id	sid	tid	token	lemma	pos
ijassa-1111	1	1	microsoft	microsoft	PROPN
ijassa-1111	1	2	word	word	PROPN
ijassa-1111	1	3	1111	1111	NUM
ijassa-1111	1	4	-	-	PUNCT
ijassa-1111	1	5	article	article	NOUN
ijassa-1111	1	6	text-7257	text-7257	NOUN
ijassa-1111	1	7	-	-	SYM
ijassa-1111	1	8	1	1	NUM
ijassa-1111	1	9	-	-	PUNCT
ijassa-1111	1	10	6	6	NUM
ijassa-1111	1	11	-	-	PUNCT
ijassa-1111	1	12	20220131	20220131	NUM
ijassa-1111	1	13	adv	adv	PROPN
ijassa-1111	1	14	syst	syst	PROPN
ijassa-1111	1	15	sci	sci	PROPN
ijassa-1111	1	16	appl	appl	PROPN
ijassa-1111	1	17	2024	2024	NUM
ijassa-1111	1	18	;	;	PUNCT
ijassa-1111	1	19	03	03	NUM
ijassa-1111	1	20	;	;	PUNCT
ijassa-1111	1	21	104	104	NUM
ijassa-1111	1	22	-	-	SYM
ijassa-1111	1	23	113	113	NUM
ijassa-1111	1	24	published	publish	VERB
ijassa-1111	1	25	online	online	ADV
ijassa-1111	1	26	at	at	ADP
ijassa-1111	1	27	https://ijassa.ipu.ru	https://ijassa.ipu.ru	ADV
ijassa-1111	1	28	.	.	PUNCT
ijassa-1111	2	1	the	the	DET
ijassa-1111	2	2	approximation	approximation	NOUN
ijassa-1111	2	3	matrix	matrix	NOUN
ijassa-1111	2	4	method	method	NOUN
ijassa-1111	2	5	and	and	CCONJ
ijassa-1111	2	6	its	its	PRON
ijassa-1111	2	7	comparison	comparison	NOUN
ijassa-1111	2	8	with	with	ADP
ijassa-1111	2	9	the	the	DET
ijassa-1111	2	10	analytical	analytical	ADJ
ijassa-1111	2	11	hierarchy	hierarchy	NOUN
ijassa-1111	2	12	process	process	NOUN
ijassa-1111	2	13	by	by	ADP
ijassa-1111	2	14	t.	t.	PROPN
ijassa-1111	2	15	saaty	saaty	PROPN
ijassa-1111	2	16	viktor	viktor	NOUN
ijassa-1111	2	17	p.	p.	NOUN
ijassa-1111	2	18	korneenko	korneenko	PROPN
ijassa-1111	3	1	v.a	v.a	PROPN
ijassa-1111	3	2	.	.	PROPN
ijassa-1111	3	3	trapeznikov	trapeznikov	PROPN
ijassa-1111	3	4	institute	institute	PROPN
ijassa-1111	3	5	of	of	ADP
ijassa-1111	3	6	control	control	PROPN
ijassa-1111	3	7	sciences	sciences	PROPN
ijassa-1111	3	8	of	of	ADP
ijassa-1111	3	9	the	the	DET
ijassa-1111	3	10	russian	russian	ADJ
ijassa-1111	3	11	academy	academy	PROPN
ijassa-1111	3	12	of	of	ADP
ijassa-1111	3	13	sciences	sciences	PROPN
ijassa-1111	3	14	,	,	PUNCT
ijassa-1111	3	15	moscow	moscow	PROPN
ijassa-1111	3	16	,	,	PUNCT
ijassa-1111	3	17	russia	russia	PROPN
ijassa-1111	3	18	e	e	NOUN
ijassa-1111	3	19	-	-	NOUN
ijassa-1111	3	20	mail	mail	NOUN
ijassa-1111	3	21	:	:	PUNCT
ijassa-1111	3	22	vkorn@ipu.ru	vkorn@ipu.ru	DET
ijassa-1111	3	23	abstract	abstract	NOUN
ijassa-1111	3	24	:	:	PUNCT
ijassa-1111	3	25	the	the	DET
ijassa-1111	3	26	article	article	NOUN
ijassa-1111	3	27	presents	present	VERB
ijassa-1111	3	28	an	an	DET
ijassa-1111	3	29	optimization	optimization	NOUN
ijassa-1111	3	30	method	method	NOUN
ijassa-1111	3	31	for	for	ADP
ijassa-1111	3	32	the	the	DET
ijassa-1111	3	33	formation	formation	NOUN
ijassa-1111	3	34	of	of	ADP
ijassa-1111	3	35	quantitative	quantitative	ADJ
ijassa-1111	3	36	weights	weight	NOUN
ijassa-1111	3	37	of	of	ADP
ijassa-1111	3	38	objects	object	NOUN
ijassa-1111	3	39	(	(	PUNCT
ijassa-1111	3	40	importance	importance	NOUN
ijassa-1111	3	41	of	of	ADP
ijassa-1111	3	42	criteria	criterion	NOUN
ijassa-1111	3	43	,	,	PUNCT
ijassa-1111	3	44	priorities	priority	NOUN
ijassa-1111	3	45	of	of	ADP
ijassa-1111	3	46	alternatives	alternative	NOUN
ijassa-1111	3	47	)	)	PUNCT
ijassa-1111	3	48	according	accord	VERB
ijassa-1111	3	49	to	to	ADP
ijassa-1111	3	50	the	the	DET
ijassa-1111	3	51	initial	initial	ADJ
ijassa-1111	3	52	expert	expert	NOUN
ijassa-1111	3	53	judgment	judgment	NOUN
ijassa-1111	3	54	matrix	matrix	NOUN
ijassa-1111	3	55	in	in	ADP
ijassa-1111	3	56	multi	multi	ADJ
ijassa-1111	3	57	-	-	ADJ
ijassa-1111	3	58	criteria	criterion	NOUN
ijassa-1111	3	59	selection	selection	NOUN
ijassa-1111	3	60	problems	problem	NOUN
ijassa-1111	3	61	.	.	PUNCT
ijassa-1111	4	1	since	since	SCONJ
ijassa-1111	4	2	the	the	DET
ijassa-1111	4	3	matrix	matrix	NOUN
ijassa-1111	4	4	of	of	ADP
ijassa-1111	4	5	pairwise	pairwise	NOUN
ijassa-1111	4	6	comparisons	comparison	NOUN
ijassa-1111	4	7	can	can	AUX
ijassa-1111	4	8	be	be	AUX
ijassa-1111	4	9	considered	consider	VERB
ijassa-1111	4	10	as	as	ADP
ijassa-1111	4	11	some	some	DET
ijassa-1111	4	12	perturbation	perturbation	NOUN
ijassa-1111	4	13	of	of	ADP
ijassa-1111	4	14	the	the	DET
ijassa-1111	4	15	multiplicative	multiplicative	ADJ
ijassa-1111	4	16	matrix	matrix	NOUN
ijassa-1111	4	17	,	,	PUNCT
ijassa-1111	4	18	the	the	DET
ijassa-1111	4	19	proposed	propose	VERB
ijassa-1111	4	20	method	method	NOUN
ijassa-1111	4	21	is	be	AUX
ijassa-1111	4	22	based	base	VERB
ijassa-1111	4	23	on	on	ADP
ijassa-1111	4	24	the	the	DET
ijassa-1111	4	25	approximation	approximation	NOUN
ijassa-1111	4	26	of	of	ADP
ijassa-1111	4	27	the	the	DET
ijassa-1111	4	28	original	original	ADJ
ijassa-1111	4	29	matrix	matrix	NOUN
ijassa-1111	4	30	of	of	ADP
ijassa-1111	4	31	pairwise	pairwise	NOUN
ijassa-1111	4	32	comparisons	comparison	NOUN
ijassa-1111	4	33	by	by	ADP
ijassa-1111	4	34	the	the	DET
ijassa-1111	4	35	multiplicative	multiplicative	ADJ
ijassa-1111	4	36	matrix	matrix	NOUN
ijassa-1111	4	37	according	accord	VERB
ijassa-1111	4	38	to	to	ADP
ijassa-1111	4	39	the	the	DET
ijassa-1111	4	40	matrix	matrix	NOUN
ijassa-1111	4	41	criterion	criterion	NOUN
ijassa-1111	4	42	of	of	ADP
ijassa-1111	4	43	minimum	minimum	ADJ
ijassa-1111	4	44	distances	distance	NOUN
ijassa-1111	4	45	between	between	ADP
ijassa-1111	4	46	matrices	matrix	NOUN
ijassa-1111	4	47	.	.	PUNCT
ijassa-1111	5	1	there	there	PRON
ijassa-1111	5	2	is	be	VERB
ijassa-1111	5	3	a	a	DET
ijassa-1111	5	4	one	one	NUM
ijassa-1111	5	5	-	-	PUNCT
ijassa-1111	5	6	to	to	ADP
ijassa-1111	5	7	-	-	PUNCT
ijassa-1111	5	8	one	one	NUM
ijassa-1111	5	9	mapping	mapping	NOUN
