam-5309	97	67	.	.	PUNCT
ejpam-5309	98	1	next	next	ADV
ejpam-5309	98	2	,	,	PUNCT
ejpam-5309	98	3	we	we	PRON
ejpam-5309	98	4	define	define	VERB
ejpam-5309	98	5	a	a	DET
ejpam-5309	98	6	fuzzy	fuzzy	ADJ
ejpam-5309	98	7	set	set	VERB
ejpam-5309	98	8	µ	µ	PROPN
ejpam-5309	98	9	of	of	ADP
ejpam-5309	98	10	t	t	PROPN
ejpam-5309	98	11	by	by	ADP
ejpam-5309	98	12	µ(a	µ(a	PROPN
ejpam-5309	98	13	)	)	PUNCT
ejpam-5309	98	14	=	=	NUM
ejpam-5309	98	15	0.2	0.2	NUM
ejpam-5309	98	16	,	,	PUNCT
ejpam-5309	98	17	µ(b	µ(b	PROPN
ejpam-5309	98	18	)	)	PUNCT
ejpam-5309	98	19	=	=	SYM
ejpam-5309	98	20	0.5	0.5	NUM
ejpam-5309	98	21	,	,	PUNCT
ejpam-5309	98	22	and	and	CCONJ
ejpam-5309	98	23	µ(c	µ(c	PROPN
ejpam-5309	98	24	)	)	PUNCT
ejpam-5309	98	25	=	=	SYM
ejpam-5309	98	26	0.9	0.9	NUM
ejpam-5309	98	27	.	.	PUNCT
ejpam-5309	99	1	following	follow	VERB
ejpam-5309	99	2	a	a	DET
ejpam-5309	99	3	careful	careful	ADJ
ejpam-5309	99	4	analysis	analysis	NOUN
ejpam-5309	99	5	,	,	PUNCT
ejpam-5309	99	6	we	we	PRON
ejpam-5309	99	7	have	have	AUX
ejpam-5309	99	8	rµ	rµ	INTJ
ejpam-5309	99	9	is	be	AUX
ejpam-5309	99	10	a	a	DET
ejpam-5309	99	11	strongest	strong	ADJ
ejpam-5309	99	12	fuzzy	fuzzy	ADJ
ejpam-5309	99	13	ternary	ternary	ADJ
ejpam-5309	99	14	γ	γ	NOUN
ejpam-5309	99	15	-	-	NOUN
ejpam-5309	99	16	subsemigroup	subsemigroup	NOUN
ejpam-5309	99	17	on	on	ADP
ejpam-5309	99	18	t	t	PROPN
ejpam-5309	99	19	,	,	PUNCT
ejpam-5309	99	20	but	but	CCONJ
ejpam-5309	99	21	it	it	PRON
ejpam-5309	99	22	is	be	AUX
ejpam-5309	99	23	not	not	PART
ejpam-5309	99	24	a	a	DET
ejpam-5309	99	25	strongest	strong	ADJ
ejpam-5309	99	26	fuzzy	fuzzy	ADJ
ejpam-5309	99	27	bi	bi	ADJ
ejpam-5309	99	28	-	-	ADJ
ejpam-5309	99	29	γ	γ	NOUN
ejpam-5309	99	30	-	-	NOUN
ejpam-5309	99	31	ideal	ideal	NOUN
ejpam-5309	99	32	on	on	ADP
ejpam-5309	99	33	t	t	PROPN
ejpam-5309	99	34	,	,	PUNCT
ejpam-5309	99	35	since	since	SCONJ
ejpam-5309	99	36	rµ(cαaβcγaδc	rµ(cαaβcγaδc	PROPN
ejpam-5309	99	37	,	,	PUNCT
ejpam-5309	99	38	cαaβcγaδc	cαaβcγaδc	PROPN
ejpam-5309	99	39	)	)	PUNCT
ejpam-5309	99	40	=	=	PUNCT
ejpam-5309	99	41	0.2	0.2	NUM
ejpam-5309	99	42	<	<	X
ejpam-5309	99	43	0.9	0.9	NUM
ejpam-5309	99	44	=	=	SYM
ejpam-5309	99	45	min{rµ(c	min{rµ(c	PROPN
ejpam-5309	99	46	,	,	PUNCT
ejpam-5309	99	47	c)rµ(c	c)rµ(c	PROPN
ejpam-5309	99	48	,	,	PUNCT
ejpam-5309	99	49	c	c	NOUN
ejpam-5309	99	50	)	)	PUNCT
ejpam-5309	99	51	,	,	PUNCT
ejpam-5309	99	52	rµ(c	rµ(c	X
ejpam-5309	99	53	,	,	PUNCT
ejpam-5309	99	54	c	c	NOUN
ejpam-5309	99	55	)	)	PUNCT
ejpam-5309	99	56	}	}	PUNCT
ejpam-5309	99	57	,	,	PUNCT
ejpam-5309	99	58	for	for	ADP
ejpam-5309	99	59	all	all	DET
ejpam-5309	99	60	α	α	PROPN
ejpam-5309	99	61	,	,	PUNCT
ejpam-5309	99	62	β	β	X
ejpam-5309	99	63	,	,	PUNCT
ejpam-5309	99	64	γ	γ	PROPN
ejpam-5309	99	65	,	,	PUNCT
ejpam-5309	99	66	δ	δ	PROPN
ejpam-5309	99	67	∈	∈	PROPN
ejpam-5309	99	68	γ	γ	PROPN
ejpam-5309	99	69	.	.	PUNCT
ejpam-5309	99	70	w.	w.	PROPN
ejpam-5309	99	71	nakkhasen	nakkhasen	PROPN
ejpam-5309	99	72	et	et	PROPN
ejpam-5309	99	73	al	al	PROPN
ejpam-5309	99	74	.	.	PUNCT
ejpam-5309	99	75	/	/	SYM
ejpam-5309	99	76	eur	eur	PROPN
ejpam-5309	99	77	.	.	PUNCT
ejpam-5309	100	1	j.	j.	PROPN
ejpam-5309	100	2	pure	pure	PROPN
ejpam-5309	100	3	appl	appl	PROPN
ejpam-5309	100	4	.	.	PROPN
ejpam-5309	100	5	math	math	PROPN
ejpam-5309	100	6	,	,	PUNCT
ejpam-5309	100	7	17	17	NUM
ejpam-5309	100	8	(	(	PUNCT
ejpam-5309	100	9	3	3	NUM
ejpam-5309	100	10	)	)	PUNCT
ejpam-5309	100	11	(	(	PUNCT
ejpam-5309	100	12	2024	2024	NUM
ejpam-5309	100	13	)	)	PUNCT
ejpam-5309	100	14	,	,	PUNCT
ejpam-5309	100	15	1417	1417	NUM
ejpam-5309	100	16	-	-	SYM
ejpam-5309	100	17	1428	1428	NUM
ejpam-5309	100	18	1421	1421	NUM
ejpam-5309	100	19	proposition	proposition	NOUN
ejpam-5309	100	20	1	1	NUM
ejpam-5309	100	21	.	.	PUNCT
ejpam-5309	101	1	let	let	VERB
ejpam-5309	101	2	t	t	NOUN
ejpam-5309	101	3	be	be	AUX
ejpam-5309	101	4	a	a	DET
ejpam-5309	101	5	ternary	ternary	ADJ
ejpam-5309	101	6	γ	γ	NOUN
ejpam-5309	101	7	-	-	PUNCT
ejpam-5309	101	8	semigroup	semigroup	NOUN
ejpam-5309	101	9	.	.	PUNCT
ejpam-5309	102	1	then	then	ADV
ejpam-5309	102	2	:	:	PUNCT
ejpam-5309	102	3	(	(	PUNCT
ejpam-5309	102	4	i	i	NOUN
ejpam-5309	102	5	)	)	PUNCT
ejpam-5309	102	6	every	every	PRON
ejpam-5309	102	7	strongest	strong	ADJ
ejpam-5309	102	8	fuzzy	fuzzy	ADJ
ejpam-5309	102	9	left	leave	VERB
ejpam-5309	102	10	γ	γ	NOUN
ejpam-5309	102	11	-	-	NOUN
ejpam-5309	102	12	ideal	ideal	NOUN
ejpam-5309	102	13	on	on	ADP
ejpam-5309	102	14	t	t	PROPN
ejpam-5309	102	15	is	be	AUX
ejpam-5309	102	16	also	also	ADV
ejpam-5309	102	17	a	a	DET
ejpam-5309	102	18	strongest	strong	ADJ
ejpam-5309	102	19	fuzzy	fuzzy	ADJ
ejpam-5309	102	20	bi	bi	ADJ
ejpam-5309	102	21	-	-	ADJ
ejpam-5309	102	22	γ	γ	NOUN
ejpam-5309	102	23	-	-	PUNCT
ejpam-5309	102	24	ideal	ideal	NOUN
ejpam-5309	102	25	;	;	PUNCT
ejpam-5309	102	26	(	(	PUNCT
ejpam-5309	102	27	ii	ii	NOUN
ejpam-5309	102	28	)	)	PUNCT
ejpam-5309	102	29	every	every	PRON
ejpam-5309	102	30	strongest	strong	ADJ
ejpam-5309	102	31	fuzzy	fuzzy	ADJ
ejpam-5309	102	32	right	right	ADJ
ejpam-5309	102	33	γ	γ	X
ejpam-5309	102	34	-	-	NOUN
ejpam-5309	102	35	ideal	ideal	NOUN
ejpam-5309	102	36	on	on	ADP
ejpam-5309	102	37	t	t	PROPN
ejpam-5309	102	38	is	be	AUX
ejpam-5309	102	39	also	also	ADV
ejpam-5309	102	40	a	a	DET
ejpam-5309	102	41	strongest	strong	ADJ
ejpam-5309	102	42	fuzzy	fuzzy	ADJ
ejpam-5309	102	43	bi	bi	ADJ
ejpam-5309	102	44	-	-	ADJ
ejpam-5309	102	45	γ	γ	NOUN
ejpam-5309	102	46	-	-	PUNCT
ejpam-5309	102	47	ideal	ideal	NOUN
ejpam-5309	102	48	;	;	PUNCT
ejpam-5309	102	49	(	(	PUNCT
ejpam-5309	102	50	iii	iii	X
ejpam-5309	102	51	)	)	PUNCT
ejpam-5309	102	52	every	every	PRON
ejpam-5309	102	53	strongest	strong	ADJ
ejpam-5309	102	54	fuzzy	fuzzy	ADJ
ejpam-5309	102	55	lateral	lateral	ADJ
ejpam-5309	102	56	γ	γ	NOUN
ejpam-5309	102	57	-	-	NOUN
ejpam-5309	102	58	ideal	ideal	NOUN
ejpam-5309	102	59	on	on	ADP
ejpam-5309	102	60	t	t	PROPN
ejpam-5309	102	61	is	be	AUX
ejpam-5309	102	62	also	also	ADV
ejpam-5309	102	63	a	a	DET
ejpam-5309	102	64	strongest	strong	ADJ
ejpam-5309	102	65	fuzzy	fuzzy	ADJ
ejpam-5309	102	66	bi	bi	ADJ
ejpam-5309	102	67	-	-	ADJ
ejpam-5309	102	68	γ	γ	NOUN
ejpam-5309	102	69	-	-	PUNCT
ejpam-5309	102	70	ideal	ideal	NOUN
ejpam-5309	102	71	;	;	PUNCT
ejpam-5309	102	72	(	(	PUNCT
ejpam-5309	102	73	iv	iv	X
ejpam-5309	102	74	)	)	PUNCT
ejpam-5309	102	75	every	every	PRON
ejpam-5309	102	76	strongest	strong	ADJ
ejpam-5309	102	77	fuzzy	fuzzy	ADJ
ejpam-5309	102	78	γ	γ	NOUN
ejpam-5309	102	79	-	-	NOUN
ejpam-5309	102	80	ideal	ideal	NOUN
ejpam-5309	102	81	on	on	ADP
ejpam-5309	102	82	t	t	PROPN
ejpam-5309	102	83	is	be	AUX
ejpam-5309	102	84	also	also	ADV
ejpam-5309	102	85	a	a	DET
ejpam-5309	102	86	strongest	strong	ADJ
ejpam-5309	102	87	fuzzy	fuzzy	ADJ
ejpam-5309	102	88	bi	bi	ADJ
ejpam-5309	102	89	-	-	ADJ
ejpam-5309	102	90	γ	γ	NOUN
ejpam-5309	102	91	-	-	PUNCT
ejpam-5309	102	92	ideal	ideal	NOUN
ejpam-5309	102	93	.	.	PUNCT
ejpam-5309	103	1	proof	proof	NOUN
ejpam-5309	103	2	.	.	PUNCT
ejpam-5309	104	1	(	(	PUNCT
ejpam-5309	104	2	i	i	NOUN
ejpam-5309	104	3	)	)	PUNCT
ejpam-5309	104	4	let	let	VERB
ejpam-5309	104	5	rµ	rµ	VERB
ejpam-5309	104	6	be	be	AUX
ejpam-5309	104	7	a	a	DET
ejpam-5309	104	8	strongest	strong	ADJ
ejpam-5309	104	9	fuzzy	fuzzy	ADJ
ejpam-5309	104	10	left	leave	VERB
ejpam-5309	104	11	γ	γ	NOUN
ejpam-5309	104	12	-	-	NOUN
ejpam-5309	104	13	ideal	ideal	NOUN
ejpam-5309	104	14	on	on	ADP
ejpam-5309	104	15	t	t	PROPN
ejpam-5309	104	16	.	.	PUNCT
ejpam-5309	105	1	it	it	PRON
ejpam-5309	105	2	is	be	AUX
ejpam-5309	105	3	not	not	PART
ejpam-5309	105	4	difficult	difficult	ADJ
ejpam-5309	105	5	to	to	PART
ejpam-5309	105	6	verify	verify	VERB
ejpam-5309	106	1	that	that	SCONJ
ejpam-5309	106	2	rµ	rµ	INTJ
ejpam-5309	106	3	is	be	AUX
ejpam-5309	106	4	a	a	DET
ejpam-5309	106	5	strongest	strong	ADJ
ejpam-5309	106	6	fuzzy	fuzzy	ADJ
ejpam-5309	106	7	ternary	ternary	ADJ
ejpam-5309	106	8	γ	γ	NOUN
ejpam-5309	106	9	-	-	NOUN
ejpam-5309	106	10	subsemigroup	subsemigroup	NOUN
ejpam-5309	106	11	on	on	ADP
ejpam-5309	106	12	t	t	PROPN
ejpam-5309	106	13	.	.	PUNCT
ejpam-5309	107	1	for	for	ADP
ejpam-5309	107	2	any	any	DET
ejpam-5309	107	3	a1	a1	NOUN
ejpam-5309	107	4	,	,	PUNCT
ejpam-5309	107	5	a2	a2	PROPN
ejpam-5309	107	6	,	,	PUNCT
ejpam-5309	107	7	b1	b1	NOUN
ejpam-5309	107	8	,	,	PUNCT
ejpam-5309	107	9	b2	b2	NOUN
ejpam-5309	107	10	,	,	PUNCT
ejpam-5309	107	11	c1	c1	PROPN
ejpam-5309	107	12	,	,	PUNCT
ejpam-5309	107	13	c2	c2	PROPN
ejpam-5309	107	14	,	,	PUNCT
ejpam-5309	107	15	d1	d1	PROPN
ejpam-5309	107	16	,	,	PUNCT
ejpam-5309	107	17	d2	d2	PROPN
ejpam-5309	107	18	,	,	PUNCT
ejpam-5309	107	19	e1	e1	PROPN
ejpam-5309	107	20	,	,	PUNCT
ejpam-5309	107	21	e2	e2	PROPN
ejpam-5309	107	22	∈	∈	PROPN
ejpam-5309	107	23	t	t	PROPN
ejpam-5309	107	24	,	,	PUNCT
ejpam-5309	107	25	and	and	CCONJ
ejpam-5309	107	26	any	any	DET
ejpam-5309	107	27	α	α	NOUN
ejpam-5309	107	28	,	,	PUNCT
ejpam-5309	107	29	β	β	X
ejpam-5309	107	30	,	,	PUNCT
ejpam-5309	107	31	γ	γ	PROPN
ejpam-5309	107	32	,	,	PUNCT
ejpam-5309	107	33	δ	δ	PROPN
ejpam-5309	107	34	∈	∈	PROPN
ejpam-5309	107	35	γ	γ	PROPN
ejpam-5309	107	36	,	,	PUNCT
ejpam-5309	107	37	we	we	PRON
ejpam-5309	107	38	have	have	VERB
ejpam-5309	107	39	(	(	PUNCT
ejpam-5309	107	40	a1αb1)β(c1γd1)δe1	a1αb1)β(c1γd1)δe1	PROPN
ejpam-5309	107	41	=	=	SYM
ejpam-5309	107	42	x1βy1δe1	x1βy1δe1	PROPN
ejpam-5309	107	43	and	and	CCONJ
ejpam-5309	107	44	(	(	PUNCT
ejpam-5309	107	45	a2αb2)β(c2γd2)δe2	a2αb2)β(c2γd2)δe2	PROPN
ejpam-5309	107	46	=	=	SYM
ejpam-5309	107	47	x2βy2δe2	x2βy2δe2	NUM
ejpam-5309	107	48	,	,	PUNCT
ejpam-5309	107	49	for	for	ADP
ejpam-5309	107	50	some	some	DET
ejpam-5309	107	51	x1	x1	PROPN
ejpam-5309	107	52	=	=	PUNCT
ejpam-5309	107	53	a1αb1	a1αb1	ADJ
ejpam-5309	107	54	,	,	PUNCT
ejpam-5309	107	55	y1	y1	NOUN
ejpam-5309	107	56	=	=	SYM
ejpam-5309	107	57	c1γd1	c1γd1	NOUN
ejpam-5309	107	58	,	,	PUNCT
ejpam-5309	108	1	x2	x2	NOUN
ejpam-5309	108	2	=	=	PUNCT
ejpam-5309	108	3	a2αb2	a2αb2	NOUN
ejpam-5309	108	4	,	,	PUNCT
ejpam-5309	108	5	and	and	CCONJ
ejpam-5309	108	6	y2	y2	NOUN
ejpam-5309	108	7	=	=	NOUN
ejpam-5309	108	8	c2γd2	c2γd2	NOUN
ejpam-5309	108	9	.	.	PUNCT
ejpam-5309	109	1	it	it	PRON
ejpam-5309	109	2	follows	follow	VERB
ejpam-5309	109	3	that	that	SCONJ
ejpam-5309	109	4	rµ(a1αb1βc1γd1δe1	rµ(a1αb1βc1γd1δe1	NOUN
ejpam-5309	109	5	,	,	PUNCT
ejpam-5309	109	6	a2αb2βc2γd2δe2	a2αb2βc2γd2δe2	NOUN
ejpam-5309	109	7	)	)	PUNCT
ejpam-5309	109	8	=	=	SYM
ejpam-5309	110	1	rµ(x1βy1δe1	rµ(x1βy1δe1	PROPN
ejpam-5309	110	2	,	,	PUNCT
ejpam-5309	110	3	x2βy2δe2	x2βy2δe2	NUM
ejpam-5309	110	4	)	)	PUNCT
ejpam-5309	110	5	≥	≥	NOUN
ejpam-5309	110	6	rµ(e1	rµ(e1	NOUN
ejpam-5309	110	7	,	,	PUNCT
ejpam-5309	110	8	e2	e2	PROPN
ejpam-5309	110	9	)	)	PUNCT
ejpam-5309	110	10	≥	≥	PROPN
ejpam-5309	110	11	min{rµ(a1	min{rµ(a1	PROPN
ejpam-5309	110	12	,	,	PUNCT
ejpam-5309	110	13	a2	a2	PROPN
ejpam-5309	110	14	)	)	PUNCT
ejpam-5309	110	15	,	,	PUNCT
ejpam-5309	110	16	rµ(c1	rµ(c1	PROPN
ejpam-5309	110	17	,	,	PUNCT
ejpam-5309	110	18	c2	c2	PROPN
ejpam-5309	110	19	)	)	PUNCT
ejpam-5309	110	20	,	,	PUNCT
ejpam-5309	110	21	rµ(e1	rµ(e1	NOUN
ejpam-5309	110	22	,	,	PUNCT
ejpam-5309	110	23	e2	e2	PROPN
ejpam-5309	110	24	)	)	PUNCT
ejpam-5309	110	25	}	}	PUNCT
ejpam-5309	110	26	.	.	PUNCT
ejpam-5309	111	1	hence	hence	ADV
ejpam-5309	111	2	,	,	PUNCT
ejpam-5309	111	3	rµ	rµ	INTJ
ejpam-5309	111	4	is	be	AUX
ejpam-5309	111	5	a	a	DET
ejpam-5309	111	6	strongest	strong	ADJ
ejpam-5309	111	7	fuzzy	fuzzy	ADJ
ejpam-5309	111	8	bi	bi	ADJ
ejpam-5309	111	9	-	-	ADJ
ejpam-5309	111	10	γ	γ	NOUN
ejpam-5309	111	11	-	-	NOUN
ejpam-5309	111	12	ideal	ideal	NOUN
ejpam-5309	111	13	on	on	ADP
ejpam-5309	111	14	t	t	PROPN
ejpam-5309	111	15	.	.	PUNCT
ejpam-5309	112	1	the	the	DET
ejpam-5309	112	2	proofs	proof	NOUN
ejpam-5309	112	3	of	of	ADP
ejpam-5309	112	4	(	(	PUNCT
ejpam-5309	112	5	ii	ii	NOUN
ejpam-5309	112	6	)	)	PUNCT
ejpam-5309	112	7	and	and	CCONJ
ejpam-5309	112	8	(	(	PUNCT
ejpam-5309	112	9	iii	iii	X
ejpam-5309	112	10	)	)	PUNCT
ejpam-5309	112	11	are	be	AUX
ejpam-5309	112	12	similar	similar	ADJ
ejpam-5309	112	13	to	to	ADP
ejpam-5309	112	14	the	the	DET
ejpam-5309	112	15	proof	proof	NOUN
ejpam-5309	112	16	of	of	ADP
ejpam-5309	112	17	(	(	PUNCT
ejpam-5309	112	18	i	i	NOUN
ejpam-5309	112	19	)	)	PUNCT
ejpam-5309	112	20	.	.	PUNCT
ejpam-5309	113	1	(	(	PUNCT
ejpam-5309	113	2	iv	iv	X
ejpam-5309	113	3	)	)	PUNCT
ejpam-5309	113	4	it	it	PRON
ejpam-5309	113	5	is	be	AUX
ejpam-5309	113	6	obvious	obvious	ADJ
ejpam-5309	113	7	.	.	PUNCT
ejpam-5309	114	1	the	the	DET
ejpam-5309	114	2	converses	converse	NOUN
ejpam-5309	114	3	of	of	ADP
ejpam-5309	114	4	statements	statement	NOUN
ejpam-5309	114	5	in	in	ADP
ejpam-5309	114	6	proposition	proposition	NOUN
ejpam-5309	114	7	1	1	NUM
ejpam-5309	114	8	do	do	AUX
ejpam-5309	114	9	n’t	not	PART
ejpam-5309	114	10	have	have	VERB
ejpam-5309	114	11	to	to	PART
ejpam-5309	114	12	be	be	AUX
ejpam-5309	114	13	true	true	ADJ
ejpam-5309	114	14	as	as	SCONJ
ejpam-5309	114	15	shown	show	VERB
ejpam-5309	114	16	in	in	ADP
ejpam-5309	114	17	the	the	DET
ejpam-5309	114	18	following	follow	VERB
ejpam-5309	114	19	example	example	NOUN
ejpam-5309	114	20	.	.	PUNCT
ejpam-5309	115	1	example	example	NOUN
ejpam-5309	116	1	2	2	NUM
ejpam-5309	116	2	.	.	PUNCT
ejpam-5309	116	3	let	let	VERB
ejpam-5309	116	4	t	t	NOUN
ejpam-5309	116	5	=	=	PUNCT
ejpam-5309	116	6	{	{	PUNCT
ejpam-5309	116	7	a	a	PRON
ejpam-5309	116	8	,	,	PUNCT
ejpam-5309	116	9	b	b	NOUN
ejpam-5309	116	10	,	,	PUNCT
ejpam-5309	116	11	c	c	NOUN
ejpam-5309	116	12	}	}	PUNCT
ejpam-5309	116	13	and	and	CCONJ
ejpam-5309	116	14	γ	γ	X
ejpam-5309	116	15	=	=	PROPN
ejpam-5309	116	16	t	t	PROPN
ejpam-5309	116	17	.	.	PUNCT
ejpam-5309	117	1	define	define	VERB
ejpam-5309	117	2	the	the	DET
ejpam-5309	117	3	mapping	mapping	NOUN
ejpam-5309	117	4	·	·	PUNCT
ejpam-5309	117	5	on	on	ADP
ejpam-5309	117	6	t	t	PROPN
ejpam-5309	117	7	in	in	ADP
ejpam-5309	117	8	example	example	NOUN
ejpam-5309	117	9	1	1	X
ejpam-5309	117	10	.	.	PUNCT
ejpam-5309	118	1	now	now	ADV
ejpam-5309	118	2	,	,	PUNCT
ejpam-5309	118	3	we	we	PRON
ejpam-5309	118	4	define	define	VERB
ejpam-5309	118	5	a	a	DET
ejpam-5309	118	6	fuzzy	fuzzy	ADJ
ejpam-5309	118	7	set	set	VERB
ejpam-5309	118	8	µ	µ	PROPN
ejpam-5309	118	9	of	of	ADP
ejpam-5309	118	10	t	t	PROPN
ejpam-5309	118	11	by	by	ADP
ejpam-5309	118	12	µ(a	µ(a	PROPN
ejpam-5309	118	13	)	)	PUNCT
ejpam-5309	118	14	=	=	SYM
ejpam-5309	118	15	0.7	0.7	NUM
ejpam-5309	118	16	,	,	PUNCT
ejpam-5309	118	17	µ(b	µ(b	PROPN
ejpam-5309	118	18	)	)	PUNCT
ejpam-5309	118	19	=	=	SYM
ejpam-5309	118	20	0.7	0.7	NUM
ejpam-5309	118	21	and	and	CCONJ
ejpam-5309	118	22	µ(c	µ(c	PROPN
ejpam-5309	118	23	)	)	PUNCT
ejpam-5309	118	24	=	=	PUNCT
ejpam-5309	118	25	0.2	0.2	NUM
ejpam-5309	118	26	.	.	PUNCT
ejpam-5309	119	1	after	after	ADP
ejpam-5309	119	2	a	a	DET
ejpam-5309	119	3	thorough	thorough	ADJ
ejpam-5309	119	4	examination	examination	NOUN
ejpam-5309	119	5	,	,	PUNCT
ejpam-5309	119	6	we	we	PRON
ejpam-5309	119	7	obtain	obtain	VERB
ejpam-5309	119	8	rµ	rµ	NOUN
ejpam-5309	119	9	is	be	AUX
ejpam-5309	119	10	a	a	DET
ejpam-5309	119	11	strongest	strong	ADJ
ejpam-5309	119	12	fuzzy	fuzzy	ADJ
ejpam-5309	119	13	bi	bi	ADJ
ejpam-5309	119	14	-	-	ADJ
ejpam-5309	119	15	γ	γ	NOUN
ejpam-5309	119	16	-	-	NOUN
ejpam-5309	119	17	ideal	ideal	NOUN
ejpam-5309	119	18	on	on	ADP
ejpam-5309	119	19	t	t	PROPN
ejpam-5309	119	20	.	.	PUNCT
ejpam-5309	120	1	nevertheless	nevertheless	ADV
ejpam-5309	120	2	,	,	PUNCT
ejpam-5309	120	3	rµ	rµ	INTJ
ejpam-5309	120	4	is	be	AUX
ejpam-5309	120	5	not	not	PART
ejpam-5309	120	6	a	a	DET
ejpam-5309	120	7	strongest	strong	ADJ
ejpam-5309	120	8	fuzzy	fuzzy	ADJ
ejpam-5309	120	9	left	leave	VERB
ejpam-5309	120	10	γ	γ	NOUN
ejpam-5309	120	11	-	-	NOUN
ejpam-5309	120	12	ideal	ideal	NOUN
ejpam-5309	120	13	on	on	ADP
ejpam-5309	120	14	t	t	PROPN
ejpam-5309	120	15	,	,	PUNCT
ejpam-5309	120	16	since	since	SCONJ
ejpam-5309	120	17	rµ(cαcβb	rµ(cαcβb	ADJ
ejpam-5309	120	18	,	,	PUNCT
ejpam-5309	120	19	cαcβb	cαcβb	NOUN
ejpam-5309	120	20	)	)	PUNCT
ejpam-5309	120	21	=	=	PUNCT
ejpam-5309	120	22	0.2	0.2	NUM
ejpam-5309	120	23	<	<	X
ejpam-5309	120	24	0.7	0.7	NUM
ejpam-5309	120	25	=	=	SYM
ejpam-5309	120	26	rµ(b	rµ(b	X
ejpam-5309	120	27	,	,	PUNCT
ejpam-5309	120	28	b	b	NOUN
ejpam-5309	120	29	)	)	PUNCT
ejpam-5309	120	30	,	,	PUNCT
ejpam-5309	120	31	for	for	ADP
ejpam-5309	120	32	all	all	DET
ejpam-5309	120	33	α	α	NOUN
ejpam-5309	120	34	,	,	PUNCT
ejpam-5309	120	35	β	β	PROPN
ejpam-5309	120	36	∈	∈	PROPN
ejpam-5309	120	37	γ	γ	X
ejpam-5309	120	38	.	.	PUNCT
ejpam-5309	121	1	furthermore	furthermore	ADV
ejpam-5309	121	2	,	,	PUNCT
ejpam-5309	121	3	it	it	PRON
ejpam-5309	121	4	is	be	AUX
ejpam-5309	121	5	not	not	PART
ejpam-5309	121	6	a	a	DET
ejpam-5309	121	7	strongest	strong	ADJ
ejpam-5309	121	8	fuzzy	fuzzy	ADJ
ejpam-5309	121	9	lateral	lateral	ADJ
ejpam-5309	121	10	γ	γ	NOUN
ejpam-5309	121	11	-	-	NOUN
ejpam-5309	121	12	ideal	ideal	NOUN
ejpam-5309	121	13	on	on	ADP
ejpam-5309	121	14	t	t	PROPN
ejpam-5309	121	15	either	either	ADV
ejpam-5309	121	16	,	,	PUNCT
ejpam-5309	121	17	because	because	SCONJ
ejpam-5309	121	18	rµ(cαbβc	rµ(cαbβc	PROPN
ejpam-5309	121	19	,	,	PUNCT
ejpam-5309	121	20	cαbβc	cαbβc	PROPN
ejpam-5309	121	21	)	)	PUNCT
ejpam-5309	121	22	=	=	PUNCT
ejpam-5309	122	1	0.2	0.2	NUM
ejpam-5309	122	2	<	<	X
ejpam-5309	122	3	0.7	0.7	NUM
ejpam-5309	122	4	=	=	SYM
ejpam-5309	122	5	rµ(b	rµ(b	X
ejpam-5309	122	6	,	,	PUNCT
ejpam-5309	122	7	b	b	NOUN
ejpam-5309	122	8	)	)	PUNCT
ejpam-5309	122	9	,	,	PUNCT
ejpam-5309	122	10	for	for	ADP
ejpam-5309	122	11	all	all	DET
ejpam-5309	122	12	α	α	NOUN
ejpam-5309	122	13	,	,	PUNCT
ejpam-5309	122	14	β	β	PROPN
ejpam-5309	122	15	∈	∈	PROPN
ejpam-5309	122	16	γ	γ	PROPN
ejpam-5309	122	17	.	.	PROPN
ejpam-5309	122	18	next	next	ADV
ejpam-5309	122	19	,	,	PUNCT
ejpam-5309	122	20	we	we	PRON
ejpam-5309	122	21	present	present	VERB
ejpam-5309	122	22	the	the	DET
ejpam-5309	122	23	characterizations	characterization	NOUN
ejpam-5309	122	24	of	of	ADP
ejpam-5309	122	25	strongest	strong	ADJ
ejpam-5309	122	26	fuzzy	fuzzy	ADJ
ejpam-5309	122	27	ternary	ternary	ADJ
ejpam-5309	122	28	γ	γ	NOUN
ejpam-5309	122	29	-	-	NOUN
ejpam-5309	122	30	subsemigroups	subsemigroup	NOUN
ejpam-5309	122	31	,	,	PUNCT
ejpam-5309	122	32	strongest	strong	ADJ
ejpam-5309	122	33	fuzzy	fuzzy	ADJ
ejpam-5309	122	34	(	(	PUNCT
ejpam-5309	122	35	resp	resp	NOUN
ejpam-5309	122	36	.	.	PUNCT
ejpam-5309	123	1	left	leave	VERB
ejpam-5309	123	2	,	,	PUNCT
ejpam-5309	123	3	right	right	ADJ
ejpam-5309	123	4	,	,	PUNCT
ejpam-5309	123	5	lateral	lateral	ADJ
ejpam-5309	123	6	)	)	PUNCT
ejpam-5309	123	7	γ	γ	NOUN
ejpam-5309	123	8	-	-	NOUN
ejpam-5309	123	9	ideals	ideal	NOUN
ejpam-5309	123	10	,	,	PUNCT
ejpam-5309	123	11	and	and	CCONJ
ejpam-5309	123	12	strongest	strong	ADJ
ejpam-5309	123	13	fuzzy	fuzzy	ADJ
ejpam-5309	123	14	bi	bi	ADJ
ejpam-5309	123	15	-	-	ADJ
ejpam-5309	123	16	γ	γ	NOUN
ejpam-5309	123	17	-	-	PUNCT
ejpam-5309	123	18	ideals	ideal	NOUN
ejpam-5309	123	19	on	on	ADP
ejpam-5309	123	20	ternary	ternary	ADJ
ejpam-5309	123	21	γ	γ	NOUN
ejpam-5309	123	22	-	-	PUNCT
ejpam-5309	123	23	semigroups	semigroup	NOUN
ejpam-5309	123	24	.	.	PUNCT
ejpam-5309	124	1	theorem	theorem	NOUN
ejpam-5309	124	2	1	1	NUM
ejpam-5309	124	3	.	.	PUNCT
ejpam-5309	125	1	let	let	VERB
ejpam-5309	125	2	t	t	PROPN
ejpam-5309	125	3	be	be	AUX
ejpam-5309	125	4	a	a	DET
ejpam-5309	125	5	ternary	ternary	ADJ
ejpam-5309	125	6	γ	γ	NOUN
ejpam-5309	125	7	-	-	PUNCT
ejpam-5309	125	8	semigroup	semigroup	NOUN
ejpam-5309	125	9	,	,	PUNCT
ejpam-5309	125	10	µ	µ	X
ejpam-5309	125	11	be	be	AUX
ejpam-5309	125	12	a	a	DET
ejpam-5309	125	13	fuzzy	fuzzy	ADJ
ejpam-5309	125	14	set	set	NOUN
ejpam-5309	125	15	of	of	ADP
ejpam-5309	125	16	t	t	PROPN
ejpam-5309	125	17	,	,	PUNCT
ejpam-5309	125	18	and	and	CCONJ
ejpam-5309	125	19	rµ	rµ	INTJ
ejpam-5309	125	20	be	be	AUX
ejpam-5309	125	21	a	a	DET
ejpam-5309	125	22	strongest	strong	ADJ
ejpam-5309	125	23	fuzzy	fuzzy	ADJ
ejpam-5309	125	24	relation	relation	NOUN
ejpam-5309	125	25	on	on	ADP
ejpam-5309	125	26	t	t	PROPN
ejpam-5309	125	27	.	.	PUNCT
ejpam-5309	126	1	then	then	ADV
ejpam-5309	126	2	,	,	PUNCT
ejpam-5309	126	3	µ	µ	X
ejpam-5309	126	4	is	be	AUX
ejpam-5309	126	5	a	a	DET
ejpam-5309	126	6	fuzzy	fuzzy	ADJ
ejpam-5309	126	7	ternary	ternary	ADJ
ejpam-5309	126	8	γ	γ	X
ejpam-5309	126	9	-	-	NOUN
ejpam-5309	126	10	subsemigroup	subsemigroup	NOUN
ejpam-5309	126	11	of	of	ADP
ejpam-5309	126	12	t	t	PROPN
ejpam-5309	126	13	if	if	SCONJ
ejpam-5309	127	1	and	and	CCONJ
ejpam-5309	127	2	only	only	ADV
ejpam-5309	127	3	if	if	SCONJ
ejpam-5309	127	4	rµ	rµ	INTJ
ejpam-5309	127	5	is	be	AUX
ejpam-5309	127	6	a	a	DET
ejpam-5309	127	7	strongest	strong	ADJ
ejpam-5309	127	8	fuzzy	fuzzy	ADJ
ejpam-5309	127	9	ternary	ternary	ADJ
ejpam-5309	127	10	γ	γ	NOUN
ejpam-5309	127	11	-	-	NOUN
ejpam-5309	127	12	subsemigroup	subsemigroup	NOUN
ejpam-5309	127	13	on	on	ADP
ejpam-5309	127	14	t	t	PROPN
ejpam-5309	127	15	.	.	PUNCT
ejpam-5309	128	1	w.	w.	PROPN
ejpam-5309	128	2	nakkhasen	nakkhasen	PROPN
ejpam-5309	128	3	et	et	PROPN
ejpam-5309	128	4	al	al	PROPN
ejpam-5309	128	5	.	.	PUNCT
ejpam-5309	128	6	/	/	SYM
ejpam-5309	128	7	eur	eur	PROPN
ejpam-5309	128	8	.	.	PUNCT
ejpam-5309	129	1	j.	j.	PROPN
ejpam-5309	129	2	pure	pure	PROPN
ejpam-5309	129	3	appl	appl	PROPN
ejpam-5309	129	4	.	.	PROPN
ejpam-5309	129	5	math	math	PROPN
ejpam-5309	129	6	,	,	PUNCT
ejpam-5309	129	7	17	17	NUM
ejpam-5309	129	8	(	(	PUNCT
ejpam-5309	129	9	3	3	NUM
ejpam-5309	129	10	)	)	PUNCT
ejpam-5309	129	11	(	(	PUNCT
ejpam-5309	129	12	2024	2024	NUM
ejpam-5309	129	13	)	)	PUNCT
ejpam-5309	129	14	,	,	PUNCT
ejpam-5309	129	15	1417	1417	NUM
ejpam-5309	129	16	-	-	SYM
ejpam-5309	129	17	1428	1428	NUM
ejpam-5309	129	18	1422	1422	NUM
ejpam-5309	129	19	proof	proof	NOUN
ejpam-5309	129	20	.	.	PUNCT
ejpam-5309	130	1	assume	assume	VERB
ejpam-5309	130	2	that	that	SCONJ
ejpam-5309	130	3	µ	µ	NOUN
ejpam-5309	130	4	is	be	AUX
ejpam-5309	130	5	a	a	DET
ejpam-5309	130	6	fuzzy	fuzzy	ADJ
ejpam-5309	130	7	ternary	ternary	ADJ
ejpam-5309	130	8	γ	γ	X
ejpam-5309	130	9	-	-	NOUN
ejpam-5309	130	10	subsemigroup	subsemigroup	NOUN
ejpam-5309	130	11	of	of	ADP
ejpam-5309	130	12	t	t	PROPN
ejpam-5309	130	13	.	.	PUNCT
ejpam-5309	131	1	let	let	VERB
ejpam-5309	131	2	a1	a1	NOUN
ejpam-5309	131	3	,	,	PUNCT
ejpam-5309	131	4	a2,b1	a2,b1	PROPN
ejpam-5309	131	5	,	,	PUNCT
ejpam-5309	131	6	b2,c1	b2,c1	PROPN
ejpam-5309	131	7	,	,	PUNCT
ejpam-5309	131	8	c2	c2	PROPN
ejpam-5309	131	9	∈	∈	PROPN
ejpam-5309	131	10	t	t	PROPN
ejpam-5309	131	11	and	and	CCONJ
ejpam-5309	131	12	α	α	NOUN
ejpam-5309	131	13	,	,	PUNCT
ejpam-5309	131	14	β	β	PROPN
ejpam-5309	131	15	∈	∈	PROPN
ejpam-5309	131	16	γ	γ	X
ejpam-5309	131	17	.	.	PUNCT
ejpam-5309	132	1	then	then	ADV
ejpam-5309	132	2	,	,	PUNCT
ejpam-5309	132	3	we	we	PRON
ejpam-5309	132	4	have	have	VERB
ejpam-5309	132	5	rµ(a1αb1βc1	rµ(a1αb1βc1	NOUN
ejpam-5309	132	6	,	,	PUNCT
ejpam-5309	132	7	a2αb2βc2	a2αb2βc2	X
ejpam-5309	132	8	)	)	PUNCT
ejpam-5309	132	9	=	=	SYM
ejpam-5309	132	10	min{µ(a1αb1βc1	min{µ(a1αb1βc1	NOUN
ejpam-5309	132	11	)	)	PUNCT
ejpam-5309	132	12	,	,	PUNCT
ejpam-5309	132	13	µ(a2αb2βc2	µ(a2αb2βc2	NOUN
ejpam-5309	132	14	)	)	PUNCT
ejpam-5309	132	15	}	}	PUNCT
ejpam-5309	132	16	≥	≥	NOUN
ejpam-5309	132	17	min{min{µ(a1	min{min{µ(a1	NOUN
ejpam-5309	132	18	)	)	PUNCT
ejpam-5309	132	19	,	,	PUNCT
ejpam-5309	132	20	µ(b1	µ(b1	NOUN
ejpam-5309	132	21	)	)	PUNCT
ejpam-5309	132	22	,	,	PUNCT
ejpam-5309	132	23	µ(c1)},min{µ(a2	µ(c1)},min{µ(a2	NOUN
ejpam-5309	132	24	)	)	PUNCT
ejpam-5309	132	25	,	,	PUNCT
ejpam-5309	132	26	µ(b2	µ(b2	NOUN
ejpam-5309	132	27	)	)	PUNCT
ejpam-5309	132	28	,	,	PUNCT
ejpam-5309	132	29	µ(c2	µ(c2	ADV
ejpam-5309	132	30	)	)	PUNCT
ejpam-5309	132	31	}	}	PUNCT
ejpam-5309	132	32	}	}	PUNCT
ejpam-5309	132	33	=	=	SYM
ejpam-5309	132	34	min{min{µ(a1	min{min{µ(a1	NOUN
ejpam-5309	132	35	)	)	PUNCT
ejpam-5309	132	36	,	,	PUNCT
ejpam-5309	132	37	µ(a2)},min{µ(b1	µ(a2)},min{µ(b1	NOUN
ejpam-5309	132	38	)	)	PUNCT
ejpam-5309	132	39	,	,	PUNCT
ejpam-5309	132	40	µ(b2)},min{µ(c1	µ(b2)},min{µ(c1	PROPN
ejpam-5309	132	41	)	)	PUNCT
ejpam-5309	132	42	,	,	PUNCT
ejpam-5309	132	43	µ(c2	µ(c2	ADV
ejpam-5309	132	44	)	)	PUNCT
ejpam-5309	132	45	}	}	PUNCT
ejpam-5309	132	46	}	}	PUNCT
ejpam-5309	132	47	=	=	SYM
ejpam-5309	132	48	min{rµ(a1	min{rµ(a1	PROPN
ejpam-5309	132	49	,	,	PUNCT
ejpam-5309	132	50	a2	a2	PROPN
ejpam-5309	132	51	)	)	PUNCT
ejpam-5309	132	52	,	,	PUNCT
ejpam-5309	132	53	rµ(b1	rµ(b1	NOUN
ejpam-5309	132	54	,	,	PUNCT
ejpam-5309	132	55	b2	b2	NOUN
ejpam-5309	132	56	)	)	PUNCT
ejpam-5309	132	57	,	,	PUNCT
ejpam-5309	132	58	rµ(c1	rµ(c1	PROPN
ejpam-5309	132	59	,	,	PUNCT
ejpam-5309	132	60	c2	c2	PROPN
ejpam-5309	132	61	)	)	PUNCT
ejpam-5309	132	62	}	}	PUNCT
ejpam-5309	132	63	.	.	PUNCT
ejpam-5309	133	1	thus	thus	ADV
ejpam-5309	133	2	,	,	PUNCT
ejpam-5309	133	3	rµ	rµ	INTJ
ejpam-5309	133	4	is	be	AUX
ejpam-5309	133	5	a	a	DET
ejpam-5309	133	6	strongest	strong	ADJ
ejpam-5309	133	7	fuzzy	fuzzy	ADJ
ejpam-5309	133	8	ternary	ternary	ADJ
ejpam-5309	133	9	γ	γ	NOUN
ejpam-5309	133	10	-	-	NOUN
ejpam-5309	133	11	subsemigroup	subsemigroup	NOUN
ejpam-5309	133	12	on	on	ADP
ejpam-5309	133	13	t	t	PROPN
ejpam-5309	133	14	.	.	PUNCT
ejpam-5309	134	1	conversely	conversely	ADV
ejpam-5309	134	2	,	,	PUNCT
ejpam-5309	134	3	assume	assume	VERB
ejpam-5309	134	4	that	that	SCONJ
ejpam-5309	134	5	rµ	rµ	INTJ
ejpam-5309	134	6	is	be	AUX
ejpam-5309	134	7	a	a	DET
ejpam-5309	134	8	strongest	strong	ADJ
ejpam-5309	134	9	fuzzy	fuzzy	ADJ
ejpam-5309	134	10	ternary	ternary	ADJ
ejpam-5309	134	11	γ	γ	NOUN
ejpam-5309	134	12	-	-	NOUN
ejpam-5309	134	13	subsemigroup	subsemigroup	NOUN
ejpam-5309	134	14	on	on	ADP
ejpam-5309	134	15	t	t	PROPN
ejpam-5309	134	16	.	.	PUNCT
ejpam-5309	135	1	let	let	VERB
ejpam-5309	135	2	a	a	DET
ejpam-5309	135	3	,	,	PUNCT
ejpam-5309	135	4	b	b	NOUN
ejpam-5309	135	5	,	,	PUNCT
ejpam-5309	135	6	c	c	PROPN
ejpam-5309	135	7	∈	∈	PROPN
ejpam-5309	135	8	t	t	PROPN
ejpam-5309	135	9	and	and	CCONJ
ejpam-5309	135	10	α	α	NOUN
ejpam-5309	135	11	,	,	PUNCT
ejpam-5309	135	12	β	β	PROPN
ejpam-5309	135	13	∈	∈	PROPN
ejpam-5309	135	14	γ	γ	X
ejpam-5309	135	15	.	.	PUNCT
ejpam-5309	136	1	then	then	ADV
ejpam-5309	136	2	,	,	PUNCT
ejpam-5309	136	3	we	we	PRON
ejpam-5309	136	4	have	have	VERB
ejpam-5309	136	5	µ(aαbβc	µ(aαbβc	NOUN
ejpam-5309	136	6	)	)	PUNCT
ejpam-5309	136	7	=	=	SYM
ejpam-5309	136	8	min{µ(aαbβc	min{µ(aαbβc	PROPN
ejpam-5309	136	9	)	)	PUNCT
ejpam-5309	136	10	,	,	PUNCT
ejpam-5309	136	11	µ(aαbβc	µ(aαbβc	PROPN
ejpam-5309	136	12	)	)	PUNCT
ejpam-5309	136	13	}	}	PUNCT
ejpam-5309	137	1	=	=	SYM
ejpam-5309	137	2	rµ(aαbβc	rµ(aαbβc	PROPN
ejpam-5309	137	3	,	,	PUNCT
ejpam-5309	137	4	aαbβc	aαbβc	PROPN
ejpam-5309	137	5	)	)	PUNCT
ejpam-5309	137	6	≥	≥	NOUN
ejpam-5309	137	7	min{rµ(a	min{rµ(a	PROPN
ejpam-5309	137	8	,	,	PUNCT
ejpam-5309	137	9	a	a	PRON
ejpam-5309	137	10	)	)	PUNCT
ejpam-5309	137	11	,	,	PUNCT
ejpam-5309	137	12	rµ(b	rµ(b	X
ejpam-5309	137	13	,	,	PUNCT
ejpam-5309	137	14	b	b	NOUN
ejpam-5309	137	15	)	)	PUNCT
ejpam-5309	137	16	,	,	PUNCT
ejpam-5309	137	17	rµ(c	rµ(c	X
ejpam-5309	137	18	,	,	PUNCT
ejpam-5309	137	19	c	c	NOUN
ejpam-5309	137	20	)	)	PUNCT
ejpam-5309	137	21	}	}	PUNCT
ejpam-5309	137	22	=	=	SYM
ejpam-5309	137	23	min{min{µ(a	min{min{µ(a	NOUN
ejpam-5309	137	24	)	)	PUNCT
ejpam-5309	137	25	,	,	PUNCT
ejpam-5309	137	26	µ(a)},min{µ(b	µ(a)},min{µ(b	PROPN
ejpam-5309	137	27	)	)	PUNCT
ejpam-5309	137	28	,	,	PUNCT
ejpam-5309	137	29	µ(b)},min{µ(c	µ(b)},min{µ(c	NOUN
ejpam-5309	137	30	)	)	PUNCT
ejpam-5309	137	31	,	,	PUNCT
ejpam-5309	137	32	µ(c	µ(c	PROPN
ejpam-5309	137	33	)	)	PUNCT
ejpam-5309	137	34	}	}	PUNCT
ejpam-5309	137	35	}	}	PUNCT
ejpam-5309	137	36	=	=	SYM
ejpam-5309	137	37	min{µ(a	min{µ(a	PROPN
ejpam-5309	137	38	)	)	PUNCT
ejpam-5309	137	39	,	,	PUNCT
ejpam-5309	137	40	µ(b	µ(b	PROPN
ejpam-5309	137	41	)	)	PUNCT
ejpam-5309	137	42	,	,	PUNCT
ejpam-5309	137	43	µ(c	µ(c	PROPN
ejpam-5309	137	44	)	)	PUNCT
ejpam-5309	137	45	}	}	PUNCT
ejpam-5309	137	46	.	.	PUNCT
ejpam-5309	138	1	hence	hence	ADV
ejpam-5309	138	2	,	,	PUNCT
ejpam-5309	138	3	µ	µ	X
ejpam-5309	138	4	is	be	AUX
ejpam-5309	138	5	a	a	DET
ejpam-5309	138	6	fuzzy	fuzzy	ADJ
ejpam-5309	138	7	ternary	ternary	ADJ
ejpam-5309	138	8	γ	γ	X
ejpam-5309	138	9	-	-	NOUN
ejpam-5309	138	10	subsemigroup	subsemigroup	NOUN
ejpam-5309	138	11	of	of	ADP
ejpam-5309	138	12	t	t	PROPN
ejpam-5309	138	13	.	.	PUNCT
ejpam-5309	139	1	theorem	theorem	NOUN
ejpam-5309	139	2	2	2	NUM
ejpam-5309	139	3	.	.	PUNCT
ejpam-5309	140	1	let	let	VERB
ejpam-5309	140	2	t	t	PROPN
ejpam-5309	140	3	be	be	AUX
ejpam-5309	140	4	a	a	DET
ejpam-5309	140	5	ternary	ternary	ADJ
ejpam-5309	140	6	γ	γ	NOUN
ejpam-5309	140	7	-	-	PUNCT
ejpam-5309	140	8	semigroup	semigroup	NOUN
ejpam-5309	140	9	,	,	PUNCT
ejpam-5309	140	10	µ	µ	X
ejpam-5309	140	11	be	be	AUX
ejpam-5309	140	12	a	a	DET
ejpam-5309	140	13	fuzzy	fuzzy	ADJ
ejpam-5309	140	14	set	set	NOUN
ejpam-5309	140	15	of	of	ADP
ejpam-5309	140	16	t	t	PROPN
ejpam-5309	140	17	,	,	PUNCT
ejpam-5309	140	18	and	and	CCONJ
ejpam-5309	140	19	rµ	rµ	INTJ
ejpam-5309	140	20	be	be	AUX
ejpam-5309	140	21	a	a	DET
ejpam-5309	140	22	strongest	strong	ADJ
ejpam-5309	140	23	fuzzy	fuzzy	ADJ
ejpam-5309	140	24	relation	relation	NOUN
ejpam-5309	140	25	on	on	ADP
ejpam-5309	140	26	t	t	PROPN
ejpam-5309	140	27	.	.	PUNCT
ejpam-5309	141	1	then	then	ADV
ejpam-5309	141	2	the	the	DET
ejpam-5309	141	3	following	follow	VERB
ejpam-5309	141	4	statements	statement	NOUN
ejpam-5309	141	5	hold	hold	VERB
ejpam-5309	141	6	:	:	PUNCT
ejpam-5309	141	7	(	(	PUNCT
ejpam-5309	141	8	i	i	NOUN
ejpam-5309	141	9	)	)	PUNCT
ejpam-5309	141	10	µ	µ	PROPN
ejpam-5309	141	11	is	be	AUX
ejpam-5309	141	12	a	a	DET
ejpam-5309	141	13	fuzzy	fuzzy	ADJ
ejpam-5309	141	14	left	leave	VERB
ejpam-5309	141	15	γ	γ	NOUN
ejpam-5309	141	16	-	-	NOUN
ejpam-5309	141	17	ideal	ideal	NOUN
ejpam-5309	141	18	of	of	ADP
ejpam-5309	141	19	t	t	PROPN
ejpam-5309	141	20	if	if	SCONJ
ejpam-5309	142	1	and	and	CCONJ
ejpam-5309	142	2	only	only	ADV
ejpam-5309	142	3	if	if	SCONJ
ejpam-5309	142	4	rµ	rµ	INTJ
ejpam-5309	142	5	is	be	AUX
ejpam-5309	142	6	a	a	DET
ejpam-5309	142	7	strongest	strong	ADJ
ejpam-5309	142	8	fuzzy	fuzzy	ADJ
ejpam-5309	142	9	left	leave	VERB
ejpam-5309	142	10	γ	γ	NOUN
ejpam-5309	142	11	-	-	NOUN
ejpam-5309	142	12	ideal	ideal	NOUN
ejpam-5309	142	13	on	on	ADP
ejpam-5309	142	14	t	t	PROPN
ejpam-5309	142	15	;	;	PUNCT
ejpam-5309	142	16	(	(	PUNCT
ejpam-5309	142	17	ii	ii	NOUN
ejpam-5309	142	18	)	)	PUNCT
ejpam-5309	142	19	µ	µ	PROPN
ejpam-5309	142	20	is	be	AUX
ejpam-5309	142	21	a	a	DET
ejpam-5309	142	22	fuzzy	fuzzy	ADJ
ejpam-5309	142	23	right	right	ADJ
ejpam-5309	142	24	γ	γ	X
ejpam-5309	142	25	-	-	NOUN
ejpam-5309	142	26	ideal	ideal	NOUN
ejpam-5309	142	27	of	of	ADP
ejpam-5309	142	28	t	t	PROPN
ejpam-5309	142	29	if	if	SCONJ
ejpam-5309	143	1	and	and	CCONJ
ejpam-5309	143	2	only	only	ADV
ejpam-5309	143	3	if	if	SCONJ
ejpam-5309	143	4	rµ	rµ	INTJ
ejpam-5309	143	5	is	be	AUX
ejpam-5309	143	6	a	a	DET
ejpam-5309	143	7	strongest	strong	ADJ
ejpam-5309	143	8	fuzzy	fuzzy	ADJ
ejpam-5309	143	9	right	right	ADJ
ejpam-5309	143	10	γ	γ	X
ejpam-5309	143	11	-	-	NOUN
ejpam-5309	143	12	ideal	ideal	NOUN
ejpam-5309	143	13	on	on	ADP
ejpam-5309	143	14	t	t	PROPN
ejpam-5309	143	15	;	;	PUNCT
ejpam-5309	143	16	(	(	PUNCT
ejpam-5309	143	17	iii	iii	X
ejpam-5309	143	18	)	)	PUNCT
ejpam-5309	143	19	µ	µ	NOUN
ejpam-5309	143	20	is	be	AUX
ejpam-5309	143	21	a	a	DET
ejpam-5309	143	22	fuzzy	fuzzy	ADJ
ejpam-5309	143	23	lateral	lateral	ADJ
ejpam-5309	143	24	γ	γ	NOUN
ejpam-5309	143	25	-	-	NOUN
ejpam-5309	143	26	ideal	ideal	NOUN
ejpam-5309	143	27	of	of	ADP
ejpam-5309	143	28	t	t	PROPN
ejpam-5309	143	29	if	if	SCONJ
ejpam-5309	144	1	and	and	CCONJ
ejpam-5309	144	2	only	only	ADV
ejpam-5309	144	3	if	if	SCONJ
ejpam-5309	144	4	rµ	rµ	INTJ
ejpam-5309	144	5	is	be	AUX
ejpam-5309	144	6	a	a	DET
ejpam-5309	144	7	strongest	strong	ADJ
ejpam-5309	144	8	fuzzy	fuzzy	ADJ
ejpam-5309	144	9	lateral	lateral	ADJ
ejpam-5309	144	10	γ	γ	NOUN
ejpam-5309	144	11	-	-	NOUN
ejpam-5309	144	12	ideal	ideal	NOUN
ejpam-5309	144	13	on	on	ADP
ejpam-5309	144	14	t	t	PROPN
ejpam-5309	144	15	;	;	PUNCT
ejpam-5309	144	16	(	(	PUNCT
ejpam-5309	144	17	iv	iv	X
ejpam-5309	144	18	)	)	PUNCT
ejpam-5309	144	19	µ	µ	X
ejpam-5309	144	20	is	be	AUX
ejpam-5309	144	21	a	a	DET
ejpam-5309	144	22	fuzzy	fuzzy	ADJ
ejpam-5309	144	23	γ	γ	NOUN
ejpam-5309	144	24	-	-	NOUN
ejpam-5309	144	25	ideal	ideal	NOUN
ejpam-5309	144	26	of	of	ADP
ejpam-5309	144	27	t	t	PROPN
ejpam-5309	144	28	if	if	SCONJ
ejpam-5309	145	1	and	and	CCONJ
ejpam-5309	145	2	only	only	ADV
ejpam-5309	145	3	if	if	SCONJ
ejpam-5309	145	4	rµ	rµ	INTJ
ejpam-5309	145	5	is	be	AUX
ejpam-5309	145	6	a	a	DET
ejpam-5309	145	7	strongest	strong	ADJ
ejpam-5309	145	8	fuzzy	fuzzy	ADJ
ejpam-5309	145	9	γ	γ	NOUN
ejpam-5309	145	10	-	-	NOUN
ejpam-5309	145	11	ideal	ideal	NOUN
ejpam-5309	145	12	on	on	ADP
ejpam-5309	145	13	t	t	PROPN
ejpam-5309	145	14	.	.	PUNCT
ejpam-5309	146	1	proof	proof	NOUN
ejpam-5309	146	2	.	.	PUNCT
ejpam-5309	147	1	(	(	PUNCT
ejpam-5309	147	2	i	i	NOUN
ejpam-5309	147	3	)	)	PUNCT
ejpam-5309	147	4	assume	assume	VERB
ejpam-5309	147	5	that	that	SCONJ
ejpam-5309	147	6	µ	µ	NOUN
ejpam-5309	147	7	is	be	AUX
ejpam-5309	147	8	a	a	DET
ejpam-5309	147	9	fuzzy	fuzzy	ADJ
ejpam-5309	147	10	left	leave	VERB
ejpam-5309	147	11	γ	γ	NOUN
ejpam-5309	147	12	-	-	NOUN
ejpam-5309	147	13	ideal	ideal	NOUN
ejpam-5309	147	14	of	of	ADP
ejpam-5309	147	15	t	t	PROPN
ejpam-5309	147	16	.	.	PUNCT
ejpam-5309	148	1	let	let	VERB
ejpam-5309	148	2	a1	a1	NOUN
ejpam-5309	148	3	,	,	PUNCT
ejpam-5309	148	4	a2	a2	PROPN
ejpam-5309	148	5	,	,	PUNCT
ejpam-5309	148	6	b1	b1	NOUN
ejpam-5309	148	7	,	,	PUNCT
ejpam-5309	148	8	b2	b2	NOUN
ejpam-5309	148	9	,	,	PUNCT
ejpam-5309	148	10	c1	c1	NOUN
ejpam-5309	148	11	,	,	PUNCT
ejpam-5309	148	12	c2	c2	PROPN
ejpam-5309	148	13	∈	∈	PROPN
ejpam-5309	148	14	t	t	PROPN
ejpam-5309	148	15	and	and	CCONJ
ejpam-5309	148	16	α	α	NOUN
ejpam-5309	148	17	,	,	PUNCT
ejpam-5309	148	18	β	β	PROPN
ejpam-5309	148	19	∈	∈	PROPN
ejpam-5309	148	20	γ	γ	PROPN
ejpam-5309	148	21	.	.	PUNCT
ejpam-5309	149	1	thus	thus	ADV
ejpam-5309	149	2	,	,	PUNCT
ejpam-5309	149	3	we	we	PRON
ejpam-5309	149	4	have	have	VERB
ejpam-5309	149	5	rµ(a1αb1βc1	rµ(a1αb1βc1	NOUN
ejpam-5309	149	6	,	,	PUNCT
ejpam-5309	149	7	a2αb2βc2	a2αb2βc2	X
ejpam-5309	149	8	)	)	PUNCT
ejpam-5309	149	9	=	=	SYM
ejpam-5309	149	10	min{µ(a1αb1βc1	min{µ(a1αb1βc1	NOUN
ejpam-5309	149	11	)	)	PUNCT
ejpam-5309	149	12	,	,	PUNCT
ejpam-5309	149	13	µ(a2αb2βc2	µ(a2αb2βc2	NOUN
ejpam-5309	149	14	)	)	PUNCT
ejpam-5309	149	15	}	}	PUNCT
ejpam-5309	149	16	≥	≥	NOUN
ejpam-5309	149	17	min{µ(c1	min{µ(c1	NUM