ijassa-1111	5	10	between	between	ADP
ijassa-1111	5	11	the	the	DET
ijassa-1111	5	12	elements	element	NOUN
ijassa-1111	5	13	of	of	ADP
ijassa-1111	5	14	the	the	DET
ijassa-1111	5	15	weight	weight	NOUN
ijassa-1111	5	16	vectors	vector	NOUN
ijassa-1111	5	17	and	and	CCONJ
ijassa-1111	5	18	the	the	DET
ijassa-1111	5	19	elements	element	NOUN
ijassa-1111	5	20	of	of	ADP
ijassa-1111	5	21	the	the	DET
ijassa-1111	5	22	multiplicative	multiplicative	ADJ
ijassa-1111	5	23	matrix	matrix	NOUN
ijassa-1111	5	24	.	.	PUNCT
ijassa-1111	6	1	for	for	ADP
ijassa-1111	6	2	the	the	DET
ijassa-1111	6	3	first	first	ADJ
ijassa-1111	6	4	time	time	NOUN
ijassa-1111	6	5	,	,	PUNCT
ijassa-1111	6	6	using	use	VERB
ijassa-1111	6	7	a	a	DET
ijassa-1111	6	8	specific	specific	ADJ
ijassa-1111	6	9	example	example	NOUN
ijassa-1111	6	10	using	use	VERB
ijassa-1111	6	11	the	the	DET
ijassa-1111	6	12	matrix	matrix	NOUN
ijassa-1111	6	13	criterion	criterion	NOUN
ijassa-1111	6	14	,	,	PUNCT
ijassa-1111	6	15	a	a	DET
ijassa-1111	6	16	relative	relative	ADJ
ijassa-1111	6	17	estimate	estimate	NOUN
ijassa-1111	6	18	of	of	ADP
ijassa-1111	6	19	the	the	DET
ijassa-1111	6	20	approximate	approximate	ADJ
ijassa-1111	6	21	solution	solution	NOUN
ijassa-1111	6	22	of	of	ADP
ijassa-1111	6	23	the	the	DET
ijassa-1111	6	24	analytical	analytical	ADJ
ijassa-1111	6	25	hierarchy	hierarchy	NOUN
ijassa-1111	6	26	process	process	NOUN
ijassa-1111	6	27	by	by	ADP
ijassa-1111	6	28	t.	t.	PROPN
ijassa-1111	6	29	saaty	saaty	NOUN
ijassa-1111	6	30	concerning	concern	VERB
ijassa-1111	6	31	the	the	DET
ijassa-1111	6	32	optimal	optimal	ADJ
ijassa-1111	6	33	solution	solution	NOUN
ijassa-1111	6	34	obtained	obtain	VERB
ijassa-1111	6	35	by	by	ADP
ijassa-1111	6	36	the	the	DET
ijassa-1111	6	37	approximation	approximation	NOUN
ijassa-1111	6	38	matrix	matrix	NOUN
ijassa-1111	6	39	method	method	NOUN
ijassa-1111	6	40	is	be	AUX
ijassa-1111	6	41	given	give	VERB
ijassa-1111	6	42	.	.	PUNCT
ijassa-1111	7	1	on	on	ADP
ijassa-1111	7	2	account	account	NOUN
ijassa-1111	7	3	of	of	ADP
ijassa-1111	7	4	the	the	DET
ijassa-1111	7	5	approximation	approximation	NOUN
ijassa-1111	7	6	matrix	matrix	NOUN
ijassa-1111	7	7	method	method	NOUN
ijassa-1111	7	8	being	be	AUX
ijassa-1111	7	9	mathematically	mathematically	ADV
ijassa-1111	7	10	justified	justify	VERB
ijassa-1111	7	11	and	and	CCONJ
ijassa-1111	7	12	due	due	ADP
ijassa-1111	7	13	to	to	ADP
ijassa-1111	7	14	the	the	DET
ijassa-1111	7	15	simplicity	simplicity	NOUN
ijassa-1111	7	16	of	of	ADP
ijassa-1111	7	17	finding	find	VERB
ijassa-1111	7	18	optimal	optimal	ADJ
ijassa-1111	7	19	solutions	solution	NOUN
ijassa-1111	7	20	,	,	PUNCT
ijassa-1111	7	21	it	it	PRON
ijassa-1111	7	22	can	can	AUX
ijassa-1111	7	23	be	be	AUX
ijassa-1111	7	24	recommended	recommend	VERB
ijassa-1111	7	25	instead	instead	ADV
ijassa-1111	7	26	of	of	ADP
ijassa-1111	7	27	the	the	DET
ijassa-1111	7	28	analytical	analytical	ADJ
ijassa-1111	7	29	hierarchy	hierarchy	NOUN
ijassa-1111	7	30	process	process	NOUN
ijassa-1111	7	31	by	by	ADP
ijassa-1111	7	32	t.	t.	PROPN
ijassa-1111	7	33	saaty	saaty	NOUN
ijassa-1111	7	34	.	.	PUNCT
ijassa-1111	8	1	keywords	keyword	NOUN
ijassa-1111	8	2	:	:	PUNCT
ijassa-1111	8	3	multi	multi	ADJ
ijassa-1111	8	4	-	-	ADJ
ijassa-1111	8	5	criteria	criterion	NOUN
ijassa-1111	8	6	choice	choice	NOUN
ijassa-1111	8	7	,	,	PUNCT
ijassa-1111	8	8	normalized	normalize	VERB
ijassa-1111	8	9	object	object	NOUN
ijassa-1111	8	10	weights	weight	NOUN
ijassa-1111	8	11	,	,	PUNCT
ijassa-1111	8	12	expert	expert	ADJ
ijassa-1111	8	13	judgment	judgment	NOUN
ijassa-1111	8	14	matrix	matrix	NOUN
ijassa-1111	8	15	,	,	PUNCT
ijassa-1111	8	16	multiplicative	multiplicative	ADJ
ijassa-1111	8	17	matrix	matrix	NOUN
ijassa-1111	8	18	,	,	PUNCT
ijassa-1111	8	19	matrix	matrix	NOUN
ijassa-1111	8	20	criterion	criterion	NOUN
ijassa-1111	8	21	.	.	PUNCT
ijassa-1111	9	1	1	1	X
ijassa-1111	9	2	.	.	X
ijassa-1111	9	3	introduction	introduction	NOUN
ijassa-1111	9	4	when	when	SCONJ
ijassa-1111	9	5	solving	solve	VERB
ijassa-1111	9	6	applied	apply	VERB
ijassa-1111	9	7	problems	problem	NOUN
ijassa-1111	9	8	of	of	ADP
ijassa-1111	9	9	multicriteria	multicriteria	PROPN
ijassa-1111	9	10	choice	choice	NOUN
ijassa-1111	9	11	on	on	ADP
ijassa-1111	9	12	a	a	DET
ijassa-1111	9	13	set	set	NOUN
ijassa-1111	9	14	of	of	ADP
ijassa-1111	9	15	objects	object	NOUN
ijassa-1111	9	16	(	(	PUNCT
ijassa-1111	9	17	alternatives	alternative	NOUN
ijassa-1111	9	18	,	,	PUNCT
ijassa-1111	9	19	management	management	NOUN
ijassa-1111	9	20	decisions	decision	NOUN
ijassa-1111	9	21	,	,	PUNCT
ijassa-1111	9	22	options	option	NOUN
ijassa-1111	9	23	)	)	PUNCT
ijassa-1111	9	24	presented	present	VERB
ijassa-1111	9	25	in	in	ADP
ijassa-1111	9	26	the	the	DET
ijassa-1111	9	27	form	form	NOUN
ijassa-1111	9	28	of	of	ADP
ijassa-1111	9	29	preference	preference	NOUN
ijassa-1111	9	30	relations	relation	NOUN
ijassa-1111	9	31	,	,	PUNCT
ijassa-1111	9	32	the	the	DET
ijassa-1111	9	33	problem	problem	NOUN
ijassa-1111	9	34	of	of	ADP
ijassa-1111	9	35	their	their	PRON
ijassa-1111	9	36	expert	expert	ADJ
ijassa-1111	9	37	measurement	measurement	NOUN
ijassa-1111	9	38	in	in	ADP
ijassa-1111	9	39	the	the	DET
ijassa-1111	9	40	quantitative	quantitative	ADJ
ijassa-1111	9	41	scale	scale	NOUN
ijassa-1111	9	42	of	of	ADP
ijassa-1111	9	43	relations	relation	NOUN
ijassa-1111	9	44	arises	arise	VERB
ijassa-1111	9	45	.	.	PUNCT
ijassa-1111	10	1	to	to	ADP
ijassa-1111	10	2	date	date	NOUN
ijassa-1111	10	3	,	,	PUNCT
ijassa-1111	10	4	many	many	ADJ
ijassa-1111	10	5	approaches	approach	NOUN
ijassa-1111	10	6	and	and	CCONJ
ijassa-1111	10	7	methods	method	NOUN