ejpam-5309	149	18	)	)	PUNCT
ejpam-5309	149	19	,	,	PUNCT
ejpam-5309	149	20	µ(c2	µ(c2	ADV
ejpam-5309	149	21	)	)	PUNCT
ejpam-5309	149	22	}	}	PUNCT
ejpam-5309	149	23	=	=	SYM
ejpam-5309	149	24	rµ(c1	rµ(c1	PROPN
ejpam-5309	149	25	,	,	PUNCT
ejpam-5309	149	26	c2	c2	PROPN
ejpam-5309	149	27	)	)	PUNCT
ejpam-5309	149	28	.	.	PUNCT
ejpam-5309	150	1	this	this	PRON
ejpam-5309	150	2	implies	imply	VERB
ejpam-5309	150	3	that	that	SCONJ
ejpam-5309	150	4	rµ	rµ	INTJ
ejpam-5309	150	5	is	be	AUX
ejpam-5309	150	6	a	a	DET
ejpam-5309	150	7	strongest	strong	ADJ
ejpam-5309	150	8	fuzzy	fuzzy	ADJ
ejpam-5309	150	9	left	leave	VERB
ejpam-5309	150	10	γ	γ	NOUN
ejpam-5309	150	11	-	-	NOUN
ejpam-5309	150	12	ideal	ideal	NOUN
ejpam-5309	150	13	on	on	ADP
ejpam-5309	150	14	t	t	PROPN
ejpam-5309	150	15	.	.	PUNCT
ejpam-5309	151	1	conversely	conversely	ADV
ejpam-5309	151	2	,	,	PUNCT
ejpam-5309	151	3	assume	assume	VERB
ejpam-5309	151	4	that	that	SCONJ
ejpam-5309	151	5	rµ	rµ	INTJ
ejpam-5309	151	6	is	be	AUX
ejpam-5309	151	7	a	a	DET
ejpam-5309	151	8	strongest	strong	ADJ
ejpam-5309	151	9	fuzzy	fuzzy	ADJ
ejpam-5309	151	10	left	leave	VERB
ejpam-5309	151	11	γ	γ	NOUN
ejpam-5309	151	12	-	-	NOUN
ejpam-5309	151	13	ideal	ideal	NOUN
ejpam-5309	151	14	on	on	ADP
ejpam-5309	151	15	t	t	PROPN
ejpam-5309	151	16	.	.	PUNCT
ejpam-5309	152	1	let	let	VERB
ejpam-5309	152	2	a	a	DET
ejpam-5309	152	3	,	,	PUNCT
ejpam-5309	152	4	b	b	NOUN
ejpam-5309	152	5	,	,	PUNCT
ejpam-5309	152	6	c	c	PROPN
ejpam-5309	152	7	∈	∈	PROPN
ejpam-5309	152	8	t	t	PROPN
ejpam-5309	152	9	and	and	CCONJ
ejpam-5309	152	10	α	α	NOUN
ejpam-5309	152	11	,	,	PUNCT
ejpam-5309	152	12	β	β	PROPN
ejpam-5309	152	13	∈	∈	PROPN
ejpam-5309	152	14	γ	γ	X
ejpam-5309	152	15	.	.	PUNCT
ejpam-5309	153	1	then	then	ADV
ejpam-5309	153	2	,	,	PUNCT
ejpam-5309	153	3	we	we	PRON
ejpam-5309	153	4	have	have	VERB
ejpam-5309	153	5	µ(aαbβc	µ(aαbβc	NOUN
ejpam-5309	153	6	)	)	PUNCT
ejpam-5309	153	7	=	=	SYM
ejpam-5309	153	8	min{µ(aαbβc	min{µ(aαbβc	PROPN
ejpam-5309	153	9	)	)	PUNCT
ejpam-5309	153	10	,	,	PUNCT
ejpam-5309	153	11	µ(aαbβc	µ(aαbβc	PROPN
ejpam-5309	153	12	)	)	PUNCT
ejpam-5309	153	13	}	}	PUNCT
ejpam-5309	153	14	w.	w.	PROPN
ejpam-5309	153	15	nakkhasen	nakkhasen	PROPN
ejpam-5309	153	16	et	et	PROPN
ejpam-5309	153	17	al	al	PROPN
ejpam-5309	153	18	.	.	PUNCT
ejpam-5309	153	19	/	/	SYM
ejpam-5309	153	20	eur	eur	PROPN
ejpam-5309	153	21	.	.	PUNCT
ejpam-5309	154	1	j.	j.	PROPN
ejpam-5309	154	2	pure	pure	PROPN
ejpam-5309	154	3	appl	appl	PROPN
ejpam-5309	154	4	.	.	PROPN
ejpam-5309	154	5	math	math	PROPN
ejpam-5309	154	6	,	,	PUNCT
ejpam-5309	154	7	17	17	NUM
ejpam-5309	154	8	(	(	PUNCT
ejpam-5309	154	9	3	3	NUM
ejpam-5309	154	10	)	)	PUNCT
ejpam-5309	154	11	(	(	PUNCT
ejpam-5309	154	12	2024	2024	NUM
ejpam-5309	154	13	)	)	PUNCT
ejpam-5309	154	14	,	,	PUNCT
ejpam-5309	154	15	1417	1417	NUM
ejpam-5309	154	16	-	-	SYM
ejpam-5309	154	17	1428	1428	NUM
ejpam-5309	154	18	1423	1423	NUM
ejpam-5309	154	19	=	=	SYM
ejpam-5309	154	20	rµ(aαbβc	rµ(aαbβc	PROPN
ejpam-5309	154	21	,	,	PUNCT
ejpam-5309	154	22	aαbβc	aαbβc	PROPN
ejpam-5309	154	23	)	)	PUNCT
ejpam-5309	154	24	≥	≥	NOUN
ejpam-5309	154	25	rµ(c	rµ(c	X
ejpam-5309	154	26	,	,	PUNCT
ejpam-5309	154	27	c	c	NOUN
ejpam-5309	154	28	)	)	PUNCT
ejpam-5309	154	29	=	=	SYM
ejpam-5309	154	30	min{µ(c	min{µ(c	PROPN
ejpam-5309	154	31	)	)	PUNCT
ejpam-5309	154	32	,	,	PUNCT
ejpam-5309	154	33	µ(c	µ(c	ADP
ejpam-5309	154	34	)	)	PUNCT
ejpam-5309	154	35	}	}	PUNCT
ejpam-5309	154	36	=	=	SYM
ejpam-5309	154	37	µ(c	µ(c	PROPN
ejpam-5309	154	38	)	)	PUNCT
ejpam-5309	154	39	.	.	PUNCT
ejpam-5309	155	1	we	we	PRON
ejpam-5309	155	2	obtain	obtain	VERB
ejpam-5309	155	3	that	that	SCONJ
ejpam-5309	155	4	µ	µ	NOUN
ejpam-5309	155	5	is	be	AUX
ejpam-5309	155	6	a	a	DET
ejpam-5309	155	7	fuzzy	fuzzy	ADJ
ejpam-5309	155	8	left	leave	VERB
ejpam-5309	155	9	γ	γ	NOUN
ejpam-5309	155	10	-	-	NOUN
ejpam-5309	155	11	ideal	ideal	NOUN
ejpam-5309	155	12	of	of	ADP
ejpam-5309	155	13	t	t	PROPN
ejpam-5309	155	14	.	.	PUNCT
ejpam-5309	156	1	for	for	ADP
ejpam-5309	156	2	the	the	DET
ejpam-5309	156	3	proofs	proof	NOUN
ejpam-5309	156	4	of	of	ADP
ejpam-5309	156	5	(	(	PUNCT
ejpam-5309	156	6	ii	ii	NOUN
ejpam-5309	156	7	)	)	PUNCT
ejpam-5309	156	8	and	and	CCONJ
ejpam-5309	156	9	(	(	PUNCT
ejpam-5309	156	10	iii	iii	NOUN
ejpam-5309	156	11	)	)	PUNCT
ejpam-5309	156	12	,	,	PUNCT
ejpam-5309	156	13	we	we	PRON
ejpam-5309	156	14	can	can	AUX
ejpam-5309	156	15	prove	prove	VERB
ejpam-5309	156	16	similarly	similarly	ADV
ejpam-5309	156	17	.	.	PUNCT
ejpam-5309	157	1	(	(	PUNCT
ejpam-5309	157	2	iv	iv	X
ejpam-5309	157	3	)	)	PUNCT
ejpam-5309	157	4	it	it	PRON
ejpam-5309	157	5	follows	follow	VERB
ejpam-5309	157	6	by	by	ADP
ejpam-5309	157	7	the	the	DET
ejpam-5309	157	8	conditions	condition	NOUN
ejpam-5309	157	9	of	of	ADP
ejpam-5309	157	10	(	(	PUNCT
ejpam-5309	157	11	i	i	NOUN
ejpam-5309	157	12	)	)	PUNCT
ejpam-5309	157	13	,	,	PUNCT
ejpam-5309	157	14	(	(	PUNCT
ejpam-5309	157	15	ii	ii	NOUN
ejpam-5309	157	16	)	)	PUNCT
ejpam-5309	157	17	,	,	PUNCT
ejpam-5309	157	18	and	and	CCONJ
ejpam-5309	157	19	(	(	PUNCT
ejpam-5309	157	20	iii	iii	NOUN
ejpam-5309	157	21	)	)	PUNCT
ejpam-5309	157	22	.	.	PUNCT
ejpam-5309	158	1	theorem	theorem	NOUN
ejpam-5309	158	2	3	3	X
ejpam-5309	158	3	.	.	PUNCT
ejpam-5309	159	1	let	let	VERB
ejpam-5309	159	2	t	t	PROPN
ejpam-5309	159	3	be	be	AUX
ejpam-5309	159	4	a	a	DET
ejpam-5309	159	5	ternary	ternary	ADJ
ejpam-5309	159	6	γ	γ	NOUN
ejpam-5309	159	7	-	-	PUNCT
ejpam-5309	159	8	semigroup	semigroup	NOUN
ejpam-5309	159	9	,	,	PUNCT
ejpam-5309	159	10	µ	µ	X
ejpam-5309	159	11	be	be	AUX
ejpam-5309	159	12	a	a	DET
ejpam-5309	159	13	fuzzy	fuzzy	ADJ
ejpam-5309	159	14	set	set	NOUN
ejpam-5309	159	15	of	of	ADP
ejpam-5309	159	16	t	t	PROPN
ejpam-5309	159	17	,	,	PUNCT
ejpam-5309	159	18	and	and	CCONJ
ejpam-5309	159	19	rµ	rµ	INTJ
ejpam-5309	159	20	be	be	AUX
ejpam-5309	159	21	a	a	DET
ejpam-5309	159	22	strongest	strong	ADJ
ejpam-5309	159	23	fuzzy	fuzzy	ADJ
ejpam-5309	159	24	relation	relation	NOUN
ejpam-5309	159	25	on	on	ADP
ejpam-5309	159	26	t	t	PROPN
ejpam-5309	159	27	.	.	PUNCT
ejpam-5309	160	1	then	then	ADV
ejpam-5309	160	2	,	,	PUNCT
ejpam-5309	160	3	µ	µ	X
ejpam-5309	160	4	is	be	AUX
ejpam-5309	160	5	a	a	DET
ejpam-5309	160	6	fuzzy	fuzzy	ADJ
ejpam-5309	160	7	bi	bi	ADJ
ejpam-5309	160	8	-	-	ADJ
ejpam-5309	160	9	γ	γ	NOUN
ejpam-5309	160	10	-	-	NOUN
ejpam-5309	160	11	ideal	ideal	NOUN
ejpam-5309	160	12	of	of	ADP
ejpam-5309	160	13	t	t	PROPN
ejpam-5309	160	14	if	if	SCONJ
ejpam-5309	161	1	and	and	CCONJ
ejpam-5309	161	2	only	only	ADV
ejpam-5309	161	3	if	if	SCONJ
ejpam-5309	161	4	rµ	rµ	INTJ
ejpam-5309	161	5	is	be	AUX
ejpam-5309	161	6	a	a	DET
ejpam-5309	161	7	strongest	strong	ADJ
ejpam-5309	161	8	fuzzy	fuzzy	ADJ
ejpam-5309	161	9	bi	bi	ADJ
ejpam-5309	161	10	-	-	ADJ
ejpam-5309	161	11	γ	γ	NOUN
ejpam-5309	161	12	-	-	NOUN
ejpam-5309	161	13	ideal	ideal	NOUN
ejpam-5309	161	14	on	on	ADP
ejpam-5309	161	15	t	t	PROPN
ejpam-5309	161	16	.	.	PUNCT
ejpam-5309	162	1	proof	proof	NOUN
ejpam-5309	162	2	.	.	PUNCT
ejpam-5309	163	1	assume	assume	VERB
ejpam-5309	163	2	that	that	SCONJ
ejpam-5309	163	3	µ	µ	NOUN
ejpam-5309	163	4	is	be	AUX
ejpam-5309	163	5	a	a	DET
ejpam-5309	163	6	fuzzy	fuzzy	ADJ
ejpam-5309	163	7	bi	bi	ADJ
ejpam-5309	163	8	-	-	ADJ
ejpam-5309	163	9	γ	γ	NOUN
ejpam-5309	163	10	-	-	NOUN
ejpam-5309	163	11	ideal	ideal	NOUN
ejpam-5309	163	12	of	of	ADP
ejpam-5309	163	13	t	t	PROPN
ejpam-5309	163	14	.	.	PUNCT
ejpam-5309	164	1	then	then	ADV
ejpam-5309	164	2	µ	µ	X
ejpam-5309	164	3	is	be	AUX
ejpam-5309	164	4	a	a	DET
ejpam-5309	164	5	fuzzy	fuzzy	ADJ
ejpam-5309	164	6	ternary	ternary	ADJ
ejpam-5309	164	7	γsubsemigroup	γsubsemigroup	NOUN
ejpam-5309	164	8	of	of	ADP
ejpam-5309	164	9	t	t	PROPN
ejpam-5309	164	10	.	.	PUNCT
ejpam-5309	165	1	by	by	ADP
ejpam-5309	165	2	theorem	theorem	NOUN
ejpam-5309	165	3	1	1	NUM
ejpam-5309	165	4	,	,	PUNCT
ejpam-5309	165	5	we	we	PRON
ejpam-5309	165	6	get	get	AUX
ejpam-5309	165	7	rµ	rµ	VERB
ejpam-5309	165	8	is	be	AUX
ejpam-5309	165	9	a	a	DET
ejpam-5309	165	10	strongest	strong	ADJ
ejpam-5309	165	11	fuzzy	fuzzy	ADJ
ejpam-5309	165	12	ternary	ternary	ADJ
ejpam-5309	165	13	γ	γ	NOUN
ejpam-5309	165	14	-	-	NOUN
ejpam-5309	165	15	subsemigroup	subsemigroup	NOUN
ejpam-5309	165	16	on	on	ADP
ejpam-5309	165	17	t	t	PROPN
ejpam-5309	165	18	.	.	PUNCT
ejpam-5309	166	1	let	let	VERB
ejpam-5309	166	2	a1	a1	NOUN
ejpam-5309	166	3	,	,	PUNCT
ejpam-5309	166	4	a2	a2	PROPN
ejpam-5309	166	5	,	,	PUNCT
ejpam-5309	166	6	b1	b1	NOUN
ejpam-5309	166	7	,	,	PUNCT
ejpam-5309	166	8	b2	b2	NOUN
ejpam-5309	166	9	,	,	PUNCT
ejpam-5309	166	10	c1	c1	PROPN
ejpam-5309	166	11	,	,	PUNCT
ejpam-5309	166	12	c2	c2	PROPN
ejpam-5309	166	13	,	,	PUNCT
ejpam-5309	166	14	d1	d1	PROPN
ejpam-5309	166	15	,	,	PUNCT
ejpam-5309	166	16	d2	d2	PROPN
ejpam-5309	166	17	,	,	PUNCT
ejpam-5309	166	18	e1	e1	PROPN
ejpam-5309	166	19	,	,	PUNCT
ejpam-5309	166	20	e2	e2	PROPN
ejpam-5309	166	21	∈	∈	PROPN
ejpam-5309	166	22	t	t	PROPN
ejpam-5309	166	23	and	and	CCONJ
ejpam-5309	166	24	α	α	NOUN
ejpam-5309	166	25	,	,	PUNCT
ejpam-5309	166	26	β	β	X
ejpam-5309	166	27	,	,	PUNCT
ejpam-5309	166	28	γ	γ	PROPN
ejpam-5309	166	29	,	,	PUNCT
ejpam-5309	166	30	δ	δ	PROPN
ejpam-5309	166	31	∈	∈	PROPN
ejpam-5309	166	32	γ	γ	PROPN
ejpam-5309	166	33	.	.	PUNCT
ejpam-5309	167	1	thus	thus	ADV
ejpam-5309	167	2	,	,	PUNCT
ejpam-5309	167	3	we	we	PRON
ejpam-5309	167	4	have	have	VERB
ejpam-5309	167	5	rµ(a1αb1βc1γd1δe1	rµ(a1αb1βc1γd1δe1	NOUN
ejpam-5309	167	6	,	,	PUNCT
ejpam-5309	167	7	a2αb2βc2γd2δe2	a2αb2βc2γd2δe2	NOUN
ejpam-5309	167	8	)	)	PUNCT
ejpam-5309	167	9	=	=	PUNCT
ejpam-5309	167	10	min{µ(a1αb1βc1γd1δe1	min{µ(a1αb1βc1γd1δe1	NOUN
ejpam-5309	167	11	)	)	PUNCT
ejpam-5309	167	12	,	,	PUNCT
ejpam-5309	167	13	µ(a2αb2βc2γd2δe2	µ(a2αb2βc2γd2δe2	PROPN
ejpam-5309	167	14	)	)	PUNCT
ejpam-5309	167	15	}	}	PUNCT
ejpam-5309	167	16	≥	≥	NOUN
ejpam-5309	167	17	min{min{µ(a1	min{min{µ(a1	NOUN
ejpam-5309	167	18	)	)	PUNCT
ejpam-5309	167	19	,	,	PUNCT
ejpam-5309	167	20	µ(c1	µ(c1	PROPN
ejpam-5309	167	21	)	)	PUNCT
ejpam-5309	167	22	,	,	PUNCT
ejpam-5309	167	23	µ(e1)},min{µ(a2	µ(e1)},min{µ(a2	NOUN
ejpam-5309	167	24	)	)	PUNCT
ejpam-5309	167	25	,	,	PUNCT
ejpam-5309	167	26	µ(c2	µ(c2	ADV
ejpam-5309	167	27	)	)	PUNCT
ejpam-5309	167	28	,	,	PUNCT
ejpam-5309	167	29	µ(e2	µ(e2	NOUN
ejpam-5309	167	30	)	)	PUNCT
ejpam-5309	167	31	}	}	PUNCT
ejpam-5309	167	32	}	}	PUNCT
ejpam-5309	167	33	}	}	PUNCT
ejpam-5309	167	34	=	=	SYM
ejpam-5309	167	35	min{min{µ(a1	min{min{µ(a1	NOUN
ejpam-5309	167	36	)	)	PUNCT
ejpam-5309	167	37	,	,	PUNCT
ejpam-5309	167	38	µ(a2)},min{µ(c1	µ(a2)},min{µ(c1	NOUN
ejpam-5309	167	39	)	)	PUNCT
ejpam-5309	167	40	,	,	PUNCT
ejpam-5309	167	41	µ(c2)},min{µ(e1	µ(c2)},min{µ(e1	NOUN
ejpam-5309	167	42	)	)	PUNCT
ejpam-5309	167	43	,	,	PUNCT
ejpam-5309	167	44	µ(e2	µ(e2	NOUN
ejpam-5309	167	45	)	)	PUNCT
ejpam-5309	167	46	}	}	PUNCT
ejpam-5309	167	47	}	}	PUNCT
ejpam-5309	167	48	=	=	SYM
ejpam-5309	167	49	min{rµ(a1	min{rµ(a1	PROPN
ejpam-5309	167	50	,	,	PUNCT
ejpam-5309	167	51	a2	a2	PROPN
ejpam-5309	167	52	)	)	PUNCT
ejpam-5309	167	53	,	,	PUNCT
ejpam-5309	167	54	rµ(c1	rµ(c1	PROPN
ejpam-5309	167	55	,	,	PUNCT
ejpam-5309	167	56	c2	c2	PROPN
ejpam-5309	167	57	)	)	PUNCT
ejpam-5309	167	58	,	,	PUNCT
ejpam-5309	167	59	rµ(e1	rµ(e1	NOUN
ejpam-5309	167	60	,	,	PUNCT
ejpam-5309	167	61	e2	e2	PROPN
ejpam-5309	167	62	)	)	PUNCT
ejpam-5309	167	63	}	}	PUNCT
ejpam-5309	167	64	.	.	PUNCT
ejpam-5309	168	1	hence	hence	ADV
ejpam-5309	168	2	,	,	PUNCT
ejpam-5309	168	3	rµ	rµ	INTJ
ejpam-5309	168	4	is	be	AUX
ejpam-5309	168	5	a	a	DET
ejpam-5309	168	6	strongest	strong	ADJ
ejpam-5309	168	7	fuzzy	fuzzy	ADJ
ejpam-5309	168	8	bi	bi	ADJ
ejpam-5309	168	9	-	-	ADJ
ejpam-5309	168	10	γ	γ	NOUN
ejpam-5309	168	11	-	-	NOUN
ejpam-5309	168	12	ideal	ideal	NOUN
ejpam-5309	168	13	on	on	ADP
ejpam-5309	168	14	t	t	PROPN
ejpam-5309	168	15	.	.	PUNCT
ejpam-5309	169	1	conversely	conversely	ADV
ejpam-5309	169	2	,	,	PUNCT
ejpam-5309	169	3	assume	assume	VERB
ejpam-5309	169	4	that	that	SCONJ
ejpam-5309	169	5	rµ	rµ	INTJ
ejpam-5309	169	6	is	be	AUX
ejpam-5309	169	7	a	a	DET
ejpam-5309	169	8	strongest	strong	ADJ
ejpam-5309	169	9	fuzzy	fuzzy	ADJ
ejpam-5309	169	10	bi	bi	ADJ
ejpam-5309	169	11	-	-	ADJ
ejpam-5309	169	12	γ	γ	NOUN
ejpam-5309	169	13	-	-	NOUN
ejpam-5309	169	14	ideal	ideal	NOUN
ejpam-5309	169	15	on	on	ADP
ejpam-5309	169	16	t	t	PROPN
ejpam-5309	169	17	.	.	PUNCT
ejpam-5309	170	1	again	again	ADV
ejpam-5309	170	2	,	,	PUNCT
ejpam-5309	170	3	by	by	ADP
ejpam-5309	170	4	theorem	theorem	NOUN
ejpam-5309	170	5	1	1	NUM
ejpam-5309	170	6	,	,	PUNCT
ejpam-5309	170	7	we	we	PRON
ejpam-5309	170	8	have	have	VERB
ejpam-5309	170	9	µ	µ	NOUN
ejpam-5309	170	10	is	be	AUX
ejpam-5309	170	11	a	a	DET
ejpam-5309	170	12	fuzzy	fuzzy	ADJ
ejpam-5309	170	13	ternary	ternary	ADJ
ejpam-5309	170	14	γ	γ	X
ejpam-5309	170	15	-	-	NOUN
ejpam-5309	170	16	subsemigroup	subsemigroup	NOUN
ejpam-5309	170	17	of	of	ADP
ejpam-5309	170	18	t	t	PROPN
ejpam-5309	170	19	.	.	PUNCT
ejpam-5309	171	1	now	now	ADV
ejpam-5309	171	2	,	,	PUNCT
ejpam-5309	171	3	let	let	VERB
ejpam-5309	171	4	a	a	DET
ejpam-5309	171	5	,	,	PUNCT
ejpam-5309	171	6	b	b	NOUN
ejpam-5309	171	7	,	,	PUNCT
ejpam-5309	171	8	c	c	NOUN
ejpam-5309	171	9	,	,	PUNCT
ejpam-5309	171	10	d	d	NOUN
ejpam-5309	171	11	,	,	PUNCT
ejpam-5309	171	12	e	e	PROPN
ejpam-5309	171	13	∈	∈	PROPN
ejpam-5309	171	14	t	t	PROPN
ejpam-5309	171	15	and	and	CCONJ
ejpam-5309	171	16	α	α	NOUN
ejpam-5309	171	17	,	,	PUNCT
ejpam-5309	171	18	β	β	X
ejpam-5309	171	19	,	,	PUNCT
ejpam-5309	171	20	γ	γ	PROPN
ejpam-5309	171	21	,	,	PUNCT
ejpam-5309	171	22	δ	δ	PROPN
ejpam-5309	171	23	∈	∈	PROPN
ejpam-5309	171	24	γ	γ	X
ejpam-5309	171	25	.	.	PUNCT
ejpam-5309	172	1	it	it	PRON
ejpam-5309	172	2	follows	follow	VERB
ejpam-5309	172	3	that	that	PRON
ejpam-5309	172	4	µ(aαbβcγdδe	µ(aαbβcγdδe	ADV
ejpam-5309	172	5	)	)	PUNCT
ejpam-5309	172	6	=	=	SYM
ejpam-5309	172	7	min{µ(aαbβcγdδe	min{µ(aαbβcγdδe	NOUN
ejpam-5309	172	8	)	)	PUNCT
ejpam-5309	172	9	,	,	PUNCT
ejpam-5309	172	10	µ(aαbβcγdδe	µ(aαbβcγdδe	ADV
ejpam-5309	172	11	)	)	PUNCT
ejpam-5309	172	12	}	}	PUNCT
ejpam-5309	173	1	=	=	SYM
ejpam-5309	173	2	rµ(aαbβcγdδe	rµ(aαbβcγdδe	PROPN
ejpam-5309	173	3	,	,	PUNCT
ejpam-5309	173	4	aαbβcγdδe	aαbβcγdδe	ADV
ejpam-5309	173	5	)	)	PUNCT
ejpam-5309	173	6	≥	≥	X
ejpam-5309	173	7	min{rµ(a	min{rµ(a	PROPN
ejpam-5309	173	8	,	,	PUNCT
ejpam-5309	173	9	a	a	PRON
ejpam-5309	173	10	)	)	PUNCT
ejpam-5309	173	11	,	,	PUNCT
ejpam-5309	173	12	rµ(c	rµ(c	X
ejpam-5309	173	13	,	,	PUNCT
ejpam-5309	173	14	c	c	NOUN
ejpam-5309	173	15	)	)	PUNCT
ejpam-5309	173	16	,	,	PUNCT
ejpam-5309	173	17	rµ(e	rµ(e	X
ejpam-5309	173	18	,	,	PUNCT
ejpam-5309	173	19	e	e	NOUN
ejpam-5309	173	20	)	)	PUNCT
ejpam-5309	173	21	}	}	PUNCT
ejpam-5309	173	22	=	=	SYM
ejpam-5309	173	23	min{µ(a	min{µ(a	PROPN
ejpam-5309	173	24	)	)	PUNCT
ejpam-5309	173	25	,	,	PUNCT
ejpam-5309	173	26	µ(c	µ(c	PROPN
ejpam-5309	173	27	)	)	PUNCT
ejpam-5309	173	28	,	,	PUNCT
ejpam-5309	173	29	µ(e	µ(e	PROPN
ejpam-5309	173	30	)	)	PUNCT
ejpam-5309	173	31	}	}	PUNCT
ejpam-5309	173	32	.	.	PUNCT
ejpam-5309	174	1	therefore	therefore	ADV
ejpam-5309	174	2	,	,	PUNCT
ejpam-5309	174	3	µ	µ	X
ejpam-5309	174	4	is	be	AUX
ejpam-5309	174	5	a	a	DET
ejpam-5309	174	6	fuzzy	fuzzy	ADJ
ejpam-5309	174	7	bi	bi	ADJ
ejpam-5309	174	8	-	-	ADJ
ejpam-5309	174	9	γ	γ	NOUN
ejpam-5309	174	10	-	-	NOUN
ejpam-5309	174	11	ideal	ideal	NOUN
ejpam-5309	174	12	of	of	ADP
ejpam-5309	174	13	t	t	PROPN
ejpam-5309	174	14	.	.	PUNCT
ejpam-5309	175	1	in	in	ADP
ejpam-5309	175	2	the	the	DET
ejpam-5309	175	3	following	following	NOUN
ejpam-5309	175	4	,	,	PUNCT
ejpam-5309	175	5	we	we	PRON
ejpam-5309	175	6	will	will	AUX
ejpam-5309	175	7	write	write	VERB
ejpam-5309	175	8	t	t	PROPN
ejpam-5309	175	9	×t	×t	X
ejpam-5309	175	10	instead	instead	ADV
ejpam-5309	175	11	of	of	ADP
ejpam-5309	175	12	a	a	DET
ejpam-5309	175	13	ternary	ternary	ADJ
ejpam-5309	175	14	γ	γ	NOUN
ejpam-5309	175	15	-	-	PUNCT
ejpam-5309	175	16	semigroup	semigroup	ADJ
ejpam-5309	175	17	t	t	NOUN
ejpam-5309	175	18	×t	×t	NOUN
ejpam-5309	175	19	,	,	PUNCT
ejpam-5309	175	20	where	where	SCONJ
ejpam-5309	175	21	t	t	PROPN
ejpam-5309	175	22	is	be	AUX
ejpam-5309	175	23	a	a	DET
ejpam-5309	175	24	ternary	ternary	ADJ
ejpam-5309	175	25	γ	γ	NOUN
ejpam-5309	175	26	-	-	PUNCT
ejpam-5309	175	27	semigroup	semigroup	NOUN
ejpam-5309	175	28	.	.	PUNCT
ejpam-5309	176	1	theorem	theorem	NOUN
ejpam-5309	176	2	4	4	NUM
ejpam-5309	176	3	.	.	PUNCT
ejpam-5309	177	1	let	let	VERB
ejpam-5309	177	2	t	t	PROPN
ejpam-5309	177	3	be	be	AUX
ejpam-5309	177	4	a	a	DET
ejpam-5309	177	5	ternary	ternary	ADJ
ejpam-5309	177	6	γ	γ	NOUN
ejpam-5309	177	7	-	-	PUNCT
ejpam-5309	177	8	semigroup	semigroup	NOUN
ejpam-5309	177	9	,	,	PUNCT
ejpam-5309	177	10	µ	µ	X
ejpam-5309	177	11	be	be	AUX
ejpam-5309	177	12	a	a	DET
ejpam-5309	177	13	fuzzy	fuzzy	ADJ
ejpam-5309	177	14	set	set	NOUN
ejpam-5309	177	15	of	of	ADP
ejpam-5309	177	16	t	t	PROPN
ejpam-5309	177	17	,	,	PUNCT
ejpam-5309	177	18	and	and	CCONJ
ejpam-5309	177	19	rµ	rµ	INTJ
ejpam-5309	177	20	be	be	AUX
ejpam-5309	177	21	a	a	DET
ejpam-5309	177	22	strongest	strong	ADJ
ejpam-5309	177	23	fuzzy	fuzzy	ADJ
ejpam-5309	177	24	relation	relation	NOUN
ejpam-5309	177	25	on	on	ADP
ejpam-5309	177	26	t	t	PROPN
ejpam-5309	177	27	.	.	PUNCT
ejpam-5309	178	1	then	then	ADV