ijassa-1111	10	8	have	have	AUX
ijassa-1111	10	9	been	be	AUX
ijassa-1111	10	10	proposed	propose	VERB
ijassa-1111	10	11	to	to	PART
ijassa-1111	10	12	solve	solve	VERB
ijassa-1111	10	13	this	this	DET
ijassa-1111	10	14	problem	problem	NOUN
ijassa-1111	10	15	,	,	PUNCT
ijassa-1111	10	16	based	base	VERB
ijassa-1111	10	17	on	on	ADP
ijassa-1111	10	18	the	the	DET
ijassa-1111	10	19	resulting	result	VERB
ijassa-1111	10	20	preference	preference	NOUN
ijassa-1111	10	21	relations	relation	NOUN
ijassa-1111	10	22	to	to	PART
ijassa-1111	10	23	narrow	narrow	VERB
ijassa-1111	10	24	the	the	DET
ijassa-1111	10	25	set	set	NOUN
ijassa-1111	10	26	of	of	ADP
ijassa-1111	10	27	non	non	ADJ
ijassa-1111	10	28	-	-	ADJ
ijassa-1111	10	29	dominant	dominant	ADJ
ijassa-1111	10	30	alternatives	alternative	NOUN
ijassa-1111	10	31	,	,	PUNCT
ijassa-1111	10	32	as	as	ADV
ijassa-1111	10	33	well	well	ADV
ijassa-1111	10	34	as	as	ADP
ijassa-1111	10	35	on	on	ADP
ijassa-1111	10	36	paired	pair	VERB
ijassa-1111	10	37	comparisons	comparison	NOUN
ijassa-1111	10	38	of	of	ADP
ijassa-1111	10	39	objects	object	NOUN
ijassa-1111	10	40	(	(	PUNCT
ijassa-1111	10	41	solutions	solution	NOUN
ijassa-1111	10	42	,	,	PUNCT
ijassa-1111	10	43	criteria	criterion	NOUN
ijassa-1111	10	44	)	)	PUNCT
ijassa-1111	11	1	[	[	X
ijassa-1111	11	2	1	1	NUM
ijassa-1111	11	3	,	,	PUNCT
ijassa-1111	11	4	2	2	NUM
ijassa-1111	11	5	]	]	PUNCT
ijassa-1111	11	6	,	,	PUNCT
ijassa-1111	11	7	which	which	PRON
ijassa-1111	11	8	do	do	AUX
ijassa-1111	11	9	not	not	PART
ijassa-1111	11	10	always	always	ADV
ijassa-1111	11	11	allow	allow	VERB
ijassa-1111	11	12	us	we	PRON
ijassa-1111	11	13	to	to	PART
ijassa-1111	11	14	identify	identify	VERB
ijassa-1111	11	15	a	a	DET
ijassa-1111	11	16	single	single	ADJ
ijassa-1111	11	17	alternative	alternative	NOUN
ijassa-1111	11	18	or	or	CCONJ
ijassa-1111	11	19	management	management	NOUN
ijassa-1111	11	20	solution	solution	NOUN
ijassa-1111	11	21	without	without	ADP
ijassa-1111	11	22	attracting	attract	VERB
ijassa-1111	11	23	additional	additional	ADJ
ijassa-1111	11	24	information	information	NOUN
ijassa-1111	11	25	.	.	PUNCT
ijassa-1111	12	1	however	however	ADV
ijassa-1111	12	2	,	,	PUNCT
ijassa-1111	12	3	when	when	SCONJ
ijassa-1111	12	4	solving	solve	VERB
ijassa-1111	12	5	applied	apply	VERB
ijassa-1111	12	6	problems	problem	NOUN
ijassa-1111	12	7	related	relate	VERB
ijassa-1111	12	8	to	to	ADP
ijassa-1111	12	9	the	the	DET
ijassa-1111	12	10	measurement	measurement	NOUN
ijassa-1111	12	11	of	of	ADP
ijassa-1111	12	12	objects	object	NOUN
ijassa-1111	12	13	in	in	ADP
ijassa-1111	12	14	expert	expert	NOUN
ijassa-1111	12	15	scales	scale	NOUN
ijassa-1111	12	16	,	,	PUNCT
ijassa-1111	12	17	as	as	ADV
ijassa-1111	12	18	well	well	ADV
ijassa-1111	12	19	as	as	ADP
ijassa-1111	12	20	the	the	DET
ijassa-1111	12	21	formation	formation	NOUN
ijassa-1111	12	22	of	of	ADP
ijassa-1111	12	23	local	local	ADJ
ijassa-1111	12	24	weights	weight	NOUN
ijassa-1111	12	25	of	of	ADP
ijassa-1111	12	26	criteria	criterion	NOUN
ijassa-1111	12	27	presented	present	VERB
ijassa-1111	12	28	in	in	ADP
ijassa-1111	12	29	the	the	DET
ijassa-1111	12	30	form	form	NOUN
ijassa-1111	12	31	of	of	ADP
ijassa-1111	12	32	a	a	DET
ijassa-1111	12	33	hierarchical	hierarchical	ADJ
ijassa-1111	12	34	tree	tree	NOUN
ijassa-1111	12	35	of	of	ADP
ijassa-1111	12	36	the	the	DET
ijassa-1111	12	37	importance	importance	NOUN
ijassa-1111	12	38	of	of	ADP
ijassa-1111	12	39	criteria	criterion	NOUN
ijassa-1111	12	40	,	,	PUNCT
ijassa-1111	12	41	expert	expert	ADJ
ijassa-1111	12	42	methods	method	NOUN
ijassa-1111	12	43	of	of	ADP
ijassa-1111	12	44	evaluating	evaluate	VERB
ijassa-1111	12	45	and	and	CCONJ
ijassa-1111	12	46	ranking	ranking	ADJ
ijassa-1111	12	47	objects	object	NOUN
ijassa-1111	12	48	are	be	AUX
ijassa-1111	12	49	usually	usually	ADV
ijassa-1111	12	50	used	use	VERB
ijassa-1111	12	51	[	[	PUNCT
ijassa-1111	12	52	3	3	NUM
ijassa-1111	12	53	]	]	PUNCT
ijassa-1111	12	54	.	.	PUNCT
ijassa-1111	13	1	direct	direct	ADJ
ijassa-1111	13	2	methods	method	NOUN
ijassa-1111	13	3	of	of	ADP
ijassa-1111	13	4	expert	expert	ADJ
ijassa-1111	13	5	evaluation	evaluation	NOUN
ijassa-1111	13	6	of	of	ADP
ijassa-1111	13	7	criteria	criterion	NOUN
ijassa-1111	13	8	weights	weight	NOUN
ijassa-1111	13	9	have	have	AUX
ijassa-1111	13	10	found	find	VERB
ijassa-1111	13	11	application	application	NOUN
ijassa-1111	13	12	in	in	ADP
ijassa-1111	13	13	the	the	DET
ijassa-1111	13	14	planning	planning	NOUN
ijassa-1111	13	15	methodology	methodology	NOUN
ijassa-1111	13	16	through	through	ADP
ijassa-1111	13	17	relative	relative	ADJ
ijassa-1111	13	18	indicators	indicator	NOUN
ijassa-1111	13	19	of	of	ADP
ijassa-1111	13	20	technical	technical	ADJ
ijassa-1111	13	21	evaluation	evaluation	NOUN
ijassa-1111	13	22	(	(	PUNCT
ijassa-1111	13	23	pattern	pattern	NOUN
ijassa-1111	13	24	)	)	PUNCT
ijassa-1111	13	25	.	.	PUNCT
ijassa-1111	14	1	experts	expert	NOUN
ijassa-1111	14	2	are	be	AUX
ijassa-1111	14	3	asked	ask	VERB
ijassa-1111	14	4	to	to	PART
ijassa-1111	14	5	evaluate	evaluate	VERB
ijassa-1111	14	6	the	the	DET
ijassa-1111	14	7	normalized	normalize	VERB
ijassa-1111	14	8	local	local	ADJ
ijassa-1111	14	9	weights	weight	NOUN
ijassa-1111	14	10	of	of	ADP
ijassa-1111	14	11	criteria	criterion	NOUN
ijassa-1111	14	12	at	at	ADP
ijassa-1111	14	13	each	each	DET
ijassa-1111	14	14	level	level	NOUN
ijassa-1111	14	15	of	of	ADP
ijassa-1111	14	16	the	the	DET
ijassa-1111	14	17	hierarchy	hierarchy	NOUN
ijassa-1111	14	18	on	on	ADP
ijassa-1111	14	19	a	a	DET
ijassa-1111	14	20	quantitative	quantitative	ADJ
ijassa-1111	14	21	scale	scale	NOUN