ejpam-5309	178	2	,	,	PUNCT
ejpam-5309	178	3	rµ	rµ	INTJ
ejpam-5309	178	4	is	be	AUX
ejpam-5309	178	5	a	a	DET
ejpam-5309	178	6	strongest	strong	ADJ
ejpam-5309	178	7	fuzzy	fuzzy	ADJ
ejpam-5309	178	8	ternary	ternary	ADJ
ejpam-5309	178	9	γ	γ	NOUN
ejpam-5309	178	10	-	-	NOUN
ejpam-5309	178	11	subsemigroup	subsemigroup	NOUN
ejpam-5309	178	12	on	on	ADP
ejpam-5309	178	13	t	t	PROPN
ejpam-5309	179	1	if	if	SCONJ
ejpam-5309	180	1	and	and	CCONJ
ejpam-5309	180	2	only	only	ADV
ejpam-5309	180	3	if	if	SCONJ
ejpam-5309	180	4	for	for	ADP
ejpam-5309	180	5	every	every	DET
ejpam-5309	180	6	t	t	NOUN
ejpam-5309	180	7	∈	∈	PROPN
ejpam-5309	181	1	[	[	X
ejpam-5309	181	2	0	0	NUM
ejpam-5309	181	3	,	,	PUNCT
ejpam-5309	181	4	1	1	NUM
ejpam-5309	181	5	]	]	PUNCT
ejpam-5309	181	6	,	,	PUNCT
ejpam-5309	181	7	(	(	PUNCT
ejpam-5309	181	8	rµ)t	rµ)t	PROPN
ejpam-5309	181	9	is	be	AUX
ejpam-5309	181	10	a	a	DET
ejpam-5309	181	11	ternary	ternary	ADJ
ejpam-5309	181	12	γ	γ	NOUN
ejpam-5309	181	13	-	-	NOUN
ejpam-5309	181	14	subsemigroup	subsemigroup	NOUN
ejpam-5309	181	15	of	of	ADP
ejpam-5309	181	16	t	t	PROPN
ejpam-5309	181	17	×	×	PROPN
ejpam-5309	181	18	t	t	NOUN
ejpam-5309	181	19	if	if	SCONJ
ejpam-5309	181	20	it	it	PRON
ejpam-5309	181	21	is	be	AUX
ejpam-5309	181	22	nonempty	nonempty	ADJ
ejpam-5309	181	23	.	.	PUNCT
ejpam-5309	182	1	proof	proof	NOUN
ejpam-5309	182	2	.	.	PUNCT
ejpam-5309	183	1	assume	assume	VERB
ejpam-5309	183	2	that	that	SCONJ
ejpam-5309	183	3	rµ	rµ	INTJ
ejpam-5309	183	4	is	be	AUX
ejpam-5309	183	5	a	a	DET
ejpam-5309	183	6	strongest	strong	ADJ
ejpam-5309	183	7	fuzzy	fuzzy	ADJ
ejpam-5309	183	8	ternary	ternary	ADJ
ejpam-5309	183	9	γ	γ	NOUN
ejpam-5309	183	10	-	-	NOUN
ejpam-5309	183	11	subsemigroup	subsemigroup	NOUN
ejpam-5309	183	12	on	on	ADP
ejpam-5309	183	13	t	t	PROPN
ejpam-5309	183	14	.	.	PUNCT
ejpam-5309	184	1	let	let	VERB
ejpam-5309	184	2	t	t	PROPN
ejpam-5309	184	3	∈	∈	PROPN
ejpam-5309	185	1	[	[	X
ejpam-5309	185	2	0	0	NUM
ejpam-5309	185	3	,	,	PUNCT
ejpam-5309	185	4	1	1	NUM
ejpam-5309	185	5	]	]	PUNCT
ejpam-5309	185	6	be	be	AUX
ejpam-5309	185	7	such	such	ADJ
ejpam-5309	185	8	that	that	SCONJ
ejpam-5309	185	9	(	(	PUNCT
ejpam-5309	185	10	rµ)t	rµ)t	PROPN
ejpam-5309	185	11	̸=	̸=	PROPN
ejpam-5309	185	12	∅	∅	NOUN
ejpam-5309	185	13	,	,	PUNCT
ejpam-5309	185	14	and	and	CCONJ
ejpam-5309	185	15	let	let	VERB
ejpam-5309	185	16	(	(	PUNCT
ejpam-5309	185	17	a1	a1	NOUN
ejpam-5309	185	18	,	,	PUNCT
ejpam-5309	185	19	a2	a2	PROPN
ejpam-5309	185	20	)	)	PUNCT
ejpam-5309	185	21	,	,	PUNCT
ejpam-5309	185	22	(	(	PUNCT
ejpam-5309	185	23	b1	b1	NOUN
ejpam-5309	185	24	,	,	PUNCT
ejpam-5309	185	25	b2	b2	NOUN
ejpam-5309	185	26	)	)	PUNCT
ejpam-5309	185	27	,	,	PUNCT
ejpam-5309	185	28	(	(	PUNCT
ejpam-5309	185	29	c1	c1	PROPN
ejpam-5309	185	30	,	,	PUNCT
ejpam-5309	185	31	c2	c2	PROPN
ejpam-5309	185	32	)	)	PUNCT
ejpam-5309	185	33	∈	∈	PROPN
ejpam-5309	185	34	(	(	PUNCT
ejpam-5309	185	35	rµ)t	rµ)t	PROPN
ejpam-5309	185	36	and	and	CCONJ
ejpam-5309	185	37	α	α	PROPN
ejpam-5309	185	38	,	,	PUNCT
ejpam-5309	185	39	β	β	PROPN
ejpam-5309	185	40	∈	∈	PROPN
ejpam-5309	185	41	γ	γ	X
ejpam-5309	185	42	.	.	PROPN
ejpam-5309	185	43	then	then	ADV
ejpam-5309	185	44	rµ(a1	rµ(a1	NOUN
ejpam-5309	185	45	,	,	PUNCT
ejpam-5309	185	46	a2	a2	PROPN
ejpam-5309	185	47	)	)	PUNCT
ejpam-5309	185	48	≥	≥	PROPN
ejpam-5309	185	49	t	t	PROPN
ejpam-5309	185	50	,	,	PUNCT
ejpam-5309	185	51	rµ(b1	rµ(b1	NOUN
ejpam-5309	185	52	,	,	PUNCT
ejpam-5309	185	53	b2	b2	NOUN
ejpam-5309	185	54	)	)	PUNCT
ejpam-5309	185	55	≥	≥	NOUN
ejpam-5309	185	56	t	t	PROPN
ejpam-5309	185	57	,	,	PUNCT
ejpam-5309	185	58	and	and	CCONJ
ejpam-5309	185	59	rµ(c1	rµ(c1	PROPN
ejpam-5309	185	60	,	,	PUNCT
ejpam-5309	185	61	c2	c2	PROPN
ejpam-5309	185	62	)	)	PUNCT
ejpam-5309	185	63	≥	≥	PROPN
ejpam-5309	185	64	t.	t.	NOUN
ejpam-5309	186	1	it	it	PRON
ejpam-5309	186	2	turns	turn	VERB
ejpam-5309	186	3	out	out	ADP
ejpam-5309	186	4	that	that	SCONJ
ejpam-5309	186	5	w.	w.	PROPN
ejpam-5309	186	6	nakkhasen	nakkhasen	PROPN
ejpam-5309	186	7	et	et	PROPN
ejpam-5309	186	8	al	al	PROPN
ejpam-5309	186	9	.	.	PUNCT
ejpam-5309	186	10	/	/	SYM
ejpam-5309	186	11	eur	eur	PROPN
ejpam-5309	186	12	.	.	PUNCT
ejpam-5309	187	1	j.	j.	PROPN
ejpam-5309	187	2	pure	pure	PROPN
ejpam-5309	187	3	appl	appl	PROPN
ejpam-5309	187	4	.	.	PROPN
ejpam-5309	187	5	math	math	PROPN
ejpam-5309	187	6	,	,	PUNCT
ejpam-5309	187	7	17	17	NUM
ejpam-5309	187	8	(	(	PUNCT
ejpam-5309	187	9	3	3	NUM
ejpam-5309	187	10	)	)	PUNCT
ejpam-5309	187	11	(	(	PUNCT
ejpam-5309	187	12	2024	2024	NUM
ejpam-5309	187	13	)	)	PUNCT
ejpam-5309	187	14	,	,	PUNCT
ejpam-5309	187	15	1417	1417	NUM
ejpam-5309	187	16	-	-	SYM
ejpam-5309	187	17	1428	1428	NUM
ejpam-5309	187	18	1424	1424	NUM
ejpam-5309	187	19	rµ(a1αb1βc1	rµ(a1αb1βc1	NOUN
ejpam-5309	187	20	,	,	PUNCT
ejpam-5309	187	21	a2αb2βc2	a2αb2βc2	X
ejpam-5309	187	22	)	)	PUNCT
ejpam-5309	187	23	≥	≥	PROPN
ejpam-5309	187	24	min{rµ(a1	min{rµ(a1	PROPN
ejpam-5309	187	25	,	,	PUNCT
ejpam-5309	187	26	a2	a2	PROPN
ejpam-5309	187	27	)	)	PUNCT
ejpam-5309	187	28	,	,	PUNCT
ejpam-5309	187	29	rµ(b1	rµ(b1	NOUN
ejpam-5309	187	30	,	,	PUNCT
ejpam-5309	187	31	b2	b2	NOUN
ejpam-5309	187	32	)	)	PUNCT
ejpam-5309	187	33	,	,	PUNCT
ejpam-5309	187	34	rµ(c1	rµ(c1	PROPN
ejpam-5309	187	35	,	,	PUNCT
ejpam-5309	187	36	c2	c2	PROPN
ejpam-5309	187	37	)	)	PUNCT
ejpam-5309	187	38	}	}	PUNCT
ejpam-5309	187	39	≥	≥	NOUN
ejpam-5309	187	40	t.	t.	NOUN
ejpam-5309	188	1	this	this	PRON
ejpam-5309	188	2	means	mean	VERB
ejpam-5309	188	3	that	that	SCONJ
ejpam-5309	188	4	(	(	PUNCT
ejpam-5309	188	5	a1	a1	NOUN
ejpam-5309	188	6	,	,	PUNCT
ejpam-5309	188	7	a2)α(b1	a2)α(b1	NOUN
ejpam-5309	188	8	,	,	PUNCT
ejpam-5309	188	9	b2)β(c1	b2)β(c1	PROPN
ejpam-5309	188	10	,	,	PUNCT
ejpam-5309	188	11	c2	c2	PROPN
ejpam-5309	188	12	)	)	PUNCT
ejpam-5309	188	13	=	=	PRON
ejpam-5309	189	1	(	(	PUNCT
ejpam-5309	189	2	a1αb1βc1	a1αb1βc1	NOUN
ejpam-5309	189	3	,	,	PUNCT
ejpam-5309	189	4	a2αb2βc2	a2αb2βc2	NOUN
ejpam-5309	189	5	)	)	PUNCT
ejpam-5309	189	6	∈	∈	PROPN
ejpam-5309	189	7	(	(	PUNCT
ejpam-5309	189	8	rµ)t	rµ)t	PROPN
ejpam-5309	189	9	.	.	PUNCT
ejpam-5309	190	1	so	so	ADV
ejpam-5309	190	2	,	,	PUNCT
ejpam-5309	190	3	(	(	PUNCT
ejpam-5309	190	4	rµ)tγ(rµ)tγ(rµ)t	rµ)tγ(rµ)tγ(rµ)t	NOUN
ejpam-5309	190	5	⊆	⊆	NUM
ejpam-5309	190	6	(	(	PUNCT
ejpam-5309	190	7	rµ)t	rµ)t	NOUN
ejpam-5309	190	8	.	.	PUNCT
ejpam-5309	191	1	hence	hence	ADV
ejpam-5309	191	2	,	,	PUNCT
ejpam-5309	191	3	(	(	PUNCT
ejpam-5309	191	4	rµ)t	rµ)t	PROPN
ejpam-5309	191	5	is	be	AUX
ejpam-5309	191	6	a	a	DET
ejpam-5309	191	7	ternary	ternary	ADJ
ejpam-5309	191	8	γ	γ	NOUN
ejpam-5309	191	9	-	-	NOUN
ejpam-5309	191	10	subsemigroup	subsemigroup	NOUN
ejpam-5309	191	11	of	of	ADP
ejpam-5309	191	12	t	t	PROPN
ejpam-5309	191	13	×	×	PROPN
ejpam-5309	191	14	t	t	PROPN
ejpam-5309	191	15	.	.	PUNCT
ejpam-5309	192	1	conversely	conversely	ADV
ejpam-5309	192	2	,	,	PUNCT
ejpam-5309	192	3	for	for	ADP
ejpam-5309	192	4	any	any	DET
ejpam-5309	192	5	t	t	NOUN
ejpam-5309	192	6	∈	∈	PROPN
ejpam-5309	193	1	[	[	X
ejpam-5309	193	2	0	0	NUM
ejpam-5309	193	3	,	,	PUNCT
ejpam-5309	193	4	1	1	NUM
ejpam-5309	193	5	]	]	PUNCT
ejpam-5309	193	6	,	,	PUNCT
ejpam-5309	193	7	(	(	PUNCT
ejpam-5309	193	8	rµ)t	rµ)t	PROPN
ejpam-5309	193	9	̸=	̸=	PROPN
ejpam-5309	193	10	∅	∅	NOUN
ejpam-5309	193	11	is	be	AUX
ejpam-5309	193	12	a	a	DET
ejpam-5309	193	13	ternary	ternary	ADJ
ejpam-5309	193	14	γ	γ	NOUN
ejpam-5309	193	15	-	-	NOUN
ejpam-5309	193	16	subsemigroup	subsemigroup	NOUN
ejpam-5309	193	17	of	of	ADP
ejpam-5309	193	18	t	t	PROPN
ejpam-5309	193	19	×	×	PROPN
ejpam-5309	193	20	t	t	PROPN
ejpam-5309	193	21	.	.	PUNCT
ejpam-5309	194	1	let	let	VERB
ejpam-5309	194	2	a1	a1	NOUN
ejpam-5309	194	3	,	,	PUNCT
ejpam-5309	194	4	a2	a2	PROPN
ejpam-5309	194	5	,	,	PUNCT
ejpam-5309	194	6	b1	b1	NOUN
ejpam-5309	194	7	,	,	PUNCT
ejpam-5309	194	8	b2	b2	NOUN
ejpam-5309	194	9	,	,	PUNCT
ejpam-5309	194	10	c1	c1	NOUN
ejpam-5309	194	11	,	,	PUNCT
ejpam-5309	194	12	c2	c2	PROPN
ejpam-5309	194	13	∈	∈	PROPN
ejpam-5309	194	14	t	t	PROPN
ejpam-5309	194	15	and	and	CCONJ
ejpam-5309	194	16	α	α	NOUN
ejpam-5309	194	17	,	,	PUNCT
ejpam-5309	194	18	β	β	PROPN
ejpam-5309	194	19	∈	∈	PROPN
ejpam-5309	194	20	γ	γ	X
ejpam-5309	194	21	.	.	PROPN
ejpam-5309	194	22	choose	choose	VERB
ejpam-5309	194	23	rµ(a1	rµ(a1	NOUN
ejpam-5309	194	24	,	,	PUNCT
ejpam-5309	194	25	a2	a2	NOUN
ejpam-5309	194	26	)	)	PUNCT
ejpam-5309	194	27	=	=	SYM
ejpam-5309	194	28	t1	t1	NOUN
ejpam-5309	194	29	,	,	PUNCT
ejpam-5309	194	30	rµ(b1	rµ(b1	NOUN
ejpam-5309	194	31	,	,	PUNCT
ejpam-5309	194	32	b2	b2	NOUN
ejpam-5309	194	33	)	)	PUNCT
ejpam-5309	194	34	=	=	SYM
ejpam-5309	194	35	t2	t2	NOUN
ejpam-5309	194	36	,	,	PUNCT
ejpam-5309	194	37	and	and	CCONJ
ejpam-5309	194	38	rµ(c1	rµ(c1	PROPN
ejpam-5309	194	39	,	,	PUNCT
ejpam-5309	194	40	c2	c2	PROPN
ejpam-5309	194	41	)	)	PUNCT
ejpam-5309	195	1	=	=	SYM
ejpam-5309	195	2	t3	t3	PROPN
ejpam-5309	195	3	,	,	PUNCT
ejpam-5309	195	4	for	for	ADP
ejpam-5309	195	5	some	some	DET
ejpam-5309	195	6	t1	t1	NOUN
ejpam-5309	195	7	,	,	PUNCT
ejpam-5309	195	8	t2	t2	NOUN
ejpam-5309	195	9	,	,	PUNCT
ejpam-5309	195	10	t3	t3	PROPN
ejpam-5309	195	11	∈	∈	PROPN
ejpam-5309	196	1	[	[	X
ejpam-5309	196	2	0	0	NUM
ejpam-5309	196	3	,	,	PUNCT
ejpam-5309	196	4	1	1	NUM
ejpam-5309	196	5	]	]	PUNCT
ejpam-5309	196	6	.	.	PUNCT
ejpam-5309	197	1	let	let	VERB
ejpam-5309	197	2	t	t	NOUN
ejpam-5309	197	3	=	=	PUNCT
ejpam-5309	197	4	min{t1	min{t1	NOUN
ejpam-5309	197	5	,	,	PUNCT
ejpam-5309	197	6	t2	t2	NOUN
ejpam-5309	197	7	,	,	PUNCT
ejpam-5309	197	8	t3	t3	PROPN
ejpam-5309	197	9	}	}	PUNCT
ejpam-5309	197	10	.	.	PUNCT
ejpam-5309	198	1	then	then	ADV
ejpam-5309	198	2	,	,	PUNCT
ejpam-5309	198	3	we	we	PRON
ejpam-5309	198	4	have	have	VERB
ejpam-5309	198	5	(	(	PUNCT
ejpam-5309	198	6	a1	a1	NOUN
ejpam-5309	198	7	,	,	PUNCT
ejpam-5309	198	8	a2	a2	PROPN
ejpam-5309	198	9	)	)	PUNCT
ejpam-5309	198	10	,	,	PUNCT
ejpam-5309	198	11	(	(	PUNCT
ejpam-5309	198	12	b1	b1	NOUN
ejpam-5309	198	13	,	,	PUNCT
ejpam-5309	198	14	b2	b2	NOUN
ejpam-5309	198	15	)	)	PUNCT
ejpam-5309	198	16	,	,	PUNCT
ejpam-5309	198	17	(	(	PUNCT
ejpam-5309	198	18	c1	c1	PROPN
ejpam-5309	198	19	,	,	PUNCT
ejpam-5309	198	20	c2	c2	PROPN
ejpam-5309	198	21	)	)	PUNCT
ejpam-5309	198	22	∈	∈	PROPN
ejpam-5309	198	23	(	(	PUNCT
ejpam-5309	198	24	rµ)t	rµ)t	PROPN
ejpam-5309	198	25	.	.	PUNCT
ejpam-5309	199	1	by	by	ADP
ejpam-5309	199	2	the	the	DET
ejpam-5309	199	3	hypothesis	hypothesis	NOUN
ejpam-5309	199	4	,	,	PUNCT
ejpam-5309	199	5	we	we	PRON
ejpam-5309	199	6	get	get	VERB
ejpam-5309	199	7	(	(	PUNCT
ejpam-5309	199	8	a1	a1	NOUN
ejpam-5309	199	9	,	,	PUNCT
ejpam-5309	199	10	a2)α(b1	a2)α(b1	NOUN
ejpam-5309	199	11	,	,	PUNCT
ejpam-5309	199	12	b2)β(c1	b2)β(c1	PROPN
ejpam-5309	199	13	,	,	PUNCT
ejpam-5309	199	14	c2	c2	PROPN
ejpam-5309	199	15	)	)	PUNCT
ejpam-5309	199	16	∈	∈	PROPN
ejpam-5309	199	17	(	(	PUNCT
ejpam-5309	199	18	rµ)tγ(rµ)tγ(rµ)t	rµ)tγ(rµ)tγ(rµ)t	NOUN
ejpam-5309	199	19	⊆	⊆	NUM
ejpam-5309	199	20	(	(	PUNCT
ejpam-5309	199	21	rµ)t	rµ)t	PROPN
ejpam-5309	199	22	.	.	PUNCT
ejpam-5309	200	1	thus	thus	ADV
ejpam-5309	200	2	,	,	PUNCT
ejpam-5309	200	3	(	(	PUNCT
ejpam-5309	200	4	a1αb1βc1	a1αb1βc1	NOUN
ejpam-5309	200	5	,	,	PUNCT
ejpam-5309	200	6	a2αb2βc2	a2αb2βc2	NOUN
ejpam-5309	200	7	)	)	PUNCT
ejpam-5309	200	8	=	=	SYM
ejpam-5309	200	9	(	(	PUNCT
ejpam-5309	200	10	a1	a1	PROPN
ejpam-5309	200	11	,	,	PUNCT
ejpam-5309	200	12	a2)α(b1	a2)α(b1	NOUN
ejpam-5309	200	13	,	,	PUNCT
ejpam-5309	200	14	b2)β(c1	b2)β(c1	PROPN
ejpam-5309	200	15	,	,	PUNCT
ejpam-5309	200	16	c2	c2	PROPN
ejpam-5309	200	17	)	)	PUNCT
ejpam-5309	200	18	∈	∈	PROPN
ejpam-5309	200	19	(	(	PUNCT
ejpam-5309	200	20	rµ)t	rµ)t	PROPN
ejpam-5309	200	21	.	.	PUNCT
ejpam-5309	201	1	this	this	PRON
ejpam-5309	201	2	implies	imply	VERB
ejpam-5309	201	3	that	that	SCONJ
ejpam-5309	201	4	rµ(a1αb1βc1	rµ(a1αb1βc1	NOUN
ejpam-5309	201	5	,	,	PUNCT
ejpam-5309	201	6	a2αb2βc2	a2αb2βc2	NUM
ejpam-5309	201	7	)	)	PUNCT
ejpam-5309	201	8	≥	≥	NOUN
ejpam-5309	201	9	t	t	NOUN
ejpam-5309	201	10	=	=	PUNCT
ejpam-5309	201	11	min{t1	min{t1	NOUN
ejpam-5309	201	12	,	,	PUNCT
ejpam-5309	201	13	t2	t2	NOUN
ejpam-5309	201	14	,	,	PUNCT
ejpam-5309	201	15	t3	t3	PROPN
ejpam-5309	201	16	}	}	PUNCT
ejpam-5309	201	17	=	=	SYM
ejpam-5309	201	18	min{rµ(a1	min{rµ(a1	PROPN
ejpam-5309	201	19	,	,	PUNCT
ejpam-5309	201	20	a2	a2	PROPN
ejpam-5309	201	21	)	)	PUNCT
ejpam-5309	201	22	,	,	PUNCT
ejpam-5309	201	23	rµ(b1	rµ(b1	NOUN
ejpam-5309	201	24	,	,	PUNCT
ejpam-5309	201	25	b2	b2	NOUN
ejpam-5309	201	26	)	)	PUNCT
ejpam-5309	201	27	,	,	PUNCT
ejpam-5309	201	28	rµ(c1	rµ(c1	PROPN
ejpam-5309	201	29	,	,	PUNCT
ejpam-5309	201	30	c2	c2	PROPN
ejpam-5309	201	31	)	)	PUNCT
ejpam-5309	201	32	}	}	PUNCT
ejpam-5309	201	33	.	.	PUNCT
ejpam-5309	202	1	therefore	therefore	ADV
ejpam-5309	202	2	,	,	PUNCT
ejpam-5309	202	3	rµ	rµ	INTJ
ejpam-5309	202	4	is	be	AUX
ejpam-5309	202	5	a	a	DET
ejpam-5309	202	6	strongest	strong	ADJ
ejpam-5309	202	7	fuzzy	fuzzy	ADJ
ejpam-5309	202	8	ternary	ternary	ADJ
ejpam-5309	202	9	γ	γ	NOUN
ejpam-5309	202	10	-	-	NOUN
ejpam-5309	202	11	subsemigroup	subsemigroup	NOUN
ejpam-5309	202	12	on	on	ADP
ejpam-5309	202	13	t	t	PROPN
ejpam-5309	202	14	.	.	PUNCT
ejpam-5309	203	1	theorem	theorem	ADJ
ejpam-5309	203	2	5	5	NUM
ejpam-5309	203	3	.	.	PUNCT
ejpam-5309	204	1	let	let	VERB
ejpam-5309	204	2	t	t	PROPN
ejpam-5309	204	3	be	be	AUX
ejpam-5309	204	4	a	a	DET
ejpam-5309	204	5	ternary	ternary	ADJ
ejpam-5309	204	6	γ	γ	NOUN
ejpam-5309	204	7	-	-	PUNCT
ejpam-5309	204	8	semigroup	semigroup	NOUN
ejpam-5309	204	9	,	,	PUNCT
ejpam-5309	204	10	µ	µ	X
ejpam-5309	204	11	be	be	AUX
ejpam-5309	204	12	a	a	DET
ejpam-5309	204	13	fuzzy	fuzzy	ADJ
ejpam-5309	204	14	set	set	NOUN
ejpam-5309	204	15	of	of	ADP
ejpam-5309	204	16	t	t	PROPN
ejpam-5309	204	17	,	,	PUNCT
ejpam-5309	204	18	and	and	CCONJ
ejpam-5309	204	19	rµ	rµ	INTJ
ejpam-5309	204	20	be	be	AUX
ejpam-5309	204	21	a	a	DET
ejpam-5309	204	22	strongest	strong	ADJ
ejpam-5309	204	23	fuzzy	fuzzy	ADJ
ejpam-5309	204	24	relation	relation	NOUN
ejpam-5309	204	25	on	on	ADP
ejpam-5309	204	26	t	t	PROPN
ejpam-5309	204	27	.	.	PUNCT
ejpam-5309	205	1	then	then	ADV
ejpam-5309	205	2	the	the	DET
ejpam-5309	205	3	following	follow	VERB
ejpam-5309	205	4	statements	statement	NOUN
ejpam-5309	205	5	hold	hold	VERB
ejpam-5309	205	6	:	:	PUNCT
ejpam-5309	205	7	(	(	PUNCT
ejpam-5309	205	8	i	i	NOUN
ejpam-5309	205	9	)	)	PUNCT
ejpam-5309	205	10	rµ	rµ	VERB
ejpam-5309	205	11	is	be	AUX
ejpam-5309	205	12	a	a	DET
ejpam-5309	205	13	strongest	strong	ADJ
ejpam-5309	205	14	fuzzy	fuzzy	ADJ
ejpam-5309	205	15	left	leave	VERB
ejpam-5309	205	16	γ	γ	NOUN
ejpam-5309	205	17	-	-	NOUN
ejpam-5309	205	18	ideal	ideal	NOUN
ejpam-5309	205	19	on	on	ADP
ejpam-5309	205	20	t	t	PROPN
ejpam-5309	206	1	if	if	SCONJ
ejpam-5309	207	1	and	and	CCONJ
ejpam-5309	207	2	only	only	ADV
ejpam-5309	207	3	if	if	SCONJ
ejpam-5309	207	4	for	for	ADP
ejpam-5309	207	5	any	any	DET
ejpam-5309	207	6	t	t	NOUN
ejpam-5309	207	7	∈	∈	PROPN
ejpam-5309	208	1	[	[	X
ejpam-5309	208	2	0	0	NUM
ejpam-5309	208	3	,	,	PUNCT
ejpam-5309	208	4	1	1	NUM
ejpam-5309	208	5	]	]	PUNCT
ejpam-5309	208	6	,	,	PUNCT
ejpam-5309	208	7	(	(	PUNCT
ejpam-5309	208	8	rµ)t	rµ)t	PROPN
ejpam-5309	208	9	is	be	AUX
ejpam-5309	208	10	a	a	DET
ejpam-5309	208	11	left	left	ADJ
ejpam-5309	208	12	γ	γ	NOUN
ejpam-5309	208	13	-	-	NOUN
ejpam-5309	208	14	ideal	ideal	NOUN
ejpam-5309	208	15	of	of	ADP
ejpam-5309	208	16	t	t	PROPN
ejpam-5309	208	17	×	×	PROPN
ejpam-5309	208	18	t	t	NOUN
ejpam-5309	208	19	if	if	SCONJ
ejpam-5309	208	20	it	it	PRON
ejpam-5309	208	21	is	be	AUX
ejpam-5309	208	22	nonempty	nonempty	ADJ
ejpam-5309	208	23	;	;	PUNCT
ejpam-5309	208	24	(	(	PUNCT
ejpam-5309	208	25	ii	ii	NOUN
ejpam-5309	208	26	)	)	PUNCT
ejpam-5309	208	27	rµ	rµ	VERB
ejpam-5309	208	28	is	be	AUX
ejpam-5309	208	29	a	a	DET
ejpam-5309	208	30	strongest	strong	ADJ
ejpam-5309	208	31	fuzzy	fuzzy	ADJ
ejpam-5309	208	32	right	right	ADJ
ejpam-5309	208	33	γ	γ	X
ejpam-5309	208	34	-	-	NOUN
ejpam-5309	208	35	ideal	ideal	NOUN
ejpam-5309	208	36	on	on	ADP
ejpam-5309	208	37	t	t	PROPN
ejpam-5309	208	38	if	if	SCONJ
ejpam-5309	209	1	and	and	CCONJ
ejpam-5309	209	2	only	only	ADV
ejpam-5309	209	3	if	if	SCONJ
ejpam-5309	209	4	for	for	ADP
ejpam-5309	209	5	any	any	DET
ejpam-5309	209	6	t	t	NOUN
ejpam-5309	209	7	∈	∈	PROPN
ejpam-5309	210	1	[	[	X
ejpam-5309	210	2	0	0	NUM
ejpam-5309	210	3	,	,	PUNCT
ejpam-5309	210	4	1	1	NUM
ejpam-5309	210	5	]	]	PUNCT
ejpam-5309	210	6	,	,	PUNCT
ejpam-5309	210	7	(	(	PUNCT
ejpam-5309	210	8	rµ)t	rµ)t	PROPN
ejpam-5309	210	9	is	be	AUX
ejpam-5309	210	10	a	a	DET
ejpam-5309	210	11	right	right	ADJ
ejpam-5309	210	12	γ	γ	NOUN
ejpam-5309	210	13	-	-	NOUN
ejpam-5309	210	14	ideal	ideal	NOUN
ejpam-5309	210	15	of	of	ADP
ejpam-5309	210	16	t	t	PROPN
ejpam-5309	210	17	×	×	PROPN
ejpam-5309	210	18	t	t	NOUN
ejpam-5309	210	19	if	if	SCONJ
ejpam-5309	210	20	it	it	PRON
ejpam-5309	210	21	is	be	AUX
ejpam-5309	210	22	nonempty	nonempty	ADJ
ejpam-5309	210	23	;	;	PUNCT
ejpam-5309	210	24	(	(	PUNCT
ejpam-5309	210	25	iii	iii	X
ejpam-5309	210	26	)	)	PUNCT
ejpam-5309	210	27	rµ	rµ	NOUN
ejpam-5309	210	28	is	be	AUX
ejpam-5309	210	29	a	a	DET
ejpam-5309	210	30	strongest	strong	ADJ
ejpam-5309	210	31	fuzzy	fuzzy	ADJ
ejpam-5309	210	32	lateral	lateral	ADJ
ejpam-5309	210	33	γ	γ	NOUN
ejpam-5309	210	34	-	-	NOUN
ejpam-5309	210	35	ideal	ideal	NOUN
ejpam-5309	210	36	on	on	ADP
ejpam-5309	210	37	t	t	PROPN
ejpam-5309	210	38	if	if	SCONJ
ejpam-5309	211	1	and	and	CCONJ
ejpam-5309	211	2	only	only	ADV
ejpam-5309	211	3	if	if	SCONJ
ejpam-5309	211	4	for	for	ADP
ejpam-5309	211	5	any	any	DET
ejpam-5309	211	6	t	t	NOUN
ejpam-5309	211	7	∈	∈	PROPN
ejpam-5309	212	1	[	[	X
ejpam-5309	212	2	0	0	NUM
ejpam-5309	212	3	,	,	PUNCT
ejpam-5309	212	4	1	1	NUM
ejpam-5309	212	5	]	]	PUNCT
ejpam-5309	212	6	,	,	PUNCT
ejpam-5309	212	7	(	(	PUNCT
ejpam-5309	212	8	rµ)t	rµ)t	PROPN
ejpam-5309	212	9	is	be	AUX
ejpam-5309	212	10	a	a	DET
ejpam-5309	212	11	lateral	lateral	ADJ
ejpam-5309	212	12	γ	γ	NOUN
ejpam-5309	212	13	-	-	NOUN
ejpam-5309	212	14	ideal	ideal	NOUN
ejpam-5309	212	15	of	of	ADP
ejpam-5309	212	16	t	t	PROPN
ejpam-5309	212	17	×	×	PROPN
ejpam-5309	212	18	t	t	NOUN
ejpam-5309	212	19	if	if	SCONJ
ejpam-5309	212	20	it	it	PRON
ejpam-5309	212	21	is	be	AUX
ejpam-5309	212	22	nonempty	nonempty	ADJ
ejpam-5309	212	23	;	;	PUNCT
ejpam-5309	212	24	(	(	PUNCT
ejpam-5309	212	25	iv	iv	X
ejpam-5309	212	26	)	)	PUNCT
ejpam-5309	212	27	rµ	rµ	NOUN
ejpam-5309	212	28	is	be	AUX
ejpam-5309	212	29	a	a	DET
ejpam-5309	212	30	strongest	strong	ADJ
ejpam-5309	212	31	fuzzy	fuzzy	ADJ
ejpam-5309	212	32	γ	γ	NOUN
ejpam-5309	212	33	-	-	NOUN
ejpam-5309	212	34	ideal	ideal	NOUN
ejpam-5309	212	35	on	on	ADP
ejpam-5309	212	36	t	t	PROPN
ejpam-5309	212	37	if	if	SCONJ
ejpam-5309	213	1	and	and	CCONJ
ejpam-5309	213	2	only	only	ADV
ejpam-5309	213	3	if	if	SCONJ
ejpam-5309	213	4	for	for	ADP
ejpam-5309	213	5	any	any	DET
ejpam-5309	213	6	t	t	NOUN
ejpam-5309	213	7	∈	∈	PROPN
ejpam-5309	214	1	[	[	X
ejpam-5309	214	2	0	0	NUM
ejpam-5309	214	3	,	,	PUNCT
ejpam-5309	214	4	1	1	NUM
ejpam-5309	214	5	]	]	PUNCT
ejpam-5309	214	6	,	,	PUNCT
ejpam-5309	214	7	(	(	PUNCT
ejpam-5309	214	8	rµ)t	rµ)t	PROPN
ejpam-5309	214	9	is	be	AUX
ejpam-5309	214	10	a	a	DET
ejpam-5309	214	11	γ	γ	NOUN
ejpam-5309	214	12	-	-	NOUN
ejpam-5309	214	13	ideal	ideal	NOUN
ejpam-5309	214	14	of	of	ADP
ejpam-5309	214	15	t	t	PROPN
ejpam-5309	214	16	×	×	PROPN
ejpam-5309	214	17	t	t	NOUN
ejpam-5309	214	18	if	if	SCONJ
ejpam-5309	214	19	it	it	PRON
ejpam-5309	214	20	is	be	AUX
ejpam-5309	214	21	nonempty	nonempty	ADJ
ejpam-5309	214	22	.	.	PUNCT
ejpam-5309	215	1	proof	proof	NOUN
ejpam-5309	215	2	.	.	PUNCT
ejpam-5309	216	1	(	(	PUNCT
ejpam-5309	216	2	i	i	NOUN
ejpam-5309	216	3	)	)	PUNCT
ejpam-5309	216	4	assume	assume	VERB
ejpam-5309	216	5	that	that	SCONJ
ejpam-5309	216	6	rµ	rµ	INTJ
ejpam-5309	216	7	is	be	AUX
ejpam-5309	216	8	a	a	DET
ejpam-5309	216	9	strongest	strong	ADJ
ejpam-5309	216	10	fuzzy	fuzzy	ADJ
ejpam-5309	216	11	left	leave	VERB
ejpam-5309	216	12	γ	γ	NOUN
ejpam-5309	216	13	-	-	NOUN
ejpam-5309	216	14	ideal	ideal	NOUN
ejpam-5309	216	15	on	on	ADP
ejpam-5309	216	16	t	t	PROPN
ejpam-5309	216	17	.	.	PUNCT
ejpam-5309	217	1	let	let	VERB
ejpam-5309	217	2	(	(	PUNCT
ejpam-5309	217	3	a1	a1	NOUN
ejpam-5309	217	4	,	,	PUNCT
ejpam-5309	217	5	a2	a2	PROPN
ejpam-5309	217	6	)	)	PUNCT
ejpam-5309	217	7	,	,	PUNCT
ejpam-5309	217	8	(	(	PUNCT
ejpam-5309	217	9	b1	b1	NOUN
ejpam-5309	217	10	,	,	PUNCT
ejpam-5309	217	11	b2	b2	NOUN
ejpam-5309	217	12	)	)	PUNCT
ejpam-5309	217	13	∈	∈	PROPN
ejpam-5309	217	14	t	t	X
ejpam-5309	217	15	×	×	PROPN
ejpam-5309	217	16	t	t	PROPN
ejpam-5309	217	17	and	and	CCONJ
ejpam-5309	217	18	(	(	PUNCT
ejpam-5309	217	19	c1	c1	PROPN
ejpam-5309	217	20	,	,	PUNCT
ejpam-5309	217	21	c2	c2	PROPN
ejpam-5309	217	22	)	)	PUNCT
ejpam-5309	217	23	∈	∈	PROPN
ejpam-5309	217	24	(	(	PUNCT
ejpam-5309	217	25	rµ)t	rµ)t	PROPN
ejpam-5309	217	26	,	,	PUNCT
ejpam-5309	217	27	and	and	CCONJ
ejpam-5309	217	28	α	α	NOUN
ejpam-5309	217	29	,	,	PUNCT
ejpam-5309	217	30	β	β	PROPN
ejpam-5309	217	31	∈	∈	PROPN
ejpam-5309	217	32	γ	γ	X
ejpam-5309	217	33	.	.	PROPN
ejpam-5309	218	1	then	then	ADV
ejpam-5309	218	2	rµ(a1αb1βc1	rµ(a1αb1βc1	NOUN
ejpam-5309	218	3	,	,	PUNCT
ejpam-5309	218	4	a2αb2βc2	a2αb2βc2	NUM
ejpam-5309	218	5	)	)	PUNCT
ejpam-5309	218	6	≥	≥	PROPN
ejpam-5309	218	7	rµ(c1	rµ(c1	PROPN
ejpam-5309	218	8	,	,	PUNCT
ejpam-5309	218	9	c2	c2	PROPN
ejpam-5309	218	10	)	)	PUNCT
ejpam-5309	218	11	≥	≥	PROPN
ejpam-5309	218	12	t.	t.	NOUN
ejpam-5309	218	13	we	we	PRON
ejpam-5309	218	14	obtain	obtain	VERB
ejpam-5309	218	15	that	that	PRON
ejpam-5309	218	16	(	(	PUNCT
ejpam-5309	218	17	a1	a1	NOUN
ejpam-5309	218	18	,	,	PUNCT
ejpam-5309	218	19	a2)α(b1	a2)α(b1	NOUN
ejpam-5309	218	20	,	,	PUNCT
ejpam-5309	218	21	b2)β(c1	b2)β(c1	PROPN
ejpam-5309	218	22	,	,	PUNCT
ejpam-5309	218	23	c2	c2	PROPN
ejpam-5309	218	24	)	)	PUNCT
ejpam-5309	219	1	=	=	PRON
ejpam-5309	220	1	(	(	PUNCT
ejpam-5309	220	2	a1αb1βc1	a1αb1βc1	NOUN
ejpam-5309	220	3	,	,	PUNCT
ejpam-5309	220	4	a2αb2βc2	a2αb2βc2	NOUN
ejpam-5309	220	5	)	)	PUNCT
ejpam-5309	220	6	∈	∈	PROPN
ejpam-5309	220	7	(	(	PUNCT
ejpam-5309	220	8	rµ)t	rµ)t	PROPN
ejpam-5309	220	9	;	;	PUNCT
ejpam-5309	220	10	that	that	PRON
ejpam-5309	220	11	is	is	ADV
ejpam-5309	220	12	,	,	PUNCT
ejpam-5309	220	13	(	(	PUNCT
ejpam-5309	220	14	t	t	PROPN
ejpam-5309	220	15	×	×	PROPN
ejpam-5309	220	16	t	t	PROPN
ejpam-5309	220	17	)	)	PUNCT
ejpam-5309	221	1	γ(t	γ(t	PROPN
ejpam-5309	221	2	×	×	PROPN
ejpam-5309	221	3	t	t	NOUN
ejpam-5309	221	4	)	)	PUNCT
ejpam-5309	221	5	γ(rµ)t	γ(rµ)t	NOUN
ejpam-5309	221	6	⊆	⊆	NUM
ejpam-5309	221	7	(	(	PUNCT
ejpam-5309	221	8	rµ)t	rµ)t	PROPN
ejpam-5309	221	9	.	.	PUNCT
ejpam-5309	222	1	this	this	PRON
ejpam-5309	222	2	shows	show	VERB
ejpam-5309	222	3	that	that	SCONJ
ejpam-5309	222	4	(	(	PUNCT
ejpam-5309	222	5	rµ)t	rµ)t	PROPN
ejpam-5309	222	6	is	be	AUX
ejpam-5309	222	7	a	a	DET
ejpam-5309	222	8	left	left	ADJ
ejpam-5309	222	9	γ	γ	NOUN
ejpam-5309	222	10	-	-	NOUN
ejpam-5309	222	11	ideal	ideal	NOUN
ejpam-5309	222	12	of	of	ADP
ejpam-5309	222	13	t	t	PROPN
ejpam-5309	222	14	×	×	PROPN
ejpam-5309	222	15	t	t	PROPN
ejpam-5309	222	16	.	.	PUNCT
ejpam-5309	223	1	w.	w.	PROPN
ejpam-5309	223	2	nakkhasen	nakkhasen	PROPN
ejpam-5309	223	3	et	et	PROPN
ejpam-5309	223	4	al	al	PROPN
ejpam-5309	223	5	.	.	PUNCT
ejpam-5309	223	6	/	/	SYM
ejpam-5309	223	7	eur	eur	PROPN
ejpam-5309	223	8	.	.	PUNCT
ejpam-5309	224	1	j.	j.	PROPN
ejpam-5309	224	2	pure	pure	PROPN
ejpam-5309	224	3	appl	appl	PROPN
ejpam-5309	224	4	.	.	PROPN
ejpam-5309	224	5	math	math	PROPN
ejpam-5309	224	6	,	,	PUNCT
ejpam-5309	224	7	17	17	NUM
ejpam-5309	224	8	(	(	PUNCT
ejpam-5309	224	9	3	3	NUM
ejpam-5309	224	10	)	)	PUNCT
ejpam-5309	224	11	(	(	PUNCT
ejpam-5309	224	12	2024	2024	NUM
ejpam-5309	224	13	)	)	PUNCT
ejpam-5309	224	14	,	,	PUNCT
ejpam-5309	224	15	1417	1417	NUM
ejpam-5309	224	16	-	-	SYM
ejpam-5309	224	17	1428	1428	NUM
ejpam-5309	224	18	1425	1425	NUM
ejpam-5309	224	19	conversely	conversely	ADV
ejpam-5309	224	20	,	,	PUNCT
ejpam-5309	224	21	assume	assume	VERB
ejpam-5309	224	22	that	that	SCONJ
ejpam-5309	224	23	for	for	ADP
ejpam-5309	224	24	any	any	DET
ejpam-5309	224	25	t	t	NOUN
ejpam-5309	224	26	∈	∈	PROPN
ejpam-5309	225	1	[	[	X
ejpam-5309	225	2	0	0	NUM
ejpam-5309	225	3	,	,	PUNCT
ejpam-5309	225	4	1	1	NUM
ejpam-5309	225	5	]	]	PUNCT
ejpam-5309	225	6	,	,	PUNCT
ejpam-5309	225	7	(	(	PUNCT
ejpam-5309	225	8	rµ)t	rµ)t	PROPN
ejpam-5309	225	9	̸=	̸=	PROPN
ejpam-5309	225	10	∅	∅	NOUN
ejpam-5309	225	11	is	be	AUX
ejpam-5309	225	12	a	a	DET
ejpam-5309	225	13	left	left	ADJ
ejpam-5309	225	14	γ	γ	NOUN
ejpam-5309	225	15	-	-	NOUN
ejpam-5309	225	16	ideal	ideal	NOUN
ejpam-5309	225	17	of	of	ADP
ejpam-5309	225	18	t	t	PROPN
ejpam-5309	225	19	×	×	PROPN
ejpam-5309	225	20	t	t	PROPN
ejpam-5309	225	21	.	.	PUNCT
ejpam-5309	226	1	let	let	VERB
ejpam-5309	226	2	a1	a1	NOUN
ejpam-5309	226	3	,	,	PUNCT
ejpam-5309	226	4	a2	a2	PROPN
ejpam-5309	226	5	,	,	PUNCT
ejpam-5309	226	6	b1	b1	NOUN
ejpam-5309	226	7	,	,	PUNCT
ejpam-5309	226	8	b2	b2	NOUN
ejpam-5309	226	9	,	,	PUNCT
ejpam-5309	226	10	c1	c1	NOUN
ejpam-5309	226	11	,	,	PUNCT
ejpam-5309	226	12	c2	c2	PROPN
ejpam-5309	226	13	∈	∈	PROPN
ejpam-5309	226	14	t	t	PROPN
ejpam-5309	226	15	and	and	CCONJ
ejpam-5309	226	16	α	α	NOUN
ejpam-5309	226	17	,	,	PUNCT
ejpam-5309	226	18	β	β	PROPN
ejpam-5309	226	19	∈	∈	PROPN
ejpam-5309	226	20	γ	γ	PROPN
ejpam-5309	226	21	.	.	PROPN
ejpam-5309	226	22	take	take	PROPN
ejpam-5309	226	23	rµ(c1	rµ(c1	PROPN
ejpam-5309	226	24	,	,	PUNCT
ejpam-5309	226	25	c2	c2	PROPN
ejpam-5309	226	26	)	)	PUNCT
ejpam-5309	227	1	=	=	SYM
ejpam-5309	227	2	t	t	PROPN
ejpam-5309	227	3	,	,	PUNCT
ejpam-5309	227	4	for	for	ADP
ejpam-5309	227	5	some	some	DET
ejpam-5309	227	6	t	t	NOUN
ejpam-5309	227	7	∈	∈	PROPN
ejpam-5309	228	1	[	[	X
ejpam-5309	228	2	0	0	NUM
ejpam-5309	228	3	,	,	PUNCT
ejpam-5309	228	4	1	1	NUM
ejpam-5309	228	5	]	]	PUNCT
ejpam-5309	228	6	.	.	PUNCT
ejpam-5309	229	1	it	it	PRON
ejpam-5309	229	2	follows	follow	VERB
ejpam-5309	229	3	that	that	SCONJ
ejpam-5309	229	4	(	(	PUNCT
ejpam-5309	229	5	c1	c1	PROPN
ejpam-5309	229	6	,	,	PUNCT
ejpam-5309	229	7	c2	c2	PROPN
ejpam-5309	229	8	)	)	PUNCT
ejpam-5309	229	9	∈	∈	PROPN
ejpam-5309	229	10	(	(	PUNCT
ejpam-5309	229	11	rµ)t	rµ)t	PROPN
ejpam-5309	229	12	,	,	PUNCT
ejpam-5309	229	13	and	and	CCONJ
ejpam-5309	229	14	then	then	ADV
ejpam-5309	229	15	(	(	PUNCT
ejpam-5309	229	16	rµ)t	rµ)t	PROPN
ejpam-5309	229	17	̸=	̸=	PROPN
ejpam-5309	229	18	∅.	∅.	ADV
ejpam-5309	229	19	by	by	ADP
ejpam-5309	229	20	the	the	DET
ejpam-5309	229	21	given	give	VERB
ejpam-5309	229	22	assumption	assumption	NOUN
ejpam-5309	229	23	,	,	PUNCT
ejpam-5309	229	24	we	we	PRON
ejpam-5309	229	25	have	have	VERB
ejpam-5309	229	26	(	(	PUNCT
ejpam-5309	229	27	a1αb1βc1	a1αb1βc1	NOUN
ejpam-5309	229	28	,	,	PUNCT
ejpam-5309	229	29	a2αb2βc2	a2αb2βc2	NOUN
ejpam-5309	229	30	)	)	PUNCT
ejpam-5309	229	31	=	=	SYM
ejpam-5309	229	32	(	(	PUNCT
ejpam-5309	229	33	a1	a1	PROPN
ejpam-5309	229	34	,	,	PUNCT
ejpam-5309	229	35	a2)α(b1	a2)α(b1	NOUN
ejpam-5309	229	36	,	,	PUNCT
ejpam-5309	229	37	b2)β(c1	b2)β(c1	PROPN
ejpam-5309	229	38	,	,	PUNCT
ejpam-5309	229	39	c2	c2	PROPN
ejpam-5309	229	40	)	)	PUNCT
ejpam-5309	229	41	∈	∈	PROPN
ejpam-5309	229	42	(	(	PUNCT
ejpam-5309	229	43	t	t	PROPN
ejpam-5309	229	44	×	×	PROPN
ejpam-5309	229	45	t	t	PROPN
ejpam-5309	229	46	)	)	PUNCT
ejpam-5309	230	1	γ(t	γ(t	PROPN
ejpam-5309	230	2	×	×	PROPN
ejpam-5309	230	3	t	t	NOUN
ejpam-5309	230	4	)	)	PUNCT
ejpam-5309	230	5	γ(rµ)t	γ(rµ)t	NOUN
ejpam-5309	230	6	⊆	⊆	NUM
ejpam-5309	230	7	(	(	PUNCT
ejpam-5309	230	8	rµ)t	rµ)t	PROPN
ejpam-5309	230	9	.	.	PUNCT
ejpam-5309	231	1	this	this	PRON
ejpam-5309	231	2	implies	imply	VERB
ejpam-5309	231	3	that	that	SCONJ
ejpam-5309	231	4	rµ(a1αb1βc1	rµ(a1αb1βc1	NOUN
ejpam-5309	231	5	,	,	PUNCT
ejpam-5309	231	6	a2αb2βc2	a2αb2βc2	NUM
ejpam-5309	231	7	)	)	PUNCT
ejpam-5309	231	8	≥	≥	NOUN
ejpam-5309	231	9	t	t	NOUN
ejpam-5309	231	10	=	=	SYM
ejpam-5309	231	11	rµ(c1	rµ(c1	PROPN
ejpam-5309	231	12	,	,	PUNCT
ejpam-5309	231	13	c2	c2	PROPN
ejpam-5309	231	14	)	)	PUNCT
ejpam-5309	231	15	.	.	PUNCT
ejpam-5309	232	1	therefore	therefore	ADV
ejpam-5309	232	2	,	,	PUNCT
ejpam-5309	232	3	rµ	rµ	INTJ
ejpam-5309	232	4	is	be	AUX
ejpam-5309	232	5	a	a	DET
ejpam-5309	232	6	strongest	strong	ADJ
ejpam-5309	232	7	fuzzy	fuzzy	ADJ
ejpam-5309	232	8	left	leave	VERB
ejpam-5309	232	9	γ	γ	NOUN
ejpam-5309	232	10	-	-	NOUN
ejpam-5309	232	11	ideal	ideal	NOUN
ejpam-5309	232	12	on	on	ADP
ejpam-5309	232	13	t	t	PROPN
ejpam-5309	232	14	.	.	PUNCT
ejpam-5309	233	1	the	the	DET
ejpam-5309	233	2	proofs	proof	NOUN
ejpam-5309	233	3	of	of	ADP
ejpam-5309	233	4	(	(	PUNCT
ejpam-5309	233	5	ii	ii	NOUN
ejpam-5309	233	6	)	)	PUNCT
ejpam-5309	233	7	and	and	CCONJ
ejpam-5309	233	8	(	(	PUNCT
ejpam-5309	233	9	iii	iii	NOUN
ejpam-5309	233	10	)	)	PUNCT
ejpam-5309	233	11	can	can	AUX
ejpam-5309	233	12	proved	prove	VERB
ejpam-5309	233	13	in	in	ADP
ejpam-5309	233	14	a	a	DET
ejpam-5309	233	15	similar	similar	ADJ
ejpam-5309	233	16	way	way	NOUN
ejpam-5309	233	17	.	.	PUNCT
ejpam-5309	234	1	(	(	PUNCT
ejpam-5309	234	2	iv	iv	X
ejpam-5309	234	3	)	)	PUNCT
ejpam-5309	234	4	it	it	PRON
ejpam-5309	234	5	obtains	obtain	VERB
ejpam-5309	234	6	from	from	ADP
ejpam-5309	234	7	(	(	PUNCT
ejpam-5309	234	8	i	i	NOUN
ejpam-5309	234	9	)	)	PUNCT
ejpam-5309	234	10	,	,	PUNCT
ejpam-5309	234	11	(	(	PUNCT
ejpam-5309	234	12	ii	ii	NOUN
ejpam-5309	234	13	)	)	PUNCT
ejpam-5309	234	14	,	,	PUNCT
ejpam-5309	234	15	and	and	CCONJ
ejpam-5309	234	16	(	(	PUNCT
ejpam-5309	234	17	iii	iii	NOUN
ejpam-5309	234	18	)	)	PUNCT
ejpam-5309	234	19	.	.	PUNCT
ejpam-5309	235	1	theorem	theorem	VERB
ejpam-5309	235	2	6	6	NUM
ejpam-5309	235	3	.	.	PUNCT
ejpam-5309	236	1	let	let	VERB
ejpam-5309	236	2	t	t	PROPN
ejpam-5309	236	3	be	be	AUX
ejpam-5309	236	4	a	a	DET
ejpam-5309	236	5	ternary	ternary	ADJ
ejpam-5309	236	6	γ	γ	NOUN
ejpam-5309	236	7	-	-	PUNCT
ejpam-5309	236	8	semigroup	semigroup	NOUN
ejpam-5309	236	9	,	,	PUNCT
ejpam-5309	236	10	µ	µ	X
ejpam-5309	236	11	be	be	AUX
ejpam-5309	236	12	a	a	DET
ejpam-5309	236	13	fuzzy	fuzzy	ADJ
ejpam-5309	236	14	set	set	NOUN
ejpam-5309	236	15	of	of	ADP
ejpam-5309	236	16	t	t	PROPN
ejpam-5309	236	17	,	,	PUNCT
ejpam-5309	236	18	and	and	CCONJ
ejpam-5309	236	19	rµ	rµ	INTJ
ejpam-5309	236	20	be	be	AUX
ejpam-5309	236	21	a	a	DET
ejpam-5309	236	22	strongest	strong	ADJ
ejpam-5309	236	23	fuzzy	fuzzy	ADJ
ejpam-5309	236	24	relation	relation	NOUN
ejpam-5309	236	25	on	on	ADP
ejpam-5309	236	26	t	t	PROPN
ejpam-5309	236	27	.	.	PUNCT
ejpam-5309	237	1	then	then	ADV
ejpam-5309	237	2	,	,	PUNCT
ejpam-5309	237	3	rµ	rµ	INTJ
ejpam-5309	237	4	is	be	AUX
ejpam-5309	237	5	a	a	DET
ejpam-5309	237	6	strongest	strong	ADJ
ejpam-5309	237	7	fuzzy	fuzzy	ADJ
ejpam-5309	237	8	bi	bi	ADJ
ejpam-5309	237	9	-	-	ADJ
ejpam-5309	237	10	γ	γ	NOUN
ejpam-5309	237	11	-	-	NOUN
ejpam-5309	237	12	ideal	ideal	NOUN
ejpam-5309	237	13	on	on	ADP
ejpam-5309	237	14	t	t	PROPN
ejpam-5309	237	15	if	if	SCONJ
ejpam-5309	238	1	and	and	CCONJ
ejpam-5309	238	2	only	only	ADV
ejpam-5309	238	3	if	if	SCONJ
ejpam-5309	238	4	for	for	ADP
ejpam-5309	238	5	each	each	DET
ejpam-5309	238	6	t	t	NOUN
ejpam-5309	238	7	∈	∈	PROPN
ejpam-5309	239	1	[	[	X
ejpam-5309	239	2	0	0	NUM
ejpam-5309	239	3	,	,	PUNCT
ejpam-5309	239	4	1	1	NUM
ejpam-5309	239	5	]	]	PUNCT
ejpam-5309	239	6	,	,	PUNCT
ejpam-5309	239	7	(	(	PUNCT
ejpam-5309	239	8	rµ)t	rµ)t	PROPN
ejpam-5309	239	9	is	be	AUX
ejpam-5309	239	10	a	a	DET
ejpam-5309	239	11	bi	bi	ADJ
ejpam-5309	239	12	-	-	ADJ
ejpam-5309	239	13	γ	γ	NOUN
ejpam-5309	239	14	-	-	NOUN
ejpam-5309	239	15	ideal	ideal	NOUN
ejpam-5309	239	16	of	of	ADP
ejpam-5309	239	17	t	t	PROPN
ejpam-5309	239	18	×	×	PROPN
ejpam-5309	239	19	t	t	NOUN
ejpam-5309	239	20	when	when	SCONJ
ejpam-5309	239	21	it	it	PRON
ejpam-5309	239	22	is	be	AUX
ejpam-5309	239	23	nonempty	nonempty	ADJ
ejpam-5309	239	24	.	.	PUNCT
ejpam-5309	240	1	proof	proof	NOUN
ejpam-5309	240	2	.	.	PUNCT
ejpam-5309	241	1	assume	assume	VERB
ejpam-5309	241	2	that	that	SCONJ
ejpam-5309	241	3	rµ	rµ	INTJ
ejpam-5309	241	4	is	be	AUX
ejpam-5309	241	5	a	a	DET
ejpam-5309	241	6	strongest	strong	ADJ
ejpam-5309	241	7	fuzzy	fuzzy	ADJ
ejpam-5309	241	8	bi	bi	ADJ
ejpam-5309	241	9	-	-	ADJ
ejpam-5309	241	10	γ	γ	NOUN
ejpam-5309	241	11	-	-	NOUN
ejpam-5309	241	12	ideal	ideal	NOUN
ejpam-5309	241	13	on	on	ADP
ejpam-5309	241	14	t	t	PROPN
ejpam-5309	241	15	.	.	PUNCT
ejpam-5309	242	1	let	let	VERB
ejpam-5309	242	2	t	t	PROPN
ejpam-5309	242	3	∈	∈	PROPN
ejpam-5309	243	1	[	[	X
ejpam-5309	243	2	0	0	NUM
ejpam-5309	243	3	,	,	PUNCT
ejpam-5309	243	4	1	1	NUM
ejpam-5309	243	5	]	]	PUNCT
ejpam-5309	243	6	be	be	AUX
ejpam-5309	243	7	such	such	ADJ
ejpam-5309	243	8	that	that	SCONJ
ejpam-5309	243	9	(	(	PUNCT
ejpam-5309	243	10	rµ)t	rµ)t	PROPN
ejpam-5309	243	11	̸=	̸=	PROPN
ejpam-5309	243	12	∅.	∅.	ADV
ejpam-5309	243	13	let	let	VERB
ejpam-5309	243	14	(	(	PUNCT
ejpam-5309	243	15	a1	a1	NOUN
ejpam-5309	243	16	,	,	PUNCT
ejpam-5309	243	17	a2	a2	PROPN
ejpam-5309	243	18	)	)	PUNCT
ejpam-5309	243	19	,	,	PUNCT
ejpam-5309	243	20	(	(	PUNCT
ejpam-5309	243	21	c1	c1	PROPN
ejpam-5309	243	22	,	,	PUNCT
ejpam-5309	243	23	c2	c2	PROPN
ejpam-5309	243	24	)	)	PUNCT
ejpam-5309	243	25	,	,	PUNCT
ejpam-5309	243	26	(	(	PUNCT
ejpam-5309	243	27	e1	e1	PROPN
ejpam-5309	243	28	,	,	PUNCT
ejpam-5309	243	29	e2	e2	NOUN
ejpam-5309	243	30	)	)	PUNCT
ejpam-5309	243	31	∈	∈	PROPN
ejpam-5309	243	32	(	(	PUNCT
ejpam-5309	243	33	rµ)t	rµ)t	PROPN
ejpam-5309	243	34	and	and	CCONJ
ejpam-5309	243	35	(	(	PUNCT
ejpam-5309	243	36	b1	b1	NOUN
ejpam-5309	243	37	,	,	PUNCT
ejpam-5309	243	38	b2	b2	NOUN
ejpam-5309	243	39	)	)	PUNCT
ejpam-5309	243	40	,	,	PUNCT
ejpam-5309	243	41	(	(	PUNCT
ejpam-5309	243	42	d1	d1	NOUN
ejpam-5309	243	43	,	,	PUNCT
ejpam-5309	243	44	d2	d2	PROPN
ejpam-5309	243	45	)	)	PUNCT
ejpam-5309	243	46	∈	∈	PROPN
ejpam-5309	243	47	t	t	X
ejpam-5309	243	48	×	×	NOUN
ejpam-5309	243	49	t	t	NOUN
ejpam-5309	243	50	,	,	PUNCT
ejpam-5309	243	51	and	and	CCONJ
ejpam-5309	243	52	let	let	VERB
ejpam-5309	243	53	α	α	PRON
ejpam-5309	243	54	,	,	PUNCT
ejpam-5309	243	55	β	β	X
ejpam-5309	243	56	,	,	PUNCT
ejpam-5309	243	57	γ	γ	PROPN
ejpam-5309	243	58	,	,	PUNCT
ejpam-5309	243	59	δ	δ	PROPN
ejpam-5309	243	60	∈	∈	PROPN
ejpam-5309	243	61	γ	γ	PROPN
ejpam-5309	243	62	.	.	PUNCT
ejpam-5309	244	1	thus	thus	ADV
ejpam-5309	244	2	,	,	PUNCT
ejpam-5309	244	3	we	we	PRON
ejpam-5309	244	4	have	have	VERB
ejpam-5309	244	5	rµ(a1αc1βe1	rµ(a1αc1βe1	PROPN
ejpam-5309	244	6	,	,	PUNCT
ejpam-5309	244	7	a2αc2βe2	a2αc2βe2	NUM
ejpam-5309	244	8	)	)	PUNCT
ejpam-5309	244	9	≥	≥	NOUN
ejpam-5309	244	10	min{rµ(a1	min{rµ(a1	PROPN