ijassa-1111	14	22	,	,	PUNCT
ijassa-1111	14	23	and	and	CCONJ
ijassa-1111	14	24	then	then	ADV
ijassa-1111	14	25	the	the	DET
ijassa-1111	14	26	global	global	ADJ
ijassa-1111	14	27	weights	weight	NOUN
ijassa-1111	14	28	are	be	AUX
ijassa-1111	14	29	found	find	VERB
ijassa-1111	14	30	by	by	ADP
ijassa-1111	14	31	multiplying	multiply	VERB
ijassa-1111	14	32	local	local	ADJ
ijassa-1111	14	33	weights	weight	NOUN
ijassa-1111	14	34	along	along	ADP
ijassa-1111	14	35	the	the	DET
ijassa-1111	14	36	branches	branch	NOUN
ijassa-1111	14	37	of	of	ADP
ijassa-1111	14	38	a	a	DET
ijassa-1111	14	39	multi	multi	ADJ
ijassa-1111	14	40	-	-	ADJ
ijassa-1111	14	41	level	level	ADJ
ijassa-1111	14	42	criteria	criterion	NOUN
ijassa-1111	14	43	tree	tree	NOUN
ijassa-1111	15	1	[	[	X
ijassa-1111	15	2	4	4	NUM
ijassa-1111	15	3	]	]	PUNCT
ijassa-1111	15	4	.	.	PUNCT
ijassa-1111	16	1	another	another	DET
ijassa-1111	16	2	expert	expert	ADJ
ijassa-1111	16	3	approach	approach	NOUN
ijassa-1111	16	4	based	base	VERB
ijassa-1111	16	5	on	on	ADP
ijassa-1111	16	6	the	the	DET
ijassa-1111	16	7	matrix	matrix	NOUN
ijassa-1111	16	8	of	of	ADP
ijassa-1111	16	9	paired	pair	VERB
ijassa-1111	16	10	comparisons	comparison	NOUN
ijassa-1111	16	11	to	to	PART
ijassa-1111	16	12	assign	assign	VERB
ijassa-1111	16	13	"	"	PUNCT
ijassa-1111	16	14	weights	weight	NOUN
ijassa-1111	16	15	"	"	PUNCT
ijassa-1111	16	16	to	to	ADP
ijassa-1111	16	17	a	a	DET
ijassa-1111	16	18	finite	finite	ADJ
ijassa-1111	16	19	set	set	NOUN
ijassa-1111	16	20	of	of	ADP
ijassa-1111	16	21	compared	compare	VERB
ijassa-1111	16	22	objects	object	NOUN
ijassa-1111	16	23	is	be	AUX
ijassa-1111	16	24	the	the	DET
ijassa-1111	16	25	analytical	analytical	ADJ
ijassa-1111	16	26	hierarchy	hierarchy	NOUN
ijassa-1111	16	27	process	process	NOUN
ijassa-1111	16	28	(	(	PUNCT
ijassa-1111	16	29	ahp	ahp	NOUN
ijassa-1111	16	30	)	)	PUNCT
ijassa-1111	16	31	by	by	ADP
ijassa-1111	16	32	t.	t.	PROPN
ijassa-1111	16	33	saaty	saaty	NOUN
ijassa-1111	16	34	which	which	PRON
ijassa-1111	16	35	is	be	AUX
ijassa-1111	16	36	now	now	ADV
ijassa-1111	16	37	firmly	firmly	ADV
ijassa-1111	16	38	established	establish	VERB
ijassa-1111	16	39	in	in	ADP
ijassa-1111	16	40	the	the	DET
ijassa-1111	16	41	theory	theory	NOUN
ijassa-1111	16	42	and	and	CCONJ
ijassa-1111	16	43	practice	practice	NOUN
ijassa-1111	16	44	of	of	ADP
ijassa-1111	16	45	multicriteria	multicriteria	PROPN
ijassa-1111	16	46	selection	selection	NOUN
ijassa-1111	16	47	problems	problem	NOUN
ijassa-1111	16	48	[	[	X
ijassa-1111	16	49	5–7	5–7	X
ijassa-1111	16	50	]	]	PUNCT
ijassa-1111	16	51	.	.	PUNCT
ijassa-1111	17	1	following	follow	VERB
ijassa-1111	17	2	the	the	DET
ijassa-1111	17	3	analytical	analytical	ADJ
ijassa-1111	17	4	hierarchy	hierarchy	NOUN
ijassa-1111	17	5	process	process	NOUN
ijassa-1111	17	6	,	,	PUNCT
ijassa-1111	17	7	experts	expert	NOUN
ijassa-1111	17	8	form	form	VERB
ijassa-1111	17	9	a	a	DET
ijassa-1111	17	10	so	so	ADV
ijassa-1111	17	11	-	-	PUNCT
ijassa-1111	17	12	called	call	VERB
ijassa-1111	17	13	matrix	matrix	NOUN
ijassa-1111	17	14	of	of	ADP
ijassa-1111	17	15	paired	pair	VERB
ijassa-1111	17	16	comparisons	comparison	NOUN
ijassa-1111	17	17	(	(	PUNCT
ijassa-1111	17	18	judgments	judgment	NOUN
ijassa-1111	17	19	)	)	PUNCT
ijassa-1111	17	20	of	of	ADP
ijassa-1111	17	21	objects	object	NOUN
ijassa-1111	17	22	𝑉	𝑉	PROPN
ijassa-1111	17	23	=	=	PUNCT
ijassa-1111	18	1	[	[	X
ijassa-1111	18	2	𝑣	𝑣	X
ijassa-1111	18	3	]	]	PUNCT
ijassa-1111	18	4	,	,	PUNCT
ijassa-1111	18	5	𝑖	𝑖	PROPN
ijassa-1111	18	6	,	,	PUNCT
ijassa-1111	18	7	𝑗	𝑗	NOUN
ijassa-1111	18	8	=	=	SYM
ijassa-1111	18	9	1	1	NUM
ijassa-1111	18	10	,	,	PUNCT
ijassa-1111	18	11	𝑛	𝑛	PROPN
ijassa-1111	18	12	,	,	PUNCT
ijassa-1111	18	13	in	in	ADP
ijassa-1111	18	14	the	the	DET
ijassa-1111	18	15	scale	scale	NOUN
ijassa-1111	18	16	of	of	ADP
ijassa-1111	18	17	relations	relation	NOUN
ijassa-1111	18	18	,	,	PUNCT
ijassa-1111	18	19	and	and	CCONJ
ijassa-1111	18	20	then	then	ADV
ijassa-1111	18	21	find	find	VERB
ijassa-1111	18	22	the	the	DET
ijassa-1111	18	23	approximation	approximation	NOUN
ijassa-1111	18	24	matrix	matrix	NOUN
ijassa-1111	18	25	method	method	NOUN
ijassa-1111	18	26	and	and	CCONJ
ijassa-1111	18	27	its	its	PRON
ijassa-1111	18	28	comparison	comparison	NOUN
ijassa-1111	18	29	…	…	PUNCT
ijassa-1111	18	30	105	105	NUM
ijassa-1111	18	31	copyright	copyright	NOUN
ijassa-1111	18	32	©	©	PROPN
ijassa-1111	18	33	2024	2024	NUM
ijassa-1111	18	34	assa	assa	PROPN
ijassa-1111	18	35	adv	adv	PROPN
ijassa-1111	18	36	.	.	PUNCT
ijassa-1111	19	1	in	in	ADP
ijassa-1111	19	2	systems	system	NOUN
ijassa-1111	19	3	science	science	NOUN
ijassa-1111	19	4	and	and	CCONJ
ijassa-1111	19	5	appl	appl	NOUN
ijassa-1111	19	6	.	.	PUNCT
ijassa-1111	20	1	(	(	PUNCT
ijassa-1111	20	2	2024	2024	NUM
ijassa-1111	20	3	)	)	PUNCT
ijassa-1111	20	4	the	the	DET
ijassa-1111	20	5	right	right	PROPN
ijassa-1111	20	6	eigenvector	eigenvector	PROPN
ijassa-1111	20	7	�	�	PROPN
ijassa-1111	20	8	⃗	⃗	PROPN
ijassa-1111	20	9	�	�	NOUN
ijassa-1111	20	10	=	=	SYM
ijassa-1111	20	11	(	(	PUNCT
ijassa-1111	20	12	𝑤	𝑤	INTJ
ijassa-1111	20	13	,	,	PUNCT
ijassa-1111	20	14	.	.	PUNCT
ijassa-1111	20	15	.	.	PUNCT
ijassa-1111	21	1	.	.	PUNCT
ijassa-1111	22	1	,	,	PUNCT
ijassa-1111	22	2	𝑤	𝑤	X
ijassa-1111	22	3	)	)	PUNCT
ijassa-1111	22	4	of	of	ADP
ijassa-1111	22	5	this	this	DET
ijassa-1111	22	6	matrix	matrix	NOUN
ijassa-1111	22	7	,	,	PUNCT
ijassa-1111	22	8	corresponding	correspond	VERB
ijassa-1111	22	9	to	to	ADP
ijassa-1111	22	10	the	the	DET
ijassa-1111	22	11	maximum	maximum	ADJ
ijassa-1111	22	12	eigenvalue	eigenvalue	NOUN
ijassa-1111	22	13	.	.	PUNCT
ijassa-1111	23	1	the	the	DET
ijassa-1111	23	2	desired	desire	VERB
ijassa-1111	23	3	weight	weight	NOUN
ijassa-1111	23	4	vector	vector	NOUN
ijassa-1111	23	5	is	be	AUX
ijassa-1111	23	6	a	a	DET
ijassa-1111	23	7	vector	vector	NOUN
ijassa-1111	23	8	whose	whose	DET
ijassa-1111	23	9	elements	element	NOUN
ijassa-1111	23	10	are	be	AUX
ijassa-1111	23	11	normalized	normalize	VERB
ijassa-1111	23	12	by	by	ADP
ijassa-1111	23	13	the	the	DET
ijassa-1111	23	14	sum	sum	NOUN
ijassa-1111	23	15	of	of	ADP
ijassa-1111	23	16	the	the	DET
ijassa-1111	23	17	elements	element	NOUN
ijassa-1111	23	18	of	of	ADP
ijassa-1111	23	19	the	the	DET
ijassa-1111	23	20	right	right	ADJ
ijassa-1111	23	21	eigenvector	eigenvector	NOUN
ijassa-1111	23	22	.	.	PUNCT
ijassa-1111	24	1	since	since	SCONJ
ijassa-1111	24	2	the	the	DET
ijassa-1111	24	3	calculation	calculation	NOUN
ijassa-1111	24	4	of	of	ADP
ijassa-1111	24	5	the	the	DET
ijassa-1111	24	6	vectors	vector	NOUN
ijassa-1111	24	7	of	of	ADP
ijassa-1111	24	8	weights	weight	NOUN
ijassa-1111	24	9	of	of	ADP
ijassa-1111	24	10	objects	object	NOUN
ijassa-1111	24	11	(	(	PUNCT
ijassa-1111	24	12	criteria	criterion	NOUN
ijassa-1111	24	13	and	and	CCONJ
ijassa-1111	24	14	alternatives	alternative	NOUN
ijassa-1111	24	15	)	)	PUNCT
ijassa-1111	24	16	is	be	AUX
ijassa-1111	24	17	performed	perform	VERB
ijassa-1111	24	18	by	by	ADP
ijassa-1111	24	19	a	a	DET
ijassa-1111	24	20	numerical	numerical	ADJ
ijassa-1111	24	21	(	(	PUNCT
ijassa-1111	24	22	approximate	approximate	ADJ
ijassa-1111	24	23	)	)	PUNCT
ijassa-1111	24	24	method	method	NOUN
ijassa-1111	24	25	,	,	PUNCT
ijassa-1111	24	26	t.	t.	NOUN
ijassa-1111	24	27	saaty	saaty	NOUN
ijassa-1111	24	28	aware	aware	ADJ
ijassa-1111	24	29	of	of	ADP
ijassa-1111	24	30	this	this	PRON
ijassa-1111	24	31	,	,	PUNCT
ijassa-1111	24	32	introduced	introduce	VERB
ijassa-1111	24	33	a	a	DET
ijassa-1111	24	34	special	special	ADJ
ijassa-1111	24	35	numerical	numerical	ADJ
ijassa-1111	24	36	indicator	indicator	NOUN
ijassa-1111	24	37	:	:	PUNCT
ijassa-1111	24	38	consistency	consistency	NOUN
ijassa-1111	24	39	index	index	NOUN
ijassa-1111	24	40	the	the	DET
ijassa-1111	24	41	compatibility	compatibility	NOUN
ijassa-1111	24	42	index	index	NOUN
ijassa-1111	24	43	of	of	ADP
ijassa-1111	24	44	the	the	DET
ijassa-1111	24	45	judgment	judgment	NOUN
ijassa-1111	24	46	matrix	matrix	NOUN
ijassa-1111	24	47	𝑉	𝑉	PROPN
ijassa-1111	24	48	and	and	CCONJ
ijassa-1111	24	49	the	the	DET
ijassa-1111	24	50	multiplicative	multiplicative	ADJ
ijassa-1111	24	51	matrix	matrix	NOUN
ijassa-1111	24	52	𝑊	𝑊	PROPN
ijassa-1111	24	53	obtained	obtain	VERB
ijassa-1111	24	54	based	base	VERB
ijassa-1111	24	55	on	on	ADP
ijassa-1111	24	56	the	the	DET
ijassa-1111	24	57	values	value	NOUN
ijassa-1111	24	58	of	of	ADP
ijassa-1111	24	59	the	the	DET
ijassa-1111	24	60	eigenvector	eigenvector	NOUN
ijassa-1111	24	61	,	,	PUNCT
ijassa-1111	24	62	in	in	ADP
ijassa-1111	24	63	the	the	DET
ijassa-1111	24	64	form	form	NOUN
ijassa-1111	24	65	of	of	ADP
ijassa-1111	24	66	the	the	DET
ijassa-1111	24	67	hadamard	hadamard	ADJ
ijassa-1111	24	68	product	product	NOUN
ijassa-1111	24	69	[	[	X
ijassa-1111	24	70	9	9	NUM
ijassa-1111	24	71	]	]	SYM
ijassa-1111	24	72	:	:	PUNCT
ijassa-1111	24	73	𝑆.	𝑆.	PROPN
ijassa-1111	24	74	𝐼.	𝐼.	PROPN
ijassa-1111	24	75	=	=	SYM
ijassa-1111	24	76	𝑒	𝑒	PROPN
ijassa-1111	24	77	𝑉	𝑉	PROPN
ijassa-1111	24	78	°	°	PROPN
ijassa-1111	24	79	𝑊	𝑊	PROPN
ijassa-1111	24	80	𝑒	𝑒	NOUN
ijassa-1111	24	81	,	,	PUNCT
ijassa-1111	24	82	𝑒	𝑒	PROPN
ijassa-1111	24	83	=	=	PUNCT
ijassa-1111	24	84	(	(	PUNCT
ijassa-1111	24	85	1,1	1,1	NUM
ijassa-1111	24	86	,	,	PUNCT
ijassa-1111	24	87	…	…	PUNCT
ijassa-1111	24	88	,	,	PUNCT
ijassa-1111	24	89	1	1	NUM
ijassa-1111	24	90	)	)	PUNCT
ijassa-1111	24	91	,	,	PUNCT
ijassa-1111	24	92	where	where	SCONJ
ijassa-1111	24	93	v	v	NOUN
ijassa-1111	24	94	is	be	AUX
ijassa-1111	24	95	the	the	DET
ijassa-1111	24	96	original	original	ADJ
ijassa-1111	24	97	judgment	judgment	NOUN
ijassa-1111	24	98	matrix	matrix	NOUN
ijassa-1111	24	99	,	,	PUNCT
ijassa-1111	24	100	and	and	CCONJ
ijassa-1111	24	101	𝑊	𝑊	NOUN
ijassa-1111	24	102	=	=	SYM
ijassa-1111	25	1	[	[	X
ijassa-1111	25	2	𝑤	𝑤	X
ijassa-1111	25	3	]	]	X
ijassa-1111	25	4	=	=	VERB
ijassa-1111	25	5	is	be	AUX
ijassa-1111	25	6	a	a	DET
ijassa-1111	25	7	multiplicative	multiplicative	ADJ
ijassa-1111	25	8	square	square	ADJ
ijassa-1111	25	9	matrix	matrix	NOUN
ijassa-1111	25	10	whose	whose	DET
ijassa-1111	25	11	elements	element	NOUN
ijassa-1111	25	12	are	be	AUX
ijassa-1111	25	13	determined	determine	VERB
ijassa-1111	25	14	from	from	ADP
ijassa-1111	25	15	the	the	DET
ijassa-1111	25	16	normalized	normalize	VERB
ijassa-1111	25	17	elements	element	NOUN
ijassa-1111	25	18	of	of	ADP
ijassa-1111	25	19	the	the	DET
ijassa-1111	25	20	right	right	PROPN
ijassa-1111	25	21	eigenvector	eigenvector	PROPN
ijassa-1111	25	22	�	�	PROPN
ijassa-1111	25	23	⃗	⃗	PROPN
ijassa-1111	25	24	�	�	PROPN
ijassa-1111	25	25	of	of	ADP
ijassa-1111	25	26	the	the	DET
ijassa-1111	25	27	judgment	judgment	NOUN
ijassa-1111	25	28	matrix	matrix	NOUN
ijassa-1111	25	29	v.	v.	ADP
ijassa-1111	25	30	in	in	ADP
ijassa-1111	25	31	this	this	DET
ijassa-1111	25	32	case	case	NOUN
ijassa-1111	25	33	,	,	PUNCT
ijassa-1111	25	34	the	the	DET
ijassa-1111	25	35	ratio	ratio	NOUN
ijassa-1111	25	36	takes	take	VERB
ijassa-1111	25	37	place	place	NOUN
ijassa-1111	25	38	:	:	PUNCT
ijassa-1111	25	39	𝑤	𝑤	X
ijassa-1111	25	40	=	=	NOUN
ijassa-1111	25	41	𝑤	𝑤	PART
ijassa-1111	25	42	𝑤	𝑤	NOUN
ijassa-1111	25	43	=	=	PUNCT
ijassa-1111	25	44	𝑤	𝑤	PROPN
ijassa-1111	25	45	/	/	SYM