ejpam-5309	244	11	,	,	PUNCT
ejpam-5309	244	12	a2	a2	PROPN
ejpam-5309	244	13	)	)	PUNCT
ejpam-5309	244	14	,	,	PUNCT
ejpam-5309	244	15	rµ(c1	rµ(c1	PROPN
ejpam-5309	244	16	,	,	PUNCT
ejpam-5309	244	17	c2	c2	PROPN
ejpam-5309	244	18	)	)	PUNCT
ejpam-5309	244	19	,	,	PUNCT
ejpam-5309	244	20	rµ(e1	rµ(e1	NOUN
ejpam-5309	244	21	,	,	PUNCT
ejpam-5309	244	22	e2	e2	PROPN
ejpam-5309	244	23	)	)	PUNCT
ejpam-5309	244	24	}	}	PUNCT
ejpam-5309	244	25	≥	≥	PROPN
ejpam-5309	244	26	t	t	NOUN
ejpam-5309	244	27	and	and	CCONJ
ejpam-5309	244	28	rµ(a1αb1βc1γd1δe1	rµ(a1αb1βc1γd1δe1	NOUN
ejpam-5309	244	29	,	,	PUNCT
ejpam-5309	244	30	a2αb2βc2γd2δe2	a2αb2βc2γd2δe2	NOUN
ejpam-5309	244	31	)	)	PUNCT
ejpam-5309	244	32	≥	≥	NOUN
ejpam-5309	244	33	min{rµ(a1	min{rµ(a1	PROPN
ejpam-5309	244	34	,	,	PUNCT
ejpam-5309	244	35	a2	a2	PROPN
ejpam-5309	244	36	)	)	PUNCT
ejpam-5309	244	37	,	,	PUNCT
ejpam-5309	244	38	rµ(b1	rµ(b1	NOUN
ejpam-5309	244	39	,	,	PUNCT
ejpam-5309	244	40	b2	b2	NOUN
ejpam-5309	244	41	)	)	PUNCT
ejpam-5309	244	42	,	,	PUNCT
ejpam-5309	244	43	rµ(e1	rµ(e1	NOUN
ejpam-5309	244	44	,	,	PUNCT
ejpam-5309	244	45	e2	e2	PROPN
ejpam-5309	244	46	)	)	PUNCT
ejpam-5309	244	47	}	}	PUNCT
ejpam-5309	244	48	≥	≥	NOUN
ejpam-5309	244	49	t.	t.	PROPN
ejpam-5309	244	50	also	also	ADV
ejpam-5309	244	51	,	,	PUNCT
ejpam-5309	244	52	(	(	PUNCT
ejpam-5309	244	53	a1	a1	NOUN
ejpam-5309	244	54	,	,	PUNCT
ejpam-5309	244	55	a2)α(c1	a2)α(c1	PROPN
ejpam-5309	244	56	,	,	PUNCT
ejpam-5309	244	57	c2)β(e1	c2)β(e1	NOUN
ejpam-5309	244	58	,	,	PUNCT
ejpam-5309	244	59	e2	e2	PROPN
ejpam-5309	244	60	)	)	PUNCT
ejpam-5309	244	61	=	=	PUNCT
ejpam-5309	244	62	(	(	PUNCT
ejpam-5309	244	63	a1αc1βe1	a1αc1βe1	NOUN
ejpam-5309	244	64	,	,	PUNCT
ejpam-5309	244	65	a2αc2βe2	a2αc2βe2	NUM
ejpam-5309	244	66	)	)	PUNCT
ejpam-5309	244	67	∈	∈	NOUN
ejpam-5309	244	68	(	(	PUNCT
ejpam-5309	244	69	rµ)t	rµ)t	PROPN
ejpam-5309	244	70	and	and	CCONJ
ejpam-5309	244	71	(	(	PUNCT
ejpam-5309	244	72	a1	a1	PROPN
ejpam-5309	244	73	,	,	PUNCT
ejpam-5309	244	74	a2)α(b1	a2)α(b1	NOUN
ejpam-5309	244	75	,	,	PUNCT
ejpam-5309	244	76	b2)β(c1	b2)β(c1	PROPN
ejpam-5309	244	77	,	,	PUNCT
ejpam-5309	244	78	c2)γ(d1	c2)γ(d1	NOUN
ejpam-5309	244	79	,	,	PUNCT
ejpam-5309	244	80	d2)δ(e1	d2)δ(e1	PROPN
ejpam-5309	244	81	,	,	PUNCT
ejpam-5309	244	82	e2	e2	PROPN
ejpam-5309	244	83	)	)	PUNCT
ejpam-5309	244	84	=	=	SYM
ejpam-5309	244	85	(	(	PUNCT
ejpam-5309	244	86	a1αb1βc1γd1δe1	a1αb1βc1γd1δe1	NOUN
ejpam-5309	244	87	,	,	PUNCT
ejpam-5309	244	88	a2αb2βc2γd2δe2	a2αb2βc2γd2δe2	NOUN
ejpam-5309	244	89	)	)	PUNCT
ejpam-5309	244	90	∈	∈	PROPN
ejpam-5309	244	91	(	(	PUNCT
ejpam-5309	244	92	rµ)t	rµ)t	PROPN
ejpam-5309	244	93	,	,	PUNCT
ejpam-5309	244	94	respectively	respectively	ADV
ejpam-5309	244	95	.	.	PUNCT
ejpam-5309	245	1	this	this	PRON
ejpam-5309	245	2	shows	show	VERB
ejpam-5309	245	3	that	that	SCONJ
ejpam-5309	245	4	(	(	PUNCT
ejpam-5309	245	5	rµ)tγ(rµ)tγ(rµ)t	rµ)tγ(rµ)tγ(rµ)t	NOUN
ejpam-5309	245	6	⊆	⊆	NUM
ejpam-5309	245	7	(	(	PUNCT
ejpam-5309	245	8	rµ)t	rµ)t	PROPN
ejpam-5309	245	9	and	and	CCONJ
ejpam-5309	245	10	(	(	PUNCT
ejpam-5309	245	11	rµ)tγ(t	rµ)tγ(t	PROPN
ejpam-5309	245	12	×	×	PROPN
ejpam-5309	245	13	t	t	NOUN
ejpam-5309	245	14	)	)	PUNCT
ejpam-5309	245	15	γ(rµ)tγ(t	γ(rµ)tγ(t	INTJ
ejpam-5309	245	16	×	×	PROPN
ejpam-5309	245	17	t	t	NOUN
ejpam-5309	245	18	)	)	PUNCT
ejpam-5309	245	19	γ(rµ)t	γ(rµ)t	NOUN
ejpam-5309	245	20	⊆	⊆	NUM
ejpam-5309	245	21	(	(	PUNCT
ejpam-5309	245	22	rµ)t	rµ)t	PROPN
ejpam-5309	245	23	.	.	PUNCT
ejpam-5309	246	1	therefore	therefore	ADV
ejpam-5309	246	2	,	,	PUNCT
ejpam-5309	246	3	(	(	PUNCT
ejpam-5309	246	4	rµ)t	rµ)t	PROPN
ejpam-5309	246	5	is	be	AUX
ejpam-5309	246	6	a	a	DET
ejpam-5309	246	7	bi	bi	ADJ
ejpam-5309	246	8	-	-	ADJ
ejpam-5309	246	9	γ	γ	NOUN
ejpam-5309	246	10	-	-	NOUN
ejpam-5309	246	11	ideal	ideal	NOUN
ejpam-5309	246	12	of	of	ADP
ejpam-5309	246	13	t	t	PROPN
ejpam-5309	246	14	×	×	PROPN
ejpam-5309	246	15	t	t	PROPN
ejpam-5309	246	16	.	.	PUNCT
ejpam-5309	247	1	conversely	conversely	ADV
ejpam-5309	247	2	,	,	PUNCT
ejpam-5309	247	3	let	let	VERB
ejpam-5309	247	4	a1	a1	NOUN
ejpam-5309	247	5	,	,	PUNCT
ejpam-5309	247	6	a2	a2	PROPN
ejpam-5309	247	7	,	,	PUNCT
ejpam-5309	247	8	b1	b1	NOUN
ejpam-5309	247	9	,	,	PUNCT
ejpam-5309	247	10	b2	b2	NOUN
ejpam-5309	247	11	,	,	PUNCT
ejpam-5309	247	12	c1	c1	PROPN
ejpam-5309	247	13	,	,	PUNCT
ejpam-5309	247	14	c2	c2	PROPN
ejpam-5309	247	15	,	,	PUNCT
ejpam-5309	247	16	d1	d1	PROPN
ejpam-5309	247	17	,	,	PUNCT
ejpam-5309	247	18	d2	d2	PROPN
ejpam-5309	247	19	,	,	PUNCT
ejpam-5309	247	20	e1	e1	PROPN
ejpam-5309	247	21	,	,	PUNCT
ejpam-5309	247	22	e2	e2	PROPN
ejpam-5309	247	23	∈	∈	PROPN
ejpam-5309	247	24	t	t	PROPN
ejpam-5309	247	25	and	and	CCONJ
ejpam-5309	247	26	α	α	NOUN
ejpam-5309	247	27	,	,	PUNCT
ejpam-5309	247	28	β	β	X
ejpam-5309	247	29	,	,	PUNCT
ejpam-5309	247	30	γ	γ	PROPN
ejpam-5309	247	31	,	,	PUNCT
ejpam-5309	247	32	δ	δ	PROPN
ejpam-5309	247	33	∈	∈	PROPN
ejpam-5309	247	34	γ	γ	PROPN
ejpam-5309	247	35	.	.	PROPN
ejpam-5309	247	36	chooserµ(a1	chooserµ(a1	PROPN
ejpam-5309	247	37	,	,	PUNCT
ejpam-5309	247	38	a2	a2	PROPN
ejpam-5309	247	39	)	)	PUNCT
ejpam-5309	247	40	=	=	SYM
ejpam-5309	247	41	t1	t1	PROPN
ejpam-5309	247	42	,	,	PUNCT
ejpam-5309	247	43	rµ(c1	rµ(c1	PROPN
ejpam-5309	247	44	,	,	PUNCT
ejpam-5309	247	45	c2	c2	PROPN
ejpam-5309	247	46	)	)	PUNCT
ejpam-5309	247	47	=	=	SYM
ejpam-5309	247	48	t2	t2	NOUN
ejpam-5309	247	49	,	,	PUNCT
ejpam-5309	247	50	and	and	CCONJ
ejpam-5309	247	51	rµ(e1	rµ(e1	NOUN
ejpam-5309	247	52	,	,	PUNCT
ejpam-5309	247	53	e2	e2	PROPN
ejpam-5309	247	54	)	)	PUNCT
ejpam-5309	248	1	=	=	SYM
ejpam-5309	248	2	t3	t3	PROPN
ejpam-5309	248	3	,	,	PUNCT
ejpam-5309	248	4	for	for	ADP
ejpam-5309	248	5	some	some	DET
ejpam-5309	248	6	t1	t1	NOUN
ejpam-5309	248	7	,	,	PUNCT
ejpam-5309	248	8	t2	t2	NOUN
ejpam-5309	248	9	,	,	PUNCT
ejpam-5309	248	10	t3	t3	PROPN
ejpam-5309	248	11	∈	∈	PROPN
ejpam-5309	249	1	[	[	X
ejpam-5309	249	2	0	0	NUM
ejpam-5309	249	3	,	,	PUNCT
ejpam-5309	249	4	1	1	NUM
ejpam-5309	249	5	]	]	PUNCT
ejpam-5309	249	6	.	.	PUNCT
ejpam-5309	250	1	let	let	VERB
ejpam-5309	250	2	t	t	NOUN
ejpam-5309	250	3	=	=	PUNCT
ejpam-5309	250	4	min{t1	min{t1	NOUN
ejpam-5309	250	5	,	,	PUNCT
ejpam-5309	250	6	t2	t2	NOUN
ejpam-5309	250	7	,	,	PUNCT
ejpam-5309	250	8	t3	t3	PROPN
ejpam-5309	250	9	}	}	PUNCT
ejpam-5309	250	10	.	.	PUNCT
ejpam-5309	251	1	it	it	PRON
ejpam-5309	251	2	turns	turn	VERB
ejpam-5309	251	3	out	out	ADP
ejpam-5309	251	4	that	that	SCONJ
ejpam-5309	251	5	(	(	PUNCT
ejpam-5309	251	6	a1	a1	NOUN
ejpam-5309	251	7	,	,	PUNCT
ejpam-5309	251	8	a2	a2	PROPN
ejpam-5309	251	9	)	)	PUNCT
ejpam-5309	251	10	,	,	PUNCT
ejpam-5309	251	11	(	(	PUNCT
ejpam-5309	251	12	c1	c1	PROPN
ejpam-5309	251	13	,	,	PUNCT
ejpam-5309	251	14	c2	c2	PROPN
ejpam-5309	251	15	)	)	PUNCT
ejpam-5309	251	16	,	,	PUNCT
ejpam-5309	251	17	(	(	PUNCT
ejpam-5309	251	18	e1	e1	PROPN
ejpam-5309	251	19	,	,	PUNCT
ejpam-5309	251	20	e2	e2	NOUN
ejpam-5309	251	21	)	)	PUNCT
ejpam-5309	251	22	∈	∈	PROPN
ejpam-5309	251	23	(	(	PUNCT
ejpam-5309	251	24	rµ)t	rµ)t	PROPN
ejpam-5309	251	25	.	.	PUNCT
ejpam-5309	252	1	by	by	ADP
ejpam-5309	252	2	assumption	assumption	NOUN
ejpam-5309	252	3	,	,	PUNCT
ejpam-5309	252	4	we	we	PRON
ejpam-5309	252	5	have	have	VERB
ejpam-5309	252	6	(	(	PUNCT
ejpam-5309	252	7	rµ)t	rµ)t	PROPN
ejpam-5309	252	8	is	be	AUX
ejpam-5309	252	9	a	a	DET
ejpam-5309	252	10	bi	bi	ADJ
ejpam-5309	252	11	-	-	ADJ
ejpam-5309	252	12	γ	γ	NOUN
ejpam-5309	252	13	-	-	NOUN
ejpam-5309	252	14	ideal	ideal	NOUN
ejpam-5309	252	15	of	of	ADP
ejpam-5309	252	16	t	t	PROPN
ejpam-5309	252	17	×	×	PROPN
ejpam-5309	252	18	t	t	PROPN
ejpam-5309	252	19	.	.	PUNCT
ejpam-5309	253	1	so	so	ADV
ejpam-5309	253	2	,	,	PUNCT
ejpam-5309	253	3	we	we	PRON
ejpam-5309	253	4	obtain	obtain	VERB
ejpam-5309	253	5	(	(	PUNCT
ejpam-5309	253	6	a1αc1βe1	a1αc1βe1	NOUN
ejpam-5309	253	7	,	,	PUNCT
ejpam-5309	253	8	a2αc2βe2	a2αc2βe2	NUM
ejpam-5309	253	9	)	)	PUNCT
ejpam-5309	253	10	=	=	SYM
ejpam-5309	253	11	(	(	PUNCT
ejpam-5309	253	12	a1	a1	PROPN
ejpam-5309	253	13	,	,	PUNCT
ejpam-5309	253	14	a2)α(c1	a2)α(c1	PROPN
ejpam-5309	253	15	,	,	PUNCT
ejpam-5309	253	16	c2)β(e1	c2)β(e1	NOUN
ejpam-5309	253	17	,	,	PUNCT
ejpam-5309	253	18	e2	e2	PROPN
ejpam-5309	253	19	)	)	PUNCT
ejpam-5309	253	20	∈	∈	PROPN
ejpam-5309	253	21	(	(	PUNCT
ejpam-5309	253	22	rµ)t	rµ)t	PROPN
ejpam-5309	253	23	and	and	CCONJ
ejpam-5309	253	24	(	(	PUNCT
ejpam-5309	253	25	a1αb1βc1γd1δe1	a1αb1βc1γd1δe1	NOUN
ejpam-5309	253	26	,	,	PUNCT
ejpam-5309	253	27	a2αb2βc2γd2δe2	a2αb2βc2γd2δe2	NOUN
ejpam-5309	253	28	)	)	PUNCT
ejpam-5309	253	29	=	=	SYM
ejpam-5309	253	30	(	(	PUNCT
ejpam-5309	253	31	a1	a1	PROPN
ejpam-5309	253	32	,	,	PUNCT
ejpam-5309	253	33	a2)α(b1	a2)α(b1	NOUN
ejpam-5309	253	34	,	,	PUNCT
ejpam-5309	253	35	b2)β(c1	b2)β(c1	PROPN
ejpam-5309	253	36	,	,	PUNCT
ejpam-5309	253	37	c2)γ(d1	c2)γ(d1	NOUN
ejpam-5309	253	38	,	,	PUNCT
ejpam-5309	253	39	d2)δ(e1	d2)δ(e1	PROPN
ejpam-5309	253	40	,	,	PUNCT
ejpam-5309	253	41	e2	e2	PROPN
ejpam-5309	253	42	)	)	PUNCT
ejpam-5309	253	43	∈	∈	PROPN
ejpam-5309	253	44	(	(	PUNCT
ejpam-5309	253	45	rµ)t	rµ)t	PROPN
ejpam-5309	253	46	.	.	PUNCT
ejpam-5309	254	1	w.	w.	PROPN
ejpam-5309	254	2	nakkhasen	nakkhasen	PROPN
ejpam-5309	254	3	et	et	PROPN
ejpam-5309	254	4	al	al	PROPN
ejpam-5309	254	5	.	.	PUNCT
ejpam-5309	254	6	/	/	SYM
ejpam-5309	254	7	eur	eur	PROPN
ejpam-5309	254	8	.	.	PUNCT
ejpam-5309	255	1	j.	j.	PROPN
ejpam-5309	255	2	pure	pure	PROPN
ejpam-5309	255	3	appl	appl	PROPN
ejpam-5309	255	4	.	.	PROPN
ejpam-5309	255	5	math	math	PROPN
ejpam-5309	255	6	,	,	PUNCT
ejpam-5309	255	7	17	17	NUM
ejpam-5309	255	8	(	(	PUNCT
ejpam-5309	255	9	3	3	NUM
ejpam-5309	255	10	)	)	PUNCT
ejpam-5309	255	11	(	(	PUNCT
ejpam-5309	255	12	2024	2024	NUM
ejpam-5309	255	13	)	)	PUNCT
ejpam-5309	255	14	,	,	PUNCT
ejpam-5309	255	15	1417	1417	NUM
ejpam-5309	255	16	-	-	SYM
ejpam-5309	255	17	1428	1428	NUM
ejpam-5309	255	18	1426	1426	NUM
ejpam-5309	255	19	it	it	PRON
ejpam-5309	255	20	means	mean	VERB
ejpam-5309	255	21	that	that	SCONJ
ejpam-5309	255	22	rµ(a1αc1βe1	rµ(a1αc1βe1	PROPN
ejpam-5309	255	23	,	,	PUNCT
ejpam-5309	255	24	a2αc2βe2	a2αc2βe2	NUM
ejpam-5309	255	25	)	)	PUNCT
ejpam-5309	255	26	≥	≥	NOUN
ejpam-5309	255	27	t	t	NOUN
ejpam-5309	255	28	=	=	PUNCT
ejpam-5309	255	29	min{t1	min{t1	NOUN
ejpam-5309	255	30	,	,	PUNCT
ejpam-5309	255	31	t2	t2	NOUN
ejpam-5309	255	32	,	,	PUNCT
ejpam-5309	255	33	t3	t3	PROPN
ejpam-5309	255	34	}	}	PUNCT
ejpam-5309	255	35	=	=	SYM
ejpam-5309	255	36	min{rµ(a1	min{rµ(a1	PROPN
ejpam-5309	255	37	,	,	PUNCT
ejpam-5309	255	38	a2	a2	PROPN
ejpam-5309	255	39	)	)	PUNCT
ejpam-5309	255	40	,	,	PUNCT
ejpam-5309	255	41	rµ(c1	rµ(c1	PROPN
ejpam-5309	255	42	,	,	PUNCT
ejpam-5309	255	43	c2	c2	PROPN
ejpam-5309	255	44	)	)	PUNCT
ejpam-5309	255	45	,	,	PUNCT
ejpam-5309	255	46	rµ(e1	rµ(e1	NOUN
ejpam-5309	255	47	,	,	PUNCT
ejpam-5309	255	48	e2	e2	PROPN
ejpam-5309	255	49	)	)	PUNCT
ejpam-5309	255	50	}	}	PUNCT
ejpam-5309	255	51	and	and	CCONJ
ejpam-5309	255	52	rµ(a1αb1βc1γd1δe1	rµ(a1αb1βc1γd1δe1	ADV
ejpam-5309	255	53	,	,	PUNCT
ejpam-5309	255	54	a2αb2βc2γd2δe2	a2αb2βc2γd2δe2	NOUN
ejpam-5309	255	55	)	)	PUNCT
ejpam-5309	255	56	≥	≥	NOUN
ejpam-5309	255	57	t	t	NOUN
ejpam-5309	255	58	=	=	PUNCT
ejpam-5309	255	59	min{t1	min{t1	NOUN
ejpam-5309	255	60	,	,	PUNCT
ejpam-5309	255	61	t2	t2	NOUN
ejpam-5309	255	62	,	,	PUNCT
ejpam-5309	255	63	t3	t3	PROPN
ejpam-5309	255	64	}	}	PUNCT
ejpam-5309	255	65	=	=	SYM
ejpam-5309	255	66	min{rµ(a1	min{rµ(a1	PROPN
ejpam-5309	255	67	,	,	PUNCT
ejpam-5309	255	68	a2	a2	PROPN
ejpam-5309	255	69	)	)	PUNCT
ejpam-5309	255	70	,	,	PUNCT
ejpam-5309	255	71	rµ(c1	rµ(c1	PROPN
ejpam-5309	255	72	,	,	PUNCT
ejpam-5309	255	73	c2	c2	PROPN
ejpam-5309	255	74	)	)	PUNCT
ejpam-5309	255	75	,	,	PUNCT
ejpam-5309	255	76	rµ(e1	rµ(e1	NOUN
ejpam-5309	255	77	,	,	PUNCT
ejpam-5309	255	78	e2	e2	PROPN
ejpam-5309	255	79	)	)	PUNCT
ejpam-5309	255	80	}	}	PUNCT
ejpam-5309	255	81	.	.	PUNCT
ejpam-5309	256	1	consequently	consequently	ADV
ejpam-5309	256	2	,	,	PUNCT
ejpam-5309	256	3	rµ	rµ	INTJ
ejpam-5309	256	4	is	be	AUX
ejpam-5309	256	5	a	a	DET
ejpam-5309	256	6	strongest	strong	ADJ
ejpam-5309	256	7	fuzzy	fuzzy	ADJ
ejpam-5309	256	8	bi	bi	ADJ
ejpam-5309	256	9	-	-	ADJ
ejpam-5309	256	10	γ	γ	NOUN
ejpam-5309	256	11	-	-	NOUN
ejpam-5309	256	12	ideal	ideal	NOUN
ejpam-5309	256	13	on	on	ADP
ejpam-5309	256	14	t	t	PROPN
ejpam-5309	256	15	.	.	PUNCT
ejpam-5309	257	1	example	example	NOUN
ejpam-5309	258	1	3	3	NUM
ejpam-5309	258	2	.	.	PUNCT
ejpam-5309	258	3	by	by	ADP
ejpam-5309	258	4	example	example	NOUN
ejpam-5309	258	5	1	1	NUM
ejpam-5309	258	6	,	,	PUNCT
ejpam-5309	258	7	we	we	PRON
ejpam-5309	258	8	obtain	obtain	VERB
ejpam-5309	258	9	rµ	rµ	NOUN
ejpam-5309	258	10	is	be	AUX
ejpam-5309	258	11	a	a	DET
ejpam-5309	258	12	strongest	strong	ADJ
ejpam-5309	258	13	fuzzy	fuzzy	ADJ
ejpam-5309	258	14	bi	bi	ADJ
ejpam-5309	258	15	-	-	ADJ
ejpam-5309	258	16	γ	γ	NOUN
ejpam-5309	258	17	-	-	NOUN
ejpam-5309	258	18	ideal	ideal	NOUN
ejpam-5309	258	19	on	on	ADP
ejpam-5309	258	20	a	a	DET
ejpam-5309	258	21	ternary	ternary	ADJ
ejpam-5309	258	22	γsemigroup	γsemigroup	NOUN
ejpam-5309	258	23	t	t	NOUN
ejpam-5309	258	24	.	.	PUNCT
ejpam-5309	259	1	it	it	PRON
ejpam-5309	259	2	turns	turn	VERB
ejpam-5309	259	3	out	out	ADP
ejpam-5309	259	4	that	that	SCONJ
ejpam-5309	259	5	the	the	DET
ejpam-5309	259	6	set	set	NOUN
ejpam-5309	259	7	of	of	ADP
ejpam-5309	259	8	all	all	DET
ejpam-5309	259	9	level	level	NOUN
ejpam-5309	259	10	subsets	subset	NOUN
ejpam-5309	259	11	of	of	ADP
ejpam-5309	259	12	rµ	rµ	NOUN
ejpam-5309	259	13	are	be	AUX
ejpam-5309	259	14	(	(	PUNCT
ejpam-5309	259	15	rµ)0.7	rµ)0.7	ADJ
ejpam-5309	259	16	=	=	SYM
ejpam-5309	259	17	{	{	PUNCT
ejpam-5309	259	18	(	(	PUNCT
ejpam-5309	259	19	a	a	PRON
ejpam-5309	259	20	,	,	PUNCT
ejpam-5309	259	21	a	a	NOUN
ejpam-5309	259	22	)	)	PUNCT
ejpam-5309	259	23	,	,	PUNCT
ejpam-5309	259	24	(	(	PUNCT
ejpam-5309	259	25	a	a	DET
ejpam-5309	259	26	,	,	PUNCT
ejpam-5309	259	27	b	b	NOUN
ejpam-5309	259	28	)	)	PUNCT
ejpam-5309	259	29	,	,	PUNCT
ejpam-5309	259	30	(	(	PUNCT
ejpam-5309	259	31	b	b	X
ejpam-5309	259	32	,	,	PUNCT
ejpam-5309	259	33	a	a	PRON
ejpam-5309	259	34	)	)	PUNCT
ejpam-5309	259	35	,	,	PUNCT
ejpam-5309	259	36	(	(	PUNCT
ejpam-5309	259	37	b	b	X
ejpam-5309	259	38	,	,	PUNCT
ejpam-5309	259	39	b	b	NOUN
ejpam-5309	259	40	)	)	PUNCT
ejpam-5309	259	41	}	}	PUNCT
ejpam-5309	259	42	and	and	CCONJ
ejpam-5309	259	43	(	(	PUNCT
ejpam-5309	259	44	rµ)0.2	rµ)0.2	NOUN
ejpam-5309	259	45	=	=	SYM
ejpam-5309	259	46	t	t	PROPN
ejpam-5309	259	47	×	×	NOUN
ejpam-5309	259	48	t	t	PROPN
ejpam-5309	259	49	.	.	PUNCT
ejpam-5309	260	1	by	by	ADP
ejpam-5309	260	2	theorem	theorem	NOUN
ejpam-5309	260	3	6	6	NUM
ejpam-5309	260	4	,	,	PUNCT
ejpam-5309	260	5	we	we	PRON
ejpam-5309	260	6	have	have	VERB
ejpam-5309	260	7	(	(	PUNCT
ejpam-5309	260	8	rµ)0.7	rµ)0.7	VERB
ejpam-5309	260	9	and	and	CCONJ
ejpam-5309	260	10	(	(	PUNCT
ejpam-5309	260	11	rµ)0.2	rµ)0.2	NOUN
ejpam-5309	260	12	are	be	AUX
ejpam-5309	260	13	bi	bi	ADJ
ejpam-5309	260	14	-	-	NOUN
ejpam-5309	260	15	γideals	γideal	NOUN
ejpam-5309	260	16	of	of	ADP
ejpam-5309	260	17	a	a	DET
ejpam-5309	260	18	ternary	ternary	ADJ
ejpam-5309	260	19	γ	γ	NOUN
ejpam-5309	260	20	-	-	PUNCT
ejpam-5309	260	21	semigroup	semigroup	PROPN
ejpam-5309	260	22	t	t	PROPN
ejpam-5309	260	23	×	×	NOUN
ejpam-5309	260	24	t	t	PROPN
ejpam-5309	260	25	.	.	PUNCT
ejpam-5309	261	1	this	this	PRON
ejpam-5309	261	2	is	be	AUX
ejpam-5309	261	3	the	the	DET
ejpam-5309	261	4	process	process	NOUN
ejpam-5309	261	5	of	of	ADP
ejpam-5309	261	6	finding	find	VERB
ejpam-5309	261	7	some	some	DET
ejpam-5309	261	8	bi	bi	ADJ
ejpam-5309	261	9	-	-	ADJ
ejpam-5309	261	10	γ	γ	NOUN
ejpam-5309	261	11	-	-	PUNCT
ejpam-5309	261	12	ideals	ideal	NOUN
ejpam-5309	261	13	of	of	ADP
ejpam-5309	261	14	a	a	DET
ejpam-5309	261	15	ternary	ternary	ADJ
ejpam-5309	261	16	γ	γ	NOUN
ejpam-5309	261	17	-	-	PUNCT
ejpam-5309	261	18	semigroup	semigroup	PROPN
ejpam-5309	261	19	t	t	PROPN
ejpam-5309	261	20	×	×	PROPN
ejpam-5309	261	21	t	t	PROPN
ejpam-5309	261	22	using	use	VERB
ejpam-5309	261	23	theorem	theorem	NOUN
ejpam-5309	261	24	6	6	NUM
ejpam-5309	261	25	such	such	ADJ
ejpam-5309	261	26	as	as	ADP
ejpam-5309	261	27	the	the	DET
ejpam-5309	261	28	sets	set	NOUN
ejpam-5309	261	29	{	{	PUNCT
ejpam-5309	261	30	(	(	PUNCT
ejpam-5309	261	31	a	a	DET
ejpam-5309	261	32	,	,	PUNCT
ejpam-5309	261	33	a	a	NOUN
ejpam-5309	261	34	)	)	PUNCT
ejpam-5309	261	35	,	,	PUNCT
ejpam-5309	261	36	(	(	PUNCT
ejpam-5309	261	37	a	a	DET
ejpam-5309	261	38	,	,	PUNCT
ejpam-5309	261	39	b	b	NOUN
ejpam-5309	261	40	)	)	PUNCT
ejpam-5309	261	41	,	,	PUNCT
ejpam-5309	261	42	(	(	PUNCT
ejpam-5309	261	43	b	b	X
ejpam-5309	261	44	,	,	PUNCT
ejpam-5309	261	45	a	a	PRON
ejpam-5309	261	46	)	)	PUNCT
ejpam-5309	261	47	,	,	PUNCT
ejpam-5309	261	48	(	(	PUNCT
ejpam-5309	261	49	b	b	X
ejpam-5309	261	50	,	,	PUNCT
ejpam-5309	261	51	b	b	NOUN
ejpam-5309	261	52	)	)	PUNCT
ejpam-5309	261	53	}	}	PUNCT
ejpam-5309	261	54	and	and	CCONJ
ejpam-5309	261	55	t	t	X
ejpam-5309	261	56	×	×	PROPN
ejpam-5309	261	57	t	t	PROPN
ejpam-5309	261	58	.	.	PUNCT
ejpam-5309	262	1	let	let	VERB
ejpam-5309	262	2	x	x	PRON
ejpam-5309	262	3	be	be	AUX
ejpam-5309	262	4	a	a	DET
ejpam-5309	262	5	nonempty	nonempty	ADJ
ejpam-5309	262	6	set	set	NOUN
ejpam-5309	262	7	,	,	PUNCT
ejpam-5309	262	8	and	and	CCONJ