ijassa-1111	25	46	∑	∑	PROPN
ijassa-1111	25	47	𝑤	𝑤	PART
ijassa-1111	25	48	𝑤	𝑤	PART
ijassa-1111	25	49	/	/	SYM
ijassa-1111	25	50	∑	∑	PROPN
ijassa-1111	25	51	𝑤	𝑤	SYM
ijassa-1111	25	52	=	=	PUNCT
ijassa-1111	25	53	𝑤	𝑤	PART
ijassa-1111	25	54	𝑤	𝑤	PROPN
ijassa-1111	25	55	,	,	PUNCT
ijassa-1111	25	56	𝑖	𝑖	PROPN
ijassa-1111	25	57	,	,	PUNCT
ijassa-1111	25	58	𝑗	𝑗	NOUN
ijassa-1111	25	59	=	=	SYM
ijassa-1111	25	60	1	1	NUM
ijassa-1111	25	61	,	,	PUNCT
ijassa-1111	25	62	𝑛.	𝑛.	NOUN
ijassa-1111	25	63	the	the	DET
ijassa-1111	25	64	s.i	s.i	PROPN
ijassa-1111	25	65	.	.	PROPN
ijassa-1111	25	66	index	index	NOUN
ijassa-1111	25	67	it	it	PRON
ijassa-1111	25	68	characterizes	characterize	VERB
ijassa-1111	25	69	the	the	DET
ijassa-1111	25	70	degree	degree	NOUN
ijassa-1111	25	71	of	of	ADP
ijassa-1111	25	72	confidence	confidence	NOUN
ijassa-1111	25	73	in	in	ADP
ijassa-1111	25	74	the	the	DET
ijassa-1111	25	75	results	result	NOUN
ijassa-1111	25	76	obtained	obtain	VERB
ijassa-1111	25	77	with	with	ADP
ijassa-1111	25	78	the	the	DET
ijassa-1111	25	79	help	help	NOUN
ijassa-1111	25	80	of	of	ADP
ijassa-1111	25	81	ahp	ahp	NOUN
ijassa-1111	25	82	and	and	CCONJ
ijassa-1111	25	83	is	be	AUX
ijassa-1111	25	84	interpreted	interpret	VERB
ijassa-1111	25	85	as	as	ADP
ijassa-1111	25	86	a	a	DET
ijassa-1111	25	87	kind	kind	NOUN
ijassa-1111	25	88	of	of	ADP
ijassa-1111	25	89	measure	measure	NOUN
ijassa-1111	25	90	of	of	ADP
ijassa-1111	25	91	the	the	DET
ijassa-1111	25	92	deviation	deviation	NOUN
ijassa-1111	25	93	of	of	ADP
ijassa-1111	25	94	the	the	DET
ijassa-1111	25	95	initial	initial	ADJ
ijassa-1111	25	96	perturbed	perturb	VERB
ijassa-1111	25	97	judgment	judgment	NOUN
ijassa-1111	25	98	matrix	matrix	NOUN
ijassa-1111	25	99	𝑉	𝑉	PROPN
ijassa-1111	25	100	from	from	ADP
ijassa-1111	25	101	the	the	DET
ijassa-1111	25	102	multiplicative	multiplicative	ADJ
ijassa-1111	25	103	one	one	NUM
ijassa-1111	25	104	w.	w.	NOUN
ijassa-1111	25	105	in	in	ADP
ijassa-1111	25	106	the	the	DET
ijassa-1111	25	107	work	work	NOUN
ijassa-1111	25	108	of	of	ADP
ijassa-1111	25	109	t.	t.	PROPN
ijassa-1111	25	110	saaty	saaty	NOUN
ijassa-1111	25	111	[	[	X
ijassa-1111	25	112	8	8	NUM
ijassa-1111	25	113	,	,	PUNCT
ijassa-1111	25	114	p.	p.	NOUN
ijassa-1111	25	115	76	76	NUM
ijassa-1111	25	116	]	]	PUNCT
ijassa-1111	25	117	,	,	PUNCT
ijassa-1111	25	118	it	it	PRON
ijassa-1111	25	119	is	be	AUX
ijassa-1111	25	120	shown	show	VERB
ijassa-1111	25	121	that	that	SCONJ
ijassa-1111	25	122	if	if	SCONJ
ijassa-1111	25	123	we	we	PRON
ijassa-1111	25	124	perform	perform	VERB
ijassa-1111	25	125	the	the	DET
ijassa-1111	25	126	hadamard	hadamard	ADJ
ijassa-1111	25	127	matrix	matrix	NOUN
ijassa-1111	25	128	product	product	NOUN
ijassa-1111	25	129	,	,	PUNCT
ijassa-1111	25	130	then	then	ADV
ijassa-1111	25	131	the	the	DET
ijassa-1111	25	132	compatibility	compatibility	NOUN
ijassa-1111	25	133	index	index	NOUN
ijassa-1111	25	134	takes	take	VERB
ijassa-1111	25	135	the	the	DET
ijassa-1111	25	136	form	form	NOUN
ijassa-1111	25	137	𝑆.	𝑆.	PROPN
ijassa-1111	25	138	𝐼.	𝐼.	PROPN
ijassa-1111	25	139	=	=	PUNCT
ijassa-1111	25	140	>	>	X
ijassa-1111	25	141	1	1	NUM
ijassa-1111	25	142	,	,	PUNCT
ijassa-1111	25	143	where	where	SCONJ
ijassa-1111	25	144	λ	λ	PROPN
ijassa-1111	25	145	is	be	AUX
ijassa-1111	25	146	the	the	DET
ijassa-1111	25	147	maximum	maximum	PROPN
ijassa-1111	25	148	eigenvalue	eigenvalue	NOUN
ijassa-1111	25	149	of	of	ADP
ijassa-1111	25	150	the	the	DET
ijassa-1111	25	151	matrix	matrix	NOUN
ijassa-1111	25	152	𝑉.	𝑉.	NOUN
ijassa-1111	25	153	with	with	ADP
ijassa-1111	25	154	a	a	DET
ijassa-1111	25	155	sufficiently	sufficiently	ADV
ijassa-1111	25	156	close	close	ADJ
ijassa-1111	25	157	approximation	approximation	NOUN
ijassa-1111	25	158	to	to	ADP
ijassa-1111	25	159	the	the	DET
ijassa-1111	25	160	unit	unit	NOUN
ijassa-1111	25	161	value	value	NOUN
ijassa-1111	25	162	of	of	ADP
ijassa-1111	25	163	the	the	DET
ijassa-1111	25	164	index	index	NOUN
ijassa-1111	25	165	,	,	PUNCT
ijassa-1111	25	166	the	the	DET
ijassa-1111	25	167	matrix	matrix	NOUN
ijassa-1111	25	168	of	of	ADP
ijassa-1111	25	169	paired	pair	VERB
ijassa-1111	25	170	comparisons	comparison	NOUN
ijassa-1111	25	171	𝑉	𝑉	PROPN
ijassa-1111	25	172	is	be	AUX
ijassa-1111	25	173	"	"	PUNCT
ijassa-1111	25	174	close	close	ADJ
ijassa-1111	25	175	"	"	PUNCT
ijassa-1111	25	176	to	to	ADP
ijassa-1111	25	177	the	the	DET
ijassa-1111	25	178	multiplicative	multiplicative	ADJ
ijassa-1111	25	179	matrix	matrix	NOUN
ijassa-1111	25	180	w.	w.	NOUN
ijassa-1111	25	181	if	if	SCONJ
ijassa-1111	25	182	the	the	DET
ijassa-1111	25	183	consistency	consistency	NOUN
ijassa-1111	25	184	index	index	NOUN
ijassa-1111	25	185	exceeds	exceed	VERB
ijassa-1111	25	186	a	a	DET
ijassa-1111	25	187	certain	certain	ADJ
ijassa-1111	25	188	"	"	PUNCT
ijassa-1111	25	189	threshold	threshold	NOUN
ijassa-1111	25	190	"	"	PUNCT
ijassa-1111	25	191	value	value	NOUN
ijassa-1111	25	192	,	,	PUNCT
ijassa-1111	25	193	then	then	ADV
ijassa-1111	25	194	it	it	PRON
ijassa-1111	25	195	is	be	AUX
ijassa-1111	25	196	impossible	impossible	ADJ
ijassa-1111	25	197	to	to	PART
ijassa-1111	25	198	conclude	conclude	VERB
ijassa-1111	25	199	the	the	DET
ijassa-1111	25	200	proximity	proximity	NOUN
ijassa-1111	25	201	of	of	ADP
ijassa-1111	25	202	these	these	DET
ijassa-1111	25	203	matrices	matrix	NOUN
ijassa-1111	25	204	,	,	PUNCT
ijassa-1111	25	205	and	and	CCONJ
ijassa-1111	25	206	therefore	therefore	ADV
ijassa-1111	25	207	it	it	PRON
ijassa-1111	25	208	is	be	AUX
ijassa-1111	25	209	not	not	PART
ijassa-1111	25	210	recommended	recommend	VERB
ijassa-1111	25	211	to	to	PART
ijassa-1111	25	212	use	use	VERB