ejpam-5309	262	9	µ	µ	X
ejpam-5309	262	10	be	be	AUX
ejpam-5309	262	11	a	a	DET
ejpam-5309	262	12	fuzzy	fuzzy	ADJ
ejpam-5309	262	13	set	set	NOUN
ejpam-5309	262	14	of	of	ADP
ejpam-5309	262	15	x.	x.	NOUN
ejpam-5309	262	16	we	we	PRON
ejpam-5309	262	17	observe	observe	VERB
ejpam-5309	262	18	that	that	SCONJ
ejpam-5309	262	19	all	all	DET
ejpam-5309	262	20	level	level	NOUN
ejpam-5309	262	21	subsets	subset	NOUN
ejpam-5309	262	22	of	of	ADP
ejpam-5309	262	23	the	the	DET
ejpam-5309	262	24	strongest	strong	ADJ
ejpam-5309	262	25	fuzzy	fuzzy	ADJ
ejpam-5309	262	26	relation	relation	NOUN
ejpam-5309	262	27	χa	χa	ADP
ejpam-5309	262	28	µ	µ	NOUN
ejpam-5309	262	29	on	on	ADP
ejpam-5309	262	30	x	x	SYM
ejpam-5309	262	31	only	only	ADV
ejpam-5309	262	32	include	include	VERB
ejpam-5309	262	33	that	that	SCONJ
ejpam-5309	262	34	the	the	DET
ejpam-5309	262	35	sets	set	NOUN
ejpam-5309	262	36	a	a	PRON
ejpam-5309	262	37	and	and	CCONJ
ejpam-5309	262	38	x	x	NOUN
ejpam-5309	262	39	,	,	PUNCT
ejpam-5309	262	40	for	for	SCONJ
ejpam-5309	262	41	each	each	DET
ejpam-5309	262	42	subset	subset	VERB
ejpam-5309	262	43	a	a	PRON
ejpam-5309	262	44	of	of	ADP
ejpam-5309	262	45	x.	x.	NOUN
ejpam-5309	262	46	therefore	therefore	ADV
ejpam-5309	262	47	,	,	PUNCT
ejpam-5309	262	48	we	we	PRON
ejpam-5309	262	49	obtain	obtain	VERB
ejpam-5309	262	50	the	the	DET
ejpam-5309	262	51	following	follow	VERB
ejpam-5309	262	52	results	result	NOUN
ejpam-5309	262	53	by	by	ADP
ejpam-5309	262	54	theorem	theorem	ADJ
ejpam-5309	262	55	4	4	NUM
ejpam-5309	262	56	,	,	PUNCT
ejpam-5309	262	57	theorem	theorem	VERB
ejpam-5309	262	58	5	5	NUM
ejpam-5309	262	59	,	,	PUNCT
ejpam-5309	262	60	and	and	CCONJ
ejpam-5309	262	61	theorem	theorem	VERB
ejpam-5309	262	62	6	6	NUM
ejpam-5309	262	63	,	,	PUNCT
ejpam-5309	262	64	respectively	respectively	ADV
ejpam-5309	262	65	.	.	PUNCT
ejpam-5309	263	1	corollary	corollary	ADJ
ejpam-5309	263	2	1	1	NUM
ejpam-5309	263	3	.	.	PUNCT
ejpam-5309	264	1	let	let	VERB
ejpam-5309	264	2	t	t	NOUN
ejpam-5309	264	3	be	be	AUX
ejpam-5309	264	4	a	a	DET
ejpam-5309	264	5	ternary	ternary	ADJ
ejpam-5309	264	6	γ	γ	NOUN
ejpam-5309	264	7	-	-	PUNCT
ejpam-5309	264	8	semigroup	semigroup	NOUN
ejpam-5309	264	9	,	,	PUNCT
ejpam-5309	264	10	µ	µ	X
ejpam-5309	264	11	be	be	AUX
ejpam-5309	264	12	a	a	DET
ejpam-5309	264	13	fuzzy	fuzzy	ADJ
ejpam-5309	264	14	set	set	NOUN
ejpam-5309	264	15	of	of	ADP
ejpam-5309	264	16	t	t	PROPN
ejpam-5309	264	17	,	,	PUNCT
ejpam-5309	264	18	and	and	CCONJ
ejpam-5309	264	19	a	a	PRON
ejpam-5309	264	20	be	be	AUX
ejpam-5309	264	21	a	a	DET
ejpam-5309	264	22	nonempty	nonempty	ADJ
ejpam-5309	264	23	subset	subset	NOUN
ejpam-5309	264	24	of	of	ADP
ejpam-5309	264	25	t	t	PROPN
ejpam-5309	264	26	.	.	PUNCT
ejpam-5309	265	1	then	then	ADV
ejpam-5309	265	2	,	,	PUNCT
ejpam-5309	265	3	χa	χa	PROPN
ejpam-5309	265	4	µ	µ	PROPN
ejpam-5309	265	5	is	be	AUX
ejpam-5309	265	6	a	a	DET
ejpam-5309	265	7	strongest	strong	ADJ
ejpam-5309	265	8	fuzzy	fuzzy	ADJ
ejpam-5309	265	9	ternary	ternary	ADJ
ejpam-5309	265	10	γ	γ	NOUN
ejpam-5309	265	11	-	-	NOUN
ejpam-5309	265	12	subsemigroup	subsemigroup	NOUN
ejpam-5309	265	13	on	on	ADP
ejpam-5309	265	14	t	t	PROPN
ejpam-5309	266	1	if	if	SCONJ
ejpam-5309	267	1	and	and	CCONJ
ejpam-5309	267	2	only	only	ADV
ejpam-5309	267	3	if	if	SCONJ
ejpam-5309	267	4	a	a	PRON
ejpam-5309	267	5	is	be	AUX
ejpam-5309	267	6	a	a	DET
ejpam-5309	267	7	ternary	ternary	ADJ
ejpam-5309	267	8	γ	γ	NOUN
ejpam-5309	267	9	-	-	NOUN
ejpam-5309	267	10	subsemigroup	subsemigroup	NOUN
ejpam-5309	267	11	of	of	ADP
ejpam-5309	267	12	t	t	PROPN
ejpam-5309	267	13	.	.	PUNCT
ejpam-5309	268	1	corollary	corollary	ADJ
ejpam-5309	268	2	2	2	NUM
ejpam-5309	268	3	.	.	PUNCT
ejpam-5309	269	1	let	let	VERB
ejpam-5309	269	2	t	t	PROPN
ejpam-5309	269	3	be	be	AUX
ejpam-5309	269	4	a	a	DET
ejpam-5309	269	5	ternary	ternary	ADJ
ejpam-5309	269	6	γ	γ	NOUN
ejpam-5309	269	7	-	-	PUNCT
ejpam-5309	269	8	semigroup	semigroup	NOUN
ejpam-5309	269	9	,	,	PUNCT
ejpam-5309	269	10	µ	µ	X
ejpam-5309	269	11	be	be	AUX
ejpam-5309	269	12	a	a	DET
ejpam-5309	269	13	fuzzy	fuzzy	ADJ
ejpam-5309	269	14	set	set	NOUN
ejpam-5309	269	15	of	of	ADP
ejpam-5309	269	16	t	t	PROPN
ejpam-5309	269	17	,	,	PUNCT
ejpam-5309	269	18	and	and	CCONJ
ejpam-5309	269	19	a	a	PRON
ejpam-5309	269	20	be	be	AUX
ejpam-5309	269	21	a	a	DET
ejpam-5309	269	22	nonempty	nonempty	ADJ
ejpam-5309	269	23	subset	subset	NOUN
ejpam-5309	269	24	of	of	ADP
ejpam-5309	269	25	t	t	PROPN
ejpam-5309	269	26	.	.	PUNCT
ejpam-5309	270	1	then	then	ADV
ejpam-5309	270	2	the	the	DET
ejpam-5309	270	3	following	follow	VERB
ejpam-5309	270	4	conditions	condition	NOUN
ejpam-5309	270	5	hold	hold	VERB
ejpam-5309	270	6	:	:	PUNCT
ejpam-5309	270	7	(	(	PUNCT
ejpam-5309	270	8	i	i	NOUN
ejpam-5309	270	9	)	)	PUNCT
ejpam-5309	270	10	χa	χa	PROPN
ejpam-5309	270	11	µ	µ	PROPN
ejpam-5309	270	12	is	be	AUX
ejpam-5309	270	13	a	a	DET
ejpam-5309	270	14	strongest	strong	ADJ
ejpam-5309	270	15	fuzzy	fuzzy	ADJ
ejpam-5309	270	16	left	leave	VERB
ejpam-5309	270	17	γ	γ	NOUN
ejpam-5309	270	18	-	-	NOUN
ejpam-5309	270	19	ideal	ideal	NOUN
ejpam-5309	270	20	on	on	ADP
ejpam-5309	270	21	t	t	PROPN
ejpam-5309	270	22	if	if	SCONJ
ejpam-5309	271	1	and	and	CCONJ
ejpam-5309	271	2	only	only	ADV
ejpam-5309	271	3	if	if	SCONJ
ejpam-5309	271	4	a	a	PRON
ejpam-5309	271	5	is	be	AUX
ejpam-5309	271	6	a	a	DET
ejpam-5309	271	7	left	left	ADJ
ejpam-5309	271	8	γ	γ	NOUN
ejpam-5309	271	9	-	-	NOUN
ejpam-5309	271	10	ideal	ideal	NOUN
ejpam-5309	271	11	of	of	ADP
ejpam-5309	271	12	t	t	PROPN
ejpam-5309	271	13	;	;	PUNCT
ejpam-5309	271	14	(	(	PUNCT
ejpam-5309	271	15	ii	ii	X
ejpam-5309	271	16	)	)	PUNCT
ejpam-5309	271	17	χa	χa	PROPN
ejpam-5309	271	18	µ	µ	PROPN
ejpam-5309	271	19	is	be	AUX
ejpam-5309	271	20	a	a	DET
ejpam-5309	271	21	strongest	strong	ADJ
ejpam-5309	271	22	fuzzy	fuzzy	ADJ
ejpam-5309	271	23	right	right	ADJ
ejpam-5309	271	24	γ	γ	X
ejpam-5309	271	25	-	-	NOUN
ejpam-5309	271	26	ideal	ideal	NOUN
ejpam-5309	271	27	on	on	ADP
ejpam-5309	271	28	t	t	PROPN
ejpam-5309	271	29	if	if	SCONJ
ejpam-5309	272	1	and	and	CCONJ
ejpam-5309	272	2	only	only	ADV
ejpam-5309	272	3	if	if	SCONJ
ejpam-5309	272	4	a	a	PRON
ejpam-5309	272	5	is	be	AUX
ejpam-5309	272	6	a	a	DET
ejpam-5309	272	7	right	right	ADJ
ejpam-5309	272	8	γ	γ	NOUN
ejpam-5309	272	9	-	-	NOUN
ejpam-5309	272	10	ideal	ideal	NOUN
ejpam-5309	272	11	of	of	ADP
ejpam-5309	272	12	t	t	PROPN
ejpam-5309	272	13	;	;	PUNCT
ejpam-5309	272	14	(	(	PUNCT
ejpam-5309	272	15	iii	iii	X
ejpam-5309	272	16	)	)	PUNCT
ejpam-5309	272	17	χa	χa	PROPN
ejpam-5309	272	18	µ	µ	PROPN
ejpam-5309	272	19	is	be	AUX
ejpam-5309	272	20	a	a	DET
ejpam-5309	272	21	strongest	strong	ADJ
ejpam-5309	272	22	fuzzy	fuzzy	ADJ
ejpam-5309	272	23	lateral	lateral	ADJ
ejpam-5309	272	24	γ	γ	NOUN
ejpam-5309	272	25	-	-	NOUN
ejpam-5309	272	26	ideal	ideal	NOUN
ejpam-5309	272	27	on	on	ADP
ejpam-5309	272	28	t	t	PROPN
ejpam-5309	272	29	if	if	SCONJ
ejpam-5309	273	1	and	and	CCONJ
ejpam-5309	273	2	only	only	ADV
ejpam-5309	273	3	if	if	SCONJ
ejpam-5309	273	4	a	a	PRON
ejpam-5309	273	5	is	be	AUX
ejpam-5309	273	6	a	a	DET
ejpam-5309	273	7	lateral	lateral	ADJ
ejpam-5309	273	8	γ	γ	NOUN
ejpam-5309	273	9	-	-	NOUN
ejpam-5309	273	10	ideal	ideal	NOUN
ejpam-5309	273	11	of	of	ADP
ejpam-5309	273	12	t	t	PROPN
ejpam-5309	273	13	;	;	PUNCT
ejpam-5309	273	14	(	(	PUNCT
ejpam-5309	273	15	iv	iv	X
ejpam-5309	273	16	)	)	PUNCT
ejpam-5309	273	17	χa	χa	PROPN
ejpam-5309	273	18	µ	µ	PROPN
ejpam-5309	273	19	is	be	AUX
ejpam-5309	273	20	a	a	DET
ejpam-5309	273	21	strongest	strong	ADJ
ejpam-5309	273	22	fuzzy	fuzzy	ADJ
ejpam-5309	273	23	γ	γ	NOUN
ejpam-5309	273	24	-	-	NOUN
ejpam-5309	273	25	ideal	ideal	NOUN
ejpam-5309	273	26	on	on	ADP
ejpam-5309	273	27	t	t	PROPN
ejpam-5309	273	28	if	if	SCONJ
ejpam-5309	274	1	and	and	CCONJ
ejpam-5309	274	2	only	only	ADV
ejpam-5309	274	3	if	if	SCONJ
ejpam-5309	274	4	a	a	PRON
ejpam-5309	274	5	is	be	AUX
ejpam-5309	274	6	a	a	DET
ejpam-5309	274	7	γ	γ	NOUN
ejpam-5309	274	8	-	-	NOUN
ejpam-5309	274	9	ideal	ideal	NOUN
ejpam-5309	274	10	of	of	ADP
ejpam-5309	274	11	t	t	PROPN
ejpam-5309	274	12	.	.	PUNCT
ejpam-5309	275	1	corollary	corollary	ADJ
ejpam-5309	275	2	3	3	X
ejpam-5309	275	3	.	.	PUNCT
ejpam-5309	276	1	let	let	VERB
ejpam-5309	276	2	t	t	NOUN
ejpam-5309	276	3	be	be	AUX
ejpam-5309	276	4	a	a	DET
ejpam-5309	276	5	ternary	ternary	ADJ
ejpam-5309	276	6	γ	γ	NOUN
ejpam-5309	276	7	-	-	PUNCT
ejpam-5309	276	8	semigroup	semigroup	NOUN
ejpam-5309	276	9	,	,	PUNCT
ejpam-5309	276	10	µ	µ	X
ejpam-5309	276	11	be	be	AUX
ejpam-5309	276	12	a	a	DET
ejpam-5309	276	13	fuzzy	fuzzy	ADJ
ejpam-5309	276	14	set	set	NOUN
ejpam-5309	276	15	of	of	ADP
ejpam-5309	276	16	t	t	PROPN
ejpam-5309	276	17	,	,	PUNCT
ejpam-5309	276	18	and	and	CCONJ
ejpam-5309	276	19	a	a	PRON
ejpam-5309	276	20	be	be	AUX
ejpam-5309	276	21	a	a	DET
ejpam-5309	276	22	nonempty	nonempty	ADJ
ejpam-5309	276	23	subset	subset	NOUN
ejpam-5309	276	24	of	of	ADP
ejpam-5309	276	25	t	t	PROPN
ejpam-5309	276	26	.	.	PUNCT
ejpam-5309	277	1	then	then	ADV
ejpam-5309	277	2	,	,	PUNCT
ejpam-5309	277	3	χa	χa	PROPN
ejpam-5309	277	4	µ	µ	PROPN
ejpam-5309	277	5	is	be	AUX
ejpam-5309	277	6	a	a	DET
ejpam-5309	277	7	strongest	strong	ADJ
ejpam-5309	277	8	fuzzy	fuzzy	ADJ
ejpam-5309	277	9	bi	bi	ADJ
ejpam-5309	277	10	-	-	ADJ
ejpam-5309	277	11	γ	γ	NOUN
ejpam-5309	277	12	-	-	NOUN
ejpam-5309	277	13	ideal	ideal	NOUN
ejpam-5309	277	14	on	on	ADP
ejpam-5309	277	15	t	t	PROPN
ejpam-5309	277	16	if	if	SCONJ
ejpam-5309	278	1	and	and	CCONJ
ejpam-5309	278	2	only	only	ADV
ejpam-5309	278	3	if	if	SCONJ
ejpam-5309	278	4	a	a	PRON
ejpam-5309	278	5	is	be	AUX
ejpam-5309	278	6	a	a	DET
ejpam-5309	278	7	bi	bi	ADJ
ejpam-5309	278	8	-	-	ADJ
ejpam-5309	278	9	γ	γ	NOUN
ejpam-5309	278	10	-	-	NOUN
ejpam-5309	278	11	ideal	ideal	NOUN
ejpam-5309	278	12	of	of	ADP
ejpam-5309	278	13	t	t	PROPN
ejpam-5309	278	14	.	.	PUNCT
ejpam-5309	279	1	references	reference	NOUN
ejpam-5309	279	2	1427	1427	NUM
ejpam-5309	279	3	4	4	NUM
ejpam-5309	279	4	.	.	PUNCT
ejpam-5309	279	5	conclusions	conclusion	NOUN
ejpam-5309	279	6	the	the	DET
ejpam-5309	279	7	concept	concept	NOUN
ejpam-5309	279	8	of	of	ADP
ejpam-5309	279	9	fuzzy	fuzzy	ADJ
ejpam-5309	279	10	relation	relation	NOUN
ejpam-5309	279	11	was	be	AUX
ejpam-5309	279	12	applied	apply	VERB
ejpam-5309	279	13	to	to	PART
ejpam-5309	279	14	define	define	VERB
ejpam-5309	279	15	the	the	DET
ejpam-5309	279	16	notions	notion	NOUN
ejpam-5309	279	17	of	of	ADP
ejpam-5309	279	18	strongest	strong	ADJ
ejpam-5309	279	19	fuzzy	fuzzy	ADJ
ejpam-5309	279	20	ternary	ternary	ADJ
ejpam-5309	279	21	γ	γ	NOUN
ejpam-5309	279	22	-	-	NOUN
ejpam-5309	279	23	subsemigroups	subsemigroup	NOUN
ejpam-5309	279	24	,	,	PUNCT
ejpam-5309	279	25	strongest	strong	ADJ
ejpam-5309	279	26	fuzzy	fuzzy	ADJ
ejpam-5309	279	27	(	(	PUNCT
ejpam-5309	279	28	resp	resp	NOUN
ejpam-5309	279	29	.	.	PUNCT
ejpam-5309	280	1	left	leave	VERB
ejpam-5309	280	2	,	,	PUNCT
ejpam-5309	280	3	right	right	ADJ
ejpam-5309	280	4	,	,	PUNCT
ejpam-5309	280	5	lateral	lateral	ADJ
ejpam-5309	280	6	)	)	PUNCT
ejpam-5309	280	7	γ	γ	NOUN
ejpam-5309	280	8	-	-	NOUN
ejpam-5309	280	9	ideals	ideal	NOUN
ejpam-5309	280	10	,	,	PUNCT
ejpam-5309	280	11	and	and	CCONJ
ejpam-5309	280	12	strongest	strong	ADJ
ejpam-5309	280	13	fuzzy	fuzzy	ADJ
ejpam-5309	280	14	bi	bi	ADJ
ejpam-5309	280	15	-	-	ADJ
ejpam-5309	280	16	γ	γ	NOUN
ejpam-5309	280	17	-	-	PUNCT
ejpam-5309	280	18	ideals	ideal	NOUN
ejpam-5309	280	19	on	on	ADP
ejpam-5309	280	20	ternary	ternary	ADJ
ejpam-5309	280	21	γ	γ	NOUN
ejpam-5309	280	22	-	-	PUNCT
ejpam-5309	280	23	semigroups	semigroup	NOUN
ejpam-5309	280	24	.	.	PUNCT
ejpam-5309	281	1	following	follow	VERB
ejpam-5309	281	2	this	this	PRON
ejpam-5309	281	3	,	,	PUNCT
ejpam-5309	281	4	we	we	PRON
ejpam-5309	281	5	investigated	investigate	VERB
ejpam-5309	281	6	the	the	DET
ejpam-5309	281	7	connections	connection	NOUN
ejpam-5309	281	8	of	of	ADP
ejpam-5309	281	9	these	these	DET
ejpam-5309	281	10	concepts	concept	NOUN
ejpam-5309	281	11	that	that	SCONJ
ejpam-5309	281	12	every	every	DET
ejpam-5309	281	13	strongest	strong	ADJ
ejpam-5309	281	14	fuzzy	fuzzy	ADJ
ejpam-5309	281	15	(	(	PUNCT
ejpam-5309	281	16	resp	resp	NOUN
ejpam-5309	281	17	.	.	PUNCT
ejpam-5309	282	1	left	leave	VERB
ejpam-5309	282	2	,	,	PUNCT
ejpam-5309	282	3	right	right	ADJ
ejpam-5309	282	4	,	,	PUNCT
ejpam-5309	282	5	lateral	lateral	ADJ
ejpam-5309	282	6	)	)	PUNCT
ejpam-5309	282	7	γ	γ	NOUN
ejpam-5309	282	8	-	-	PUNCT
ejpam-5309	282	9	ideal	ideal	NOUN
ejpam-5309	282	10	is	be	AUX
ejpam-5309	282	11	also	also	ADV
ejpam-5309	282	12	a	a	DET
ejpam-5309	282	13	strongest	strong	ADJ
ejpam-5309	282	14	fuzzy	fuzzy	ADJ
ejpam-5309	282	15	bi	bi	ADJ
ejpam-5309	282	16	-	-	ADJ
ejpam-5309	282	17	γ	γ	NOUN
ejpam-5309	282	18	-	-	PUNCT
ejpam-5309	282	19	ideal	ideal	NOUN
ejpam-5309	282	20	,	,	PUNCT
ejpam-5309	282	21	while	while	SCONJ
ejpam-5309	282	22	every	every	DET
ejpam-5309	282	23	strongest	strong	ADJ
ejpam-5309	282	24	fuzzy	fuzzy	ADJ
ejpam-5309	282	25	bi	bi	ADJ
ejpam-5309	282	26	-	-	ADJ
ejpam-5309	282	27	γ	γ	NOUN
ejpam-5309	282	28	-	-	PUNCT
ejpam-5309	282	29	ideal	ideal	NOUN
ejpam-5309	282	30	is	be	AUX
ejpam-5309	282	31	also	also	ADV
ejpam-5309	282	32	a	a	DET
ejpam-5309	282	33	strongest	strong	ADJ
ejpam-5309	282	34	fuzzy	fuzzy	ADJ
ejpam-5309	282	35	ternary	ternary	ADJ
ejpam-5309	282	36	γ	γ	NOUN
ejpam-5309	282	37	-	-	NOUN
ejpam-5309	282	38	subsemigroup	subsemigroup	NOUN
ejpam-5309	282	39	on	on	ADP
ejpam-5309	282	40	a	a	DET
ejpam-5309	282	41	ternary	ternary	ADJ
ejpam-5309	282	42	γ	γ	NOUN
ejpam-5309	282	43	-	-	PUNCT
ejpam-5309	282	44	semigroup	semigroup	NOUN
ejpam-5309	282	45	.	.	PUNCT
ejpam-5309	283	1	in	in	ADP
ejpam-5309	283	2	addition	addition	NOUN
ejpam-5309	283	3	,	,	PUNCT
ejpam-5309	283	4	as	as	SCONJ
ejpam-5309	283	5	example	example	NOUN
ejpam-5309	283	6	1	1	NUM
ejpam-5309	283	7	and	and	CCONJ
ejpam-5309	283	8	example	example	NOUN
ejpam-5309	283	9	2	2	NUM
ejpam-5309	283	10	indicate	indicate	VERB
ejpam-5309	283	11	,	,	PUNCT
ejpam-5309	283	12	the	the	DET
ejpam-5309	283	13	converses	converse	NOUN
ejpam-5309	283	14	of	of	ADP
ejpam-5309	283	15	the	the	DET
ejpam-5309	283	16	above	above	ADJ
ejpam-5309	283	17	mentioned	mention	VERB
ejpam-5309	283	18	relationships	relationship	NOUN
ejpam-5309	283	19	are	be	AUX
ejpam-5309	283	20	not	not	PART
ejpam-5309	283	21	true	true	ADJ
ejpam-5309	283	22	.	.	PUNCT
ejpam-5309	284	1	after	after	ADP
ejpam-5309	284	2	that	that	PRON
ejpam-5309	284	3	,	,	PUNCT
ejpam-5309	284	4	we	we	PRON
ejpam-5309	284	5	studied	study	VERB
ejpam-5309	284	6	the	the	DET
ejpam-5309	284	7	links	link	NOUN
ejpam-5309	284	8	between	between	ADP
ejpam-5309	284	9	different	different	ADJ
ejpam-5309	284	10	types	type	NOUN
ejpam-5309	284	11	of	of	ADP
ejpam-5309	284	12	fuzzy	fuzzy	ADJ
ejpam-5309	284	13	γ	γ	NOUN
ejpam-5309	284	14	-	-	NOUN
ejpam-5309	284	15	ideals	ideal	NOUN
ejpam-5309	284	16	of	of	ADP
ejpam-5309	284	17	ternary	ternary	ADJ
ejpam-5309	284	18	γ	γ	NOUN
ejpam-5309	284	19	-	-	PUNCT
ejpam-5309	284	20	semigroups	semigroup	NOUN
ejpam-5309	284	21	and	and	CCONJ
ejpam-5309	284	22	their	their	PRON
ejpam-5309	284	23	respective	respective	ADJ
ejpam-5309	284	24	types	type	NOUN
ejpam-5309	284	25	of	of	ADP
ejpam-5309	284	26	strongest	strong	ADJ
ejpam-5309	284	27	fuzzy	fuzzy	ADJ
ejpam-5309	284	28	γ	γ	NOUN
ejpam-5309	284	29	-	-	NOUN
ejpam-5309	284	30	ideals	ideal	NOUN
ejpam-5309	284	31	on	on	ADP
ejpam-5309	284	32	ternary	ternary	ADJ
ejpam-5309	284	33	γ	γ	NOUN
ejpam-5309	284	34	-	-	PUNCT
ejpam-5309	284	35	semigroups	semigroup	NOUN
ejpam-5309	284	36	,	,	PUNCT
ejpam-5309	284	37	which	which	PRON
ejpam-5309	284	38	occurred	occur	VERB
ejpam-5309	284	39	in	in	ADP
ejpam-5309	284	40	theorem	theorem	ADJ
ejpam-5309	284	41	1	1	NUM
ejpam-5309	284	42	,	,	PUNCT
ejpam-5309	284	43	theorem	theorem	ADJ
ejpam-5309	284	44	2	2	NUM
ejpam-5309	284	45	,	,	PUNCT
ejpam-5309	284	46	and	and	CCONJ
ejpam-5309	284	47	theorem	theorem	VERB
ejpam-5309	284	48	3	3	NUM
ejpam-5309	284	49	.	.	PUNCT
ejpam-5309	284	50	finally	finally	ADV
ejpam-5309	284	51	,	,	PUNCT
ejpam-5309	284	52	the	the	DET
ejpam-5309	284	53	characterizations	characterization	NOUN
ejpam-5309	284	54	of	of	ADP
ejpam-5309	284	55	strongest	strong	ADJ
ejpam-5309	284	56	fuzzy	fuzzy	ADJ
ejpam-5309	284	57	ternary	ternary	ADJ
ejpam-5309	284	58	γ	γ	NOUN
ejpam-5309	284	59	-	-	NOUN
ejpam-5309	284	60	subsemigroups	subsemigroup	NOUN
ejpam-5309	284	61	,	,	PUNCT
ejpam-5309	284	62	strongest	strong	ADJ
ejpam-5309	284	63	fuzzy	fuzzy	ADJ
ejpam-5309	284	64	(	(	PUNCT
ejpam-5309	284	65	resp	resp	NOUN
ejpam-5309	284	66	.	.	PUNCT
ejpam-5309	285	1	left	leave	VERB
ejpam-5309	285	2	,	,	PUNCT
ejpam-5309	285	3	right	right	ADJ
ejpam-5309	285	4	,	,	PUNCT
ejpam-5309	285	5	lateral	lateral	ADJ
ejpam-5309	285	6	)	)	PUNCT
ejpam-5309	285	7	γ	γ	NOUN
ejpam-5309	285	8	-	-	NOUN
ejpam-5309	285	9	ideals	ideal	NOUN
ejpam-5309	285	10	,	,	PUNCT
ejpam-5309	285	11	and	and	CCONJ
ejpam-5309	285	12	strongest	strong	ADJ
ejpam-5309	285	13	fuzzy	fuzzy	ADJ
ejpam-5309	285	14	bi	bi	ADJ
ejpam-5309	285	15	-	-	ADJ
ejpam-5309	285	16	γ	γ	NOUN
ejpam-5309	285	17	-	-	PUNCT
ejpam-5309	285	18	ideals	ideal	NOUN
ejpam-5309	285	19	on	on	ADP
ejpam-5309	285	20	ternary	ternary	ADJ
ejpam-5309	285	21	γ	γ	X
ejpam-5309	285	22	-	-	PUNCT
ejpam-5309	285	23	semigroups	semigroup	NOUN