ijassa-1111	25	213	ai	ai	VERB
ijassa-1111	25	214	in	in	ADP
ijassa-1111	25	215	such	such	ADJ
ijassa-1111	25	216	cases	case	NOUN
ijassa-1111	25	217	.	.	PUNCT
ijassa-1111	26	1	the	the	DET
ijassa-1111	26	2	hierarchy	hierarchy	NOUN
ijassa-1111	26	3	analysis	analysis	NOUN
ijassa-1111	26	4	method	method	NOUN
ijassa-1111	26	5	and	and	CCONJ
ijassa-1111	26	6	its	its	PRON
ijassa-1111	26	7	applications	application	NOUN
ijassa-1111	26	8	are	be	AUX
ijassa-1111	26	9	described	describe	VERB
ijassa-1111	26	10	in	in	ADP
ijassa-1111	26	11	many	many	ADJ
ijassa-1111	26	12	reviews	review	NOUN
ijassa-1111	26	13	,	,	PUNCT
ijassa-1111	26	14	monographs	monograph	NOUN
ijassa-1111	26	15	,	,	PUNCT
ijassa-1111	26	16	scientific	scientific	ADJ
ijassa-1111	26	17	articles	article	NOUN
ijassa-1111	26	18	,	,	PUNCT
ijassa-1111	26	19	as	as	ADV
ijassa-1111	26	20	well	well	ADV
ijassa-1111	26	21	as	as	ADP
ijassa-1111	26	22	works	work	NOUN
ijassa-1111	26	23	popularizing	popularize	VERB
ijassa-1111	26	24	this	this	DET
ijassa-1111	26	25	method	method	NOUN
ijassa-1111	26	26	[	[	X
ijassa-1111	26	27	10–15	10–15	NUM
ijassa-1111	26	28	]	]	PUNCT
ijassa-1111	26	29	.	.	PUNCT
ijassa-1111	27	1	however	however	ADV
ijassa-1111	27	2	,	,	PUNCT
ijassa-1111	27	3	it	it	PRON
ijassa-1111	27	4	can	can	AUX
ijassa-1111	27	5	be	be	AUX
ijassa-1111	27	6	clearly	clearly	ADV
ijassa-1111	27	7	stated	state	VERB
ijassa-1111	27	8	that	that	SCONJ
ijassa-1111	27	9	the	the	DET
ijassa-1111	27	10	method	method	NOUN
ijassa-1111	27	11	of	of	ADP
ijassa-1111	27	12	hierarchy	hierarchy	NOUN
ijassa-1111	27	13	analysis	analysis	NOUN
ijassa-1111	27	14	by	by	ADP
ijassa-1111	27	15	t.	t.	PROPN
ijassa-1111	27	16	saaty	saaty	NOUN
ijassa-1111	27	17	is	be	AUX
ijassa-1111	27	18	approximate	approximate	ADJ
ijassa-1111	27	19	since	since	SCONJ
ijassa-1111	27	20	the	the	DET
ijassa-1111	27	21	method	method	NOUN
ijassa-1111	27	22	of	of	ADP
ijassa-1111	27	23	determining	determine	VERB
ijassa-1111	27	24	the	the	DET
ijassa-1111	27	25	weight	weight	NOUN
ijassa-1111	27	26	vector	vector	NOUN
ijassa-1111	27	27	is	be	AUX
ijassa-1111	27	28	based	base	VERB
ijassa-1111	27	29	on	on	ADP
ijassa-1111	27	30	numerical	numerical	ADJ
ijassa-1111	27	31	(	(	PUNCT
ijassa-1111	27	32	approximate	approximate	ADJ
ijassa-1111	27	33	)	)	PUNCT
ijassa-1111	27	34	methods	method	NOUN
ijassa-1111	27	35	for	for	ADP
ijassa-1111	27	36	calculating	calculate	VERB
ijassa-1111	27	37	the	the	DET
ijassa-1111	27	38	roots	root	NOUN
ijassa-1111	27	39	of	of	ADP
ijassa-1111	27	40	a	a	DET
ijassa-1111	27	41	polynomial	polynomial	NOUN
ijassa-1111	27	42	.	.	PUNCT
ijassa-1111	28	1	the	the	DET
ijassa-1111	28	2	problem	problem	NOUN
ijassa-1111	28	3	of	of	ADP
ijassa-1111	28	4	finding	find	VERB
ijassa-1111	28	5	the	the	DET
ijassa-1111	28	6	roots	root	NOUN
ijassa-1111	28	7	of	of	ADP
ijassa-1111	28	8	polynomials	polynomial	NOUN
ijassa-1111	28	9	of	of	ADP
ijassa-1111	28	10	degree	degree	NOUN
ijassa-1111	28	11	𝑛	𝑛	DET
ijassa-1111	28	12	≥	≥	NUM
ijassa-1111	28	13	5	5	NUM
ijassa-1111	28	14	is	be	AUX
ijassa-1111	28	15	unsolvable	unsolvable	ADJ
ijassa-1111	28	16	in	in	ADP
ijassa-1111	28	17	radicals	radical	NOUN
ijassa-1111	28	18	.	.	PUNCT
ijassa-1111	29	1	therefore	therefore	ADV
ijassa-1111	29	2	,	,	PUNCT
ijassa-1111	29	3	in	in	ADP
ijassa-1111	29	4	t.	t.	PROPN
ijassa-1111	29	5	saaty	saaty	NOUN
ijassa-1111	29	6	's	's	PART
ijassa-1111	29	7	method	method	NOUN
ijassa-1111	29	8	,	,	PUNCT
ijassa-1111	29	9	for	for	ADP
ijassa-1111	29	10	the	the	DET
ijassa-1111	29	11	number	number	NOUN
ijassa-1111	29	12	of	of	ADP
ijassa-1111	29	13	objects	object	NOUN
ijassa-1111	29	14	at	at	ADP
ijassa-1111	29	15	least	least	ADJ
ijassa-1111	29	16	five	five	NUM
ijassa-1111	29	17	,	,	PUNCT
ijassa-1111	29	18	the	the	DET
ijassa-1111	29	19	procedure	procedure	NOUN
ijassa-1111	29	20	for	for	ADP
ijassa-1111	29	21	finding	find	VERB
ijassa-1111	29	22	the	the	DET
ijassa-1111	29	23	eigenvalues	eigenvalue	NOUN
ijassa-1111	29	24	of	of	ADP
ijassa-1111	29	25	the	the	DET
ijassa-1111	29	26	matrix	matrix	NOUN
ijassa-1111	29	27	of	of	ADP
ijassa-1111	29	28	degrees	degree	NOUN
ijassa-1111	29	29	of	of	ADP
ijassa-1111	29	30	the	the	DET
ijassa-1111	29	31	superiority	superiority	NOUN
ijassa-1111	29	32	of	of	ADP
ijassa-1111	29	33	the	the	DET
ijassa-1111	29	34	importance	importance	NOUN
ijassa-1111	29	35	of	of	ADP
ijassa-1111	29	36	criteria	criterion	NOUN
ijassa-1111	29	37	or	or	CCONJ
ijassa-1111	29	38	preferences	preference	NOUN
ijassa-1111	29	39	of	of	ADP
ijassa-1111	29	40	alternatives	alternative	NOUN
ijassa-1111	29	41	is	be	AUX
ijassa-1111	29	42	carried	carry	VERB
ijassa-1111	29	43	out	out	ADP
ijassa-1111	29	44	using	use	VERB
ijassa-1111	29	45	numerical	numerical	ADJ
ijassa-1111	29	46	approximate	approximate	ADJ
ijassa-1111	29	47	methods	method	NOUN
ijassa-1111	29	48	for	for	ADP
ijassa-1111	29	49	finding	find	VERB
ijassa-1111	29	50	the	the	DET
ijassa-1111	29	51	roots	root	NOUN
ijassa-1111	29	52	of	of	ADP
ijassa-1111	29	53	a	a	DET
ijassa-1111	29	54	polynomial	polynomial	NOUN
ijassa-1111	29	55	implemented	implement	VERB
ijassa-1111	29	56	in	in	ADP
ijassa-1111	29	57	the	the	DET
ijassa-1111	29	58	package	package	NOUN
ijassa-1111	29	59	expert	expert	NOUN
ijassa-1111	29	60	choice	choice	NOUN
ijassa-1111	30	1	[	[	X
ijassa-1111	30	2	16	16	NUM
ijassa-1111	30	3	]	]	PUNCT
ijassa-1111	30	4	.	.	PUNCT
ijassa-1111	31	1	v.d	v.d	AUX
ijassa-1111	31	2	.	.	PROPN
ijassa-1111	31	3	noghin	noghin	PROPN
ijassa-1111	31	4	states	state	VERB
ijassa-1111	31	5	that	that	SCONJ
ijassa-1111	31	6	"	"	PUNCT
ijassa-1111	31	7	the	the	DET