ejpam-5309	285	24	by	by	ADP
ejpam-5309	285	25	the	the	DET
ejpam-5309	285	26	various	various	ADJ
ejpam-5309	285	27	types	type	NOUN
ejpam-5309	285	28	if	if	SCONJ
ejpam-5309	285	29	their	their	PRON
ejpam-5309	285	30	level	level	NOUN
ejpam-5309	285	31	subsets	subset	NOUN
ejpam-5309	285	32	in	in	ADP
ejpam-5309	285	33	ternary	ternary	ADJ
ejpam-5309	285	34	γ	γ	NOUN
ejpam-5309	285	35	-	-	PUNCT
ejpam-5309	285	36	semigroups	semigroup	NOUN
ejpam-5309	285	37	are	be	AUX
ejpam-5309	285	38	presented	present	VERB
ejpam-5309	285	39	in	in	ADP
ejpam-5309	285	40	theorem	theorem	ADJ
ejpam-5309	285	41	4	4	NUM
ejpam-5309	285	42	,	,	PUNCT
ejpam-5309	285	43	theorem	theorem	VERB
ejpam-5309	285	44	5	5	NUM
ejpam-5309	285	45	,	,	PUNCT
ejpam-5309	285	46	and	and	CCONJ
ejpam-5309	285	47	theorem	theorem	VERB
ejpam-5309	285	48	6	6	NUM
ejpam-5309	285	49	.	.	PUNCT
ejpam-5309	286	1	future	future	ADJ
ejpam-5309	286	2	studies	study	NOUN
ejpam-5309	286	3	will	will	AUX
ejpam-5309	286	4	be	be	AUX
ejpam-5309	286	5	possible	possible	ADJ
ejpam-5309	286	6	to	to	PART
ejpam-5309	286	7	investigate	investigate	VERB
ejpam-5309	286	8	some	some	DET
ejpam-5309	286	9	decompositions	decomposition	NOUN
ejpam-5309	286	10	of	of	ADP
ejpam-5309	286	11	many	many	ADJ
ejpam-5309	286	12	types	type	NOUN
ejpam-5309	286	13	of	of	ADP
ejpam-5309	286	14	strongest	strong	ADJ
ejpam-5309	286	15	fuzzy	fuzzy	ADJ
ejpam-5309	286	16	γ	γ	NOUN
ejpam-5309	286	17	-	-	NOUN
ejpam-5309	286	18	ideals	ideal	NOUN
ejpam-5309	286	19	on	on	ADP
ejpam-5309	286	20	ordered	order	VERB
ejpam-5309	286	21	ternary	ternary	ADJ
ejpam-5309	286	22	γ	γ	NOUN
ejpam-5309	286	23	-	-	PUNCT
ejpam-5309	286	24	semigroups	semigroup	NOUN
ejpam-5309	286	25	or	or	CCONJ
ejpam-5309	286	26	other	other	ADJ
ejpam-5309	286	27	algebraic	algebraic	ADJ
ejpam-5309	286	28	structures	structure	NOUN
ejpam-5309	286	29	.	.	PUNCT
ejpam-5309	287	1	acknowledgements	acknowledgement	NOUN
ejpam-5309	287	2	this	this	DET
ejpam-5309	287	3	research	research	NOUN
ejpam-5309	287	4	project	project	NOUN
ejpam-5309	287	5	was	be	AUX
ejpam-5309	287	6	financially	financially	ADV
ejpam-5309	287	7	supported	support	VERB
ejpam-5309	287	8	by	by	ADP
ejpam-5309	287	9	mahasarakham	mahasarakham	PROPN
ejpam-5309	287	10	university	university	PROPN
ejpam-5309	287	11	.	.	PUNCT
ejpam-5309	288	1	references	reference	NOUN
ejpam-5309	288	2	[	[	X
ejpam-5309	288	3	1	1	NUM
ejpam-5309	288	4	]	]	PUNCT
ejpam-5309	288	5	a.	a.	PROPN
ejpam-5309	288	6	ali	ali	PROPN
ejpam-5309	288	7	,	,	PUNCT
ejpam-5309	288	8	m.	m.	PROPN
ejpam-5309	288	9	y.	y.	PROPN
ejpam-5309	288	10	abbasi	abbasi	PROPN
ejpam-5309	288	11	,	,	PUNCT
ejpam-5309	288	12	and	and	CCONJ
ejpam-5309	288	13	s.	s.	PROPN
ejpam-5309	288	14	ali	ali	PROPN
ejpam-5309	288	15	khan	khan	PROPN
ejpam-5309	288	16	.	.	PUNCT
ejpam-5309	289	1	a	a	DET
ejpam-5309	289	2	note	note	NOUN
ejpam-5309	289	3	on	on	ADP
ejpam-5309	289	4	generalized	generalized	ADJ
ejpam-5309	289	5	po	po	NOUN
ejpam-5309	289	6	-	-	ADJ
ejpam-5309	289	7	bi	bi	ADJ
ejpam-5309	289	8	-	-	ADJ
ejpam-5309	289	9	quasi	quasi	ADJ
ejpam-5309	289	10	γ	γ	NOUN
ejpam-5309	289	11	-	-	NOUN
ejpam-5309	289	12	ideals	ideal	NOUN
ejpam-5309	289	13	in	in	ADP
ejpam-5309	289	14	po	po	NOUN
ejpam-5309	289	15	-	-	ADJ
ejpam-5309	289	16	bi	bi	ADJ
ejpam-5309	289	17	-	-	ADJ
ejpam-5309	289	18	ternary	ternary	ADJ
ejpam-5309	289	19	γ	γ	NOUN
ejpam-5309	289	20	-	-	PUNCT
ejpam-5309	289	21	semigroups	semigroup	NOUN
ejpam-5309	289	22	.	.	PUNCT
ejpam-5309	290	1	aip	aip	PROPN
ejpam-5309	290	2	conference	conference	NOUN
ejpam-5309	290	3	proceedings	proceeding	NOUN
ejpam-5309	290	4	,	,	PUNCT
ejpam-5309	290	5	2061:02005	2061:02005	NUM
ejpam-5309	290	6	,	,	PUNCT
ejpam-5309	290	7	2019	2019	NUM
ejpam-5309	290	8	.	.	PUNCT
ejpam-5309	291	1	[	[	X
ejpam-5309	291	2	2	2	X
ejpam-5309	291	3	]	]	X
ejpam-5309	291	4	y.	y.	NOUN
ejpam-5309	291	5	bhargavi	bhargavi	PROPN
ejpam-5309	291	6	,	,	PUNCT
ejpam-5309	291	7	t.	t.	PROPN
ejpam-5309	291	8	eswarlal	eswarlal	PROPN
ejpam-5309	291	9	,	,	PUNCT
ejpam-5309	291	10	and	and	CCONJ
ejpam-5309	291	11	s.	s.	PROPN
ejpam-5309	291	12	ragamayi	ragamayi	PROPN
ejpam-5309	291	13	.	.	PUNCT
ejpam-5309	292	1	cartesian	cartesian	ADJ
ejpam-5309	292	2	product	product	NOUN
ejpam-5309	292	3	on	on	ADP
ejpam-5309	292	4	fuzzy	fuzzy	ADJ
ejpam-5309	292	5	ideals	ideal	NOUN
ejpam-5309	292	6	of	of	ADP
ejpam-5309	292	7	a	a	DET
ejpam-5309	292	8	ternary	ternary	ADJ
ejpam-5309	292	9	γ	γ	NOUN
ejpam-5309	292	10	-	-	PUNCT
ejpam-5309	292	11	semigroup	semigroup	NOUN
ejpam-5309	292	12	.	.	PUNCT
ejpam-5309	293	1	advance	advance	NOUN
ejpam-5309	293	2	in	in	ADP
ejpam-5309	293	3	mathematics	mathematic	NOUN
ejpam-5309	293	4	:	:	PUNCT
ejpam-5309	293	5	scientific	scientific	ADJ
ejpam-5309	293	6	journal	journal	NOUN
ejpam-5309	293	7	,	,	PUNCT
ejpam-5309	293	8	9(3):1197–1203	9(3):1197–1203	PROPN
ejpam-5309	293	9	,	,	PUNCT
ejpam-5309	293	10	2020	2020	NUM
ejpam-5309	293	11	.	.	PUNCT
ejpam-5309	294	1	[	[	X
ejpam-5309	294	2	3	3	X
ejpam-5309	294	3	]	]	X
ejpam-5309	294	4	p.	p.	NOUN
ejpam-5309	294	5	bhattacharya	bhattacharya	PROPN
ejpam-5309	294	6	and	and	CCONJ
ejpam-5309	294	7	n.	n.	PROPN
ejpam-5309	294	8	p.	p.	PROPN
ejpam-5309	294	9	mukherjee	mukherjee	PROPN
ejpam-5309	294	10	.	.	PUNCT
ejpam-5309	295	1	fuzzy	fuzzy	ADJ
ejpam-5309	295	2	relations	relation	NOUN
ejpam-5309	295	3	and	and	CCONJ
ejpam-5309	295	4	fuzzy	fuzzy	ADJ
ejpam-5309	295	5	groups	group	NOUN
ejpam-5309	295	6	.	.	PUNCT
ejpam-5309	296	1	information	information	NOUN
ejpam-5309	296	2	sciences	sciences	PROPN
ejpam-5309	296	3	,	,	PUNCT
ejpam-5309	296	4	36(3):267–282	36(3):267–282	PROPN
ejpam-5309	296	5	,	,	PUNCT
ejpam-5309	296	6	1985	1985	NUM
ejpam-5309	296	7	.	.	PUNCT
ejpam-5309	297	1	[	[	X
ejpam-5309	297	2	4	4	X
ejpam-5309	297	3	]	]	X
ejpam-5309	297	4	b.	b.	PROPN
ejpam-5309	297	5	l.	l.	PROPN
ejpam-5309	297	6	derseh	derseh	PROPN
ejpam-5309	297	7	,	,	PUNCT
ejpam-5309	297	8	b.	b.	PROPN
ejpam-5309	297	9	a.	a.	PROPN
ejpam-5309	297	10	alaba	alaba	PROPN
ejpam-5309	297	11	,	,	PUNCT
ejpam-5309	297	12	and	and	CCONJ
ejpam-5309	297	13	y.	y.	PROPN
ejpam-5309	297	14	g.	g.	PROPN
ejpam-5309	297	15	wondifraw	wondifraw	PROPN
ejpam-5309	297	16	.	.	PUNCT
ejpam-5309	298	1	on	on	ADP
ejpam-5309	298	2	homomorphism	homomorphism	PROPN
ejpam-5309	298	3	and	and	CCONJ
ejpam-5309	298	4	cartesian	cartesian	ADJ
ejpam-5309	298	5	product	product	NOUN
ejpam-5309	298	6	of	of	ADP
ejpam-5309	298	7	intuitionistic	intuitionistic	ADJ
ejpam-5309	298	8	fuzzy	fuzzy	ADJ
ejpam-5309	298	9	pms	pm	NOUN
ejpam-5309	298	10	-	-	PUNCT
ejpam-5309	298	11	subalgebras	subalgebras	PROPN
ejpam-5309	298	12	of	of	ADP
ejpam-5309	298	13	a	a	DET
ejpam-5309	298	14	pms	pms	NOUN
ejpam-5309	298	15	-	-	PUNCT
ejpam-5309	298	16	algebra	algebra	NOUN
ejpam-5309	298	17	.	.	PUNCT
ejpam-5309	299	1	bulletin	bulletin	NOUN
ejpam-5309	299	2	of	of	ADP
ejpam-5309	299	3	the	the	DET
ejpam-5309	299	4	section	section	NOUN
ejpam-5309	299	5	of	of	ADP
ejpam-5309	299	6	logic	logic	NOUN
ejpam-5309	299	7	,	,	PUNCT
ejpam-5309	299	8	52(1):19–38	52(1):19–38	NUM
ejpam-5309	299	9	,	,	PUNCT
ejpam-5309	299	10	2023	2023	NUM
ejpam-5309	299	11	.	.	PUNCT
ejpam-5309	300	1	[	[	X
ejpam-5309	300	2	5	5	X
ejpam-5309	300	3	]	]	PUNCT
ejpam-5309	300	4	s.	s.	PROPN
ejpam-5309	300	5	m.	m.	PROPN
ejpam-5309	300	6	mostafa	mostafa	PROPN
ejpam-5309	300	7	,	,	PUNCT
ejpam-5309	300	8	m.	m.	PROPN
ejpam-5309	300	9	a.	a.	PROPN
ejpam-5309	300	10	abd	abd	PROPN
ejpam-5309	300	11	-	-	PUNCT
ejpam-5309	300	12	elnaby	elnaby	NOUN
ejpam-5309	300	13	,	,	PUNCT
ejpam-5309	300	14	and	and	CCONJ
ejpam-5309	300	15	m.	m.	NOUN
ejpam-5309	300	16	m.	m.	PROPN
ejpam-5309	300	17	m.	m.	PROPN
ejpam-5309	300	18	yousef	yousef	PROPN
ejpam-5309	300	19	.	.	PUNCT
ejpam-5309	301	1	fuzzy	fuzzy	ADJ
ejpam-5309	301	2	ideals	ideal	NOUN
ejpam-5309	301	3	of	of	ADP
ejpam-5309	301	4	ku	ku	PROPN
ejpam-5309	301	5	-	-	PUNCT
ejpam-5309	301	6	algebras	algebras	PROPN
ejpam-5309	301	7	.	.	PUNCT
ejpam-5309	302	1	international	international	PROPN
ejpam-5309	302	2	mathematical	mathematical	PROPN
ejpam-5309	302	3	forum	forum	PROPN
ejpam-5309	302	4	,	,	PUNCT
ejpam-5309	302	5	6(63):3139–3149	6(63):3139–3149	NUM
ejpam-5309	302	6	,	,	PUNCT
ejpam-5309	302	7	2011	2011	NUM
ejpam-5309	302	8	.	.	PUNCT
ejpam-5309	303	1	[	[	X
ejpam-5309	303	2	6	6	NUM
ejpam-5309	303	3	]	]	PUNCT
ejpam-5309	303	4	d.	d.	PROPN
ejpam-5309	303	5	madhusudhana	madhusudhana	PROPN
ejpam-5309	303	6	rao	rao	PROPN
ejpam-5309	303	7	,	,	PUNCT
ejpam-5309	303	8	m.	m.	NOUN
ejpam-5309	303	9	vasantha	vasantha	NOUN
ejpam-5309	303	10	,	,	PUNCT
ejpam-5309	303	11	and	and	CCONJ
ejpam-5309	303	12	m.	m.	PROPN
ejpam-5309	303	13	venkateswara	venkateswara	PROPN
ejpam-5309	303	14	rao	rao	PROPN
ejpam-5309	303	15	.	.	PUNCT
ejpam-5309	303	16	structure	structure	NOUN
ejpam-5309	303	17	and	and	CCONJ
ejpam-5309	303	18	study	study	NOUN
ejpam-5309	303	19	of	of	ADP
ejpam-5309	303	20	elements	element	NOUN
ejpam-5309	303	21	in	in	ADP
ejpam-5309	303	22	ternary	ternary	ADJ
ejpam-5309	303	23	γ	γ	X
ejpam-5309	303	24	-	-	PUNCT
ejpam-5309	303	25	semigroups	semigroup	NOUN
ejpam-5309	303	26	.	.	PUNCT
ejpam-5309	304	1	international	international	ADJ
ejpam-5309	304	2	journal	journal	NOUN
ejpam-5309	304	3	of	of	ADP
ejpam-5309	304	4	engineering	engineering	NOUN
ejpam-5309	304	5	research	research	NOUN
ejpam-5309	304	6	,	,	PUNCT
ejpam-5309	304	7	4(4):197–202	4(4):197–202	PROPN
ejpam-5309	304	8	,	,	PUNCT
ejpam-5309	304	9	2015	2015	NUM
ejpam-5309	304	10	.	.	PUNCT
ejpam-5309	305	1	references	reference	NOUN
ejpam-5309	305	2	1428	1428	NUM
ejpam-5309	305	3	[	[	X
ejpam-5309	305	4	7	7	NUM
ejpam-5309	305	5	]	]	PUNCT
ejpam-5309	305	6	m.	m.	NOUN
ejpam-5309	305	7	venkateswara	venkateswara	PROPN
ejpam-5309	305	8	rao	rao	PROPN
ejpam-5309	305	9	,	,	PUNCT
ejpam-5309	305	10	m.	m.	NOUN
ejpam-5309	305	11	vasantha	vasantha	NOUN
ejpam-5309	305	12	,	,	PUNCT
ejpam-5309	305	13	and	and	CCONJ
ejpam-5309	305	14	d.	d.	PROPN
ejpam-5309	305	15	madhusudhana	madhusudhana	PROPN
ejpam-5309	305	16	rao	rao	PROPN
ejpam-5309	305	17	.	.	PUNCT
ejpam-5309	306	1	a	a	DET
ejpam-5309	306	2	study	study	NOUN
ejpam-5309	306	3	on	on	ADP
ejpam-5309	306	4	pseudo	pseudo	NOUN
ejpam-5309	306	5	integral	integral	ADJ
ejpam-5309	306	6	ternary	ternary	ADJ
ejpam-5309	306	7	γ	γ	NOUN
ejpam-5309	306	8	-	-	PUNCT
ejpam-5309	306	9	semigroups	semigroup	NOUN
ejpam-5309	306	10	.	.	PUNCT
ejpam-5309	307	1	asian	asian	ADJ
ejpam-5309	307	2	journal	journal	PROPN
ejpam-5309	307	3	of	of	ADP
ejpam-5309	307	4	mathematics	mathematics	PROPN
ejpam-5309	307	5	and	and	CCONJ
ejpam-5309	307	6	computer	computer	NOUN
ejpam-5309	307	7	research	research	NOUN
ejpam-5309	307	8	,	,	PUNCT
ejpam-5309	307	9	10(2):196–202	10(2):196–202	PROPN
ejpam-5309	307	10	,	,	PUNCT
ejpam-5309	307	11	2016	2016	NUM
ejpam-5309	307	12	.	.	PUNCT
ejpam-5309	308	1	[	[	X
ejpam-5309	308	2	8	8	NUM
ejpam-5309	308	3	]	]	PUNCT
ejpam-5309	308	4	m.	m.	NOUN
ejpam-5309	308	5	vasantha	vasantha	NOUN
ejpam-5309	308	6	and	and	CCONJ
ejpam-5309	308	7	d.	d.	PROPN
ejpam-5309	308	8	madhusudhana	madhusudhana	PROPN
ejpam-5309	308	9	rao	rao	PROPN
ejpam-5309	308	10	.	.	PUNCT
ejpam-5309	309	1	properties	property	NOUN
ejpam-5309	309	2	of	of	ADP
ejpam-5309	309	3	prime	prime	ADJ
ejpam-5309	309	4	ternary	ternary	ADJ
ejpam-5309	309	5	γ	γ	X
ejpam-5309	309	6	-	-	PUNCT
ejpam-5309	309	7	semigroups	semigroup	NOUN
ejpam-5309	309	8	.	.	PUNCT
ejpam-5309	310	1	global	global	ADJ
ejpam-5309	310	2	journal	journal	PROPN
ejpam-5309	310	3	of	of	ADP
ejpam-5309	310	4	pure	pure	ADJ
ejpam-5309	310	5	and	and	CCONJ
ejpam-5309	310	6	applied	applied	ADJ
ejpam-5309	310	7	mathematics	mathematic	NOUN
ejpam-5309	310	8	,	,	PUNCT
ejpam-5309	310	9	11(6):4255–4271	11(6):4255–4271	NUM
ejpam-5309	310	10	,	,	PUNCT
ejpam-5309	310	11	2015	2015	NUM
ejpam-5309	310	12	.	.	PUNCT
ejpam-5309	311	1	[	[	X
ejpam-5309	311	2	9	9	NUM
ejpam-5309	311	3	]	]	PUNCT
ejpam-5309	311	4	m.	m.	NOUN
ejpam-5309	311	5	vasantha	vasantha	NOUN
ejpam-5309	311	6	,	,	PUNCT
ejpam-5309	311	7	d.	d.	PROPN
ejpam-5309	311	8	madhusudhana	madhusudhana	PROPN
ejpam-5309	311	9	rao	rao	PROPN
ejpam-5309	311	10	,	,	PUNCT
ejpam-5309	311	11	p.	p.	PROPN
ejpam-5309	311	12	s.	s.	PROPN
ejpam-5309	311	13	prasad	prasad	PROPN
ejpam-5309	311	14	,	,	PUNCT
ejpam-5309	311	15	b.	b.	PROPN
ejpam-5309	311	16	s.	s.	PROPN
ejpam-5309	311	17	kunmar	kunmar	PROPN
ejpam-5309	311	18	,	,	PUNCT
ejpam-5309	311	19	and	and	CCONJ
ejpam-5309	311	20	t.	t.	PROPN
ejpam-5309	311	21	satish	satish	PROPN
ejpam-5309	311	22	.	.	PUNCT
ejpam-5309	312	1	on	on	ADP
ejpam-5309	312	2	γ	γ	PROPN
ejpam-5309	312	3	-	-	PUNCT
ejpam-5309	312	4	ts	ts	NOUN
ejpam-5309	312	5	-	-	PUNCT
ejpam-5309	312	6	acts	act	NOUN
ejpam-5309	312	7	over	over	ADP
ejpam-5309	312	8	ternary	ternary	ADJ
ejpam-5309	312	9	γ	γ	X
ejpam-5309	312	10	-	-	PUNCT
ejpam-5309	312	11	semigroups	semigroup	NOUN
ejpam-5309	312	12	.	.	PUNCT
ejpam-5309	313	1	international	international	ADJ
ejpam-5309	313	2	journal	journal	NOUN
ejpam-5309	313	3	of	of	ADP
ejpam-5309	313	4	engineering	engineering	PROPN
ejpam-5309	313	5	&	&	CCONJ
ejpam-5309	313	6	technology	technology	PROPN
ejpam-5309	313	7	,	,	PUNCT
ejpam-5309	313	8	7(4.10):812–815	7(4.10):812–815	NOUN
ejpam-5309	313	9	,	,	PUNCT
ejpam-5309	313	10	2018	2018	NUM
ejpam-5309	313	11	.	.	PUNCT
ejpam-5309	314	1	[	[	X
ejpam-5309	314	2	10	10	NUM
ejpam-5309	314	3	]	]	PUNCT
ejpam-5309	314	4	m.	m.	NOUN
ejpam-5309	314	5	vasantha	vasantha	NOUN
ejpam-5309	314	6	,	,	PUNCT
ejpam-5309	314	7	d.	d.	PROPN
ejpam-5309	314	8	madhusudhana	madhusudhana	PROPN
ejpam-5309	314	9	rao	rao	PROPN
ejpam-5309	314	10	,	,	PUNCT
ejpam-5309	314	11	and	and	CCONJ
ejpam-5309	314	12	m.	m.	PROPN
ejpam-5309	314	13	venkateswara	venkateswara	PROPN
ejpam-5309	314	14	rao	rao	PROPN
ejpam-5309	314	15	.	.	PUNCT
ejpam-5309	315	1	structure	structure	NOUN
ejpam-5309	315	2	of	of	ADP
ejpam-5309	315	3	simple	simple	ADJ
ejpam-5309	315	4	ternary	ternary	ADJ
ejpam-5309	315	5	γ	γ	NOUN
ejpam-5309	315	6	-	-	PUNCT
ejpam-5309	315	7	semigroup	semigroup	NOUN
ejpam-5309	315	8	.	.	PUNCT
ejpam-5309	316	1	american	american	PROPN
ejpam-5309	316	2	international	international	PROPN
ejpam-5309	316	3	journal	journal	PROPN
ejpam-5309	316	4	of	of	ADP
ejpam-5309	316	5	research	research	NOUN
ejpam-5309	316	6	in	in	ADP
ejpam-5309	316	7	science	science	NOUN
ejpam-5309	316	8	,	,	PUNCT
ejpam-5309	316	9	technology	technology	NOUN
ejpam-5309	316	10	,	,	PUNCT
ejpam-5309	316	11	engineering	engineering	NOUN
ejpam-5309	316	12	&	&	CCONJ
ejpam-5309	316	13	mathematics	mathematic	NOUN
ejpam-5309	316	14	,	,	PUNCT
ejpam-5309	316	15	10(1):79–84	10(1):79–84	NUM
ejpam-5309	316	16	,	,	PUNCT
ejpam-5309	316	17	2015	2015	NUM
ejpam-5309	316	18	.	.	PUNCT
ejpam-5309	317	1	[	[	X
ejpam-5309	317	2	11	11	NUM
ejpam-5309	317	3	]	]	PUNCT
ejpam-5309	317	4	m.	m.	NOUN
ejpam-5309	317	5	vasantha	vasantha	NOUN
ejpam-5309	317	6	,	,	PUNCT
ejpam-5309	317	7	d.	d.	PROPN
ejpam-5309	317	8	madhusudhana	madhusudhana	PROPN
ejpam-5309	317	9	rao	rao	PROPN
ejpam-5309	317	10	,	,	PUNCT
ejpam-5309	317	11	and	and	CCONJ
ejpam-5309	317	12	t.	t.	PROPN
ejpam-5309	317	13	satish	satish	PROPN
ejpam-5309	317	14	.	.	PUNCT
ejpam-5309	318	1	on	on	ADP
ejpam-5309	318	2	trio	trio	NOUN
ejpam-5309	318	3	ternary	ternary	ADJ
ejpam-5309	318	4	γ	γ	PROPN
ejpam-5309	318	5	-	-	PUNCT
ejpam-5309	318	6	semigroups	semigroup	NOUN
ejpam-5309	318	7	.	.	PUNCT
ejpam-5309	319	1	international	international	ADJ
ejpam-5309	319	2	journal	journal	NOUN
ejpam-5309	319	3	of	of	ADP
ejpam-5309	319	4	engineering	engineering	PROPN
ejpam-5309	319	5	&	&	CCONJ
ejpam-5309	319	6	technology	technology	NOUN
ejpam-5309	319	7	,	,	PUNCT
ejpam-5309	319	8	7(3.31):157–159	7(3.31):157–159	NUM
ejpam-5309	319	9	,	,	PUNCT
ejpam-5309	319	10	2018	2018	NUM
ejpam-5309	319	11	.	.	PUNCT
ejpam-5309	320	1	[	[	X
ejpam-5309	320	2	12	12	NUM
ejpam-5309	320	3	]	]	X
ejpam-5309	320	4	c.	c.	PROPN
ejpam-5309	320	5	yamini	yamini	PROPN
ejpam-5309	320	6	and	and	CCONJ
ejpam-5309	320	7	s.	s.	PROPN
ejpam-5309	320	8	kailasavalli	kailasavalli	PROPN
ejpam-5309	320	9	.	.	PUNCT
ejpam-5309	321	1	fuzzy	fuzzy	ADJ
ejpam-5309	321	2	b	b	X
ejpam-5309	321	3	-	-	PUNCT
ejpam-5309	321	4	ideals	ideal	NOUN
ejpam-5309	321	5	on	on	ADP
ejpam-5309	321	6	b	b	NOUN
ejpam-5309	321	7	-	-	PUNCT
ejpam-5309	321	8	algebras	algebras	PROPN
ejpam-5309	321	9	.	.	PUNCT
ejpam-5309	322	1	international	international	ADJ
ejpam-5309	322	2	journal	journal	PROPN
ejpam-5309	322	3	of	of	ADP
ejpam-5309	322	4	mathematical	mathematical	ADJ
ejpam-5309	322	5	archive	archive	NOUN
ejpam-5309	322	6	,	,	PUNCT
ejpam-5309	322	7	5(2):227–233	5(2):227–233	NUM
ejpam-5309	322	8	,	,	PUNCT
ejpam-5309	322	9	2014	2014	NUM
ejpam-5309	322	10	.	.	PUNCT
ejpam-5309	323	1	[	[	X
ejpam-5309	323	2	13	13	NUM
ejpam-5309	323	3	]	]	PUNCT
ejpam-5309	323	4	l.	l.	PROPN
ejpam-5309	323	5	zadeh	zadeh	PROPN
ejpam-5309	323	6	.	.	PUNCT
ejpam-5309	323	7	fuzzy	fuzzy	ADJ
ejpam-5309	323	8	sets	set	NOUN
ejpam-5309	323	9	.	.	PUNCT
ejpam-5309	324	1	information	information	NOUN
ejpam-5309	324	2	and	and	CCONJ
ejpam-5309	324	3	control	control	NOUN
ejpam-5309	324	4	,	,	PUNCT
ejpam-5309	324	5	8(3):338–353	8(3):338–353	NUM
ejpam-5309	324	6	,	,	PUNCT
ejpam-5309	324	7	1965	1965	NUM
ejpam-5309	324	8	.	.	PUNCT