ijassa-1111	31	8	value	value	NOUN
ijassa-1111	31	9	of	of	ADP
ijassa-1111	31	10	the	the	DET
ijassa-1111	31	11	compatibility	compatibility	NOUN
ijassa-1111	31	12	index	index	NOUN
ijassa-1111	31	13	can	can	AUX
ijassa-1111	31	14	only	only	ADV
ijassa-1111	31	15	indirectly	indirectly	ADV
ijassa-1111	31	16	judge	judge	VERB
ijassa-1111	31	17	the	the	DET
ijassa-1111	31	18	magnitude	magnitude	NOUN
ijassa-1111	31	19	of	of	ADP
ijassa-1111	31	20	the	the	DET
ijassa-1111	31	21	final	final	ADJ
ijassa-1111	31	22	"	"	PUNCT
ijassa-1111	31	23	model	model	NOUN
ijassa-1111	31	24	"	"	PUNCT
ijassa-1111	31	25	error	error	NOUN
ijassa-1111	31	26	:	:	PUNCT
ijassa-1111	31	27	it	it	PRON
ijassa-1111	31	28	can	can	AUX
ijassa-1111	31	29	never	never	ADV
ijassa-1111	31	30	be	be	AUX
ijassa-1111	31	31	precisely	precisely	ADV
ijassa-1111	31	32	determined	determine	VERB
ijassa-1111	31	33	by	by	ADP
ijassa-1111	31	34	anyone	anyone	PRON
ijassa-1111	31	35	.	.	PUNCT
ijassa-1111	32	1	this	this	PRON
ijassa-1111	32	2	is	be	AUX
ijassa-1111	32	3	the	the	DET
ijassa-1111	32	4	specificity	specificity	NOUN
ijassa-1111	32	5	of	of	ADP
ijassa-1111	32	6	this	this	DET
ijassa-1111	32	7	heuristic	heuristic	ADJ
ijassa-1111	32	8	approach	approach	NOUN
ijassa-1111	32	9	"	"	PUNCT
ijassa-1111	32	10	[	[	X
ijassa-1111	32	11	10	10	NUM
ijassa-1111	32	12	,	,	PUNCT
ijassa-1111	32	13	p.	p.	NOUN
ijassa-1111	32	14	1194	1194	NUM
ijassa-1111	32	15	]	]	PUNCT
ijassa-1111	32	16	.	.	PUNCT
ijassa-1111	33	1	the	the	DET
ijassa-1111	33	2	article	article	NOUN
ijassa-1111	33	3	suggests	suggest	VERB
ijassa-1111	33	4	a	a	DET
ijassa-1111	33	5	more	more	ADV
ijassa-1111	33	6	efficient	efficient	ADJ
ijassa-1111	33	7	method	method	NOUN
ijassa-1111	33	8	of	of	ADP
ijassa-1111	33	9	the	the	DET
ijassa-1111	33	10	approximation	approximation	NOUN
ijassa-1111	33	11	matrix	matrix	NOUN
ijassa-1111	33	12	(	(	PUNCT
ijassa-1111	33	13	mam	mam	PROPN
ijassa-1111	33	14	)	)	PUNCT
ijassa-1111	33	15	for	for	ADP
ijassa-1111	33	16	forming	form	VERB
ijassa-1111	33	17	optimal	optimal	ADJ
ijassa-1111	33	18	object	object	NOUN
ijassa-1111	33	19	weights	weight	NOUN
ijassa-1111	33	20	based	base	VERB
ijassa-1111	33	21	on	on	ADP
ijassa-1111	33	22	the	the	DET
ijassa-1111	33	23	matrix	matrix	NOUN
ijassa-1111	33	24	criterion	criterion	NOUN
ijassa-1111	33	25	of	of	ADP
ijassa-1111	33	26	distance	distance	NOUN
ijassa-1111	33	27	to	to	ADP
ijassa-1111	33	28	the	the	DET
ijassa-1111	33	29	original	original	ADJ
ijassa-1111	33	30	matrix	matrix	NOUN
ijassa-1111	33	31	of	of	ADP
ijassa-1111	33	32	judgments	judgment	NOUN
ijassa-1111	33	33	than	than	ADP
ijassa-1111	33	34	the	the	DET
ijassa-1111	33	35	method	method	NOUN
ijassa-1111	33	36	of	of	ADP
ijassa-1111	33	37	analyzing	analyze	VERB
ijassa-1111	33	38	hierarchies	hierarchy	NOUN
ijassa-1111	33	39	of	of	ADP
ijassa-1111	33	40	t.	t.	PROPN
ijassa-1111	33	41	saaty	saaty	NOUN
ijassa-1111	33	42	.	.	PUNCT
ijassa-1111	34	1	2	2	X
ijassa-1111	34	2	.	.	X
ijassa-1111	34	3	statement	statement	NOUN
ijassa-1111	34	4	of	of	ADP
ijassa-1111	34	5	the	the	DET
ijassa-1111	34	6	problem	problem	NOUN
ijassa-1111	34	7	of	of	ADP
ijassa-1111	34	8	approximation	approximation	NOUN
ijassa-1111	34	9	of	of	ADP
ijassa-1111	34	10	matrices	matrix	NOUN
ijassa-1111	34	11	of	of	ADP
ijassa-1111	34	12	judgments	judgment	NOUN
ijassa-1111	34	13	in	in	ADP
ijassa-1111	34	14	multi	multi	ADJ
ijassa-1111	34	15	-	-	ADJ
ijassa-1111	34	16	criteria	criterion	NOUN
ijassa-1111	34	17	applied	apply	VERB
ijassa-1111	34	18	problems	problem	NOUN
ijassa-1111	34	19	the	the	DET
ijassa-1111	34	20	aggregation	aggregation	NOUN
ijassa-1111	34	21	mechanism	mechanism	NOUN
ijassa-1111	34	22	is	be	AUX
ijassa-1111	34	23	usually	usually	ADV
ijassa-1111	34	24	represented	represent	VERB
ijassa-1111	34	25	in	in	ADP
ijassa-1111	34	26	the	the	DET
ijassa-1111	34	27	form	form	NOUN
ijassa-1111	34	28	of	of	ADP
ijassa-1111	34	29	an	an	DET
ijassa-1111	34	30	additive	additive	ADJ
ijassa-1111	34	31	candle	candle	NOUN
ijassa-1111	34	32	of	of	ADP
ijassa-1111	34	33	object	object	NOUN
ijassa-1111	34	34	ratings	rating	NOUN
ijassa-1111	34	35	(	(	PUNCT
ijassa-1111	34	36	alternatives	alternative	NOUN
ijassa-1111	34	37	,	,	PUNCT
ijassa-1111	34	38	variants	variant	NOUN
ijassa-1111	34	39	)	)	PUNCT
ijassa-1111	35	1	𝑎	𝑎	PRON
ijassa-1111	35	2	∈	∈	PROPN
ijassa-1111	35	3	𝐴	𝐴	NOUN
ijassa-1111	35	4	=	=	PUNCT
ijassa-1111	35	5	{	{	PUNCT
ijassa-1111	35	6	𝑎	𝑎	DET
ijassa-1111	35	7	|𝑙	|𝑙	NOUN
ijassa-1111	35	8	=	=	SYM
ijassa-1111	35	9	1	1	NUM
ijassa-1111	35	10	,	,	PUNCT
ijassa-1111	35	11	𝑛	𝑛	DET
ijassa-1111	35	12	}	}	PUNCT
ijassa-1111	35	13	,	,	PUNCT
ijassa-1111	35	14	according	accord	VERB
ijassa-1111	35	15	to	to	ADP
ijassa-1111	35	16	criteria	criterion	NOUN
ijassa-1111	35	17	with	with	ADP
ijassa-1111	35	18	weights	weight	NOUN
ijassa-1111	35	19	of	of	ADP
ijassa-1111	35	20	importance	importance	NOUN
ijassa-1111	35	21	in	in	ADP
ijassa-1111	35	22	the	the	DET
ijassa-1111	35	23	form	form	NOUN
ijassa-1111	35	24	[	[	X
ijassa-1111	35	25	1	1	NUM
ijassa-1111	35	26	]	]	PUNCT
ijassa-1111	35	27	:	:	PUNCT
ijassa-1111	35	28	𝐹(𝑎	𝐹(𝑎	NUM
ijassa-1111	35	29	,	,	PUNCT
ijassa-1111	35	30	𝑤	𝑤	PART
ijassa-1111	35	31	,	,	PUNCT
ijassa-1111	35	32	…	…	PUNCT
ijassa-1111	35	33	,	,	PUNCT
ijassa-1111	35	34	𝑤	𝑤	X
ijassa-1111	35	35	)	)	PUNCT
ijassa-1111	35	36	=	=	PUNCT
ijassa-1111	35	37	∑	∑	PUNCT
ijassa-1111	35	38	𝑤	𝑤	PART
ijassa-1111	35	39	𝑓	𝑓	PROPN
ijassa-1111	35	40	(	(	PUNCT
ijassa-1111	35	41	𝑎	𝑎	NOUN
ijassa-1111	35	42	)	)	PUNCT
ijassa-1111	35	43	,	,	PUNCT
ijassa-1111	35	44	∑	∑	PUNCT
ijassa-1111	35	45	𝑤	𝑤	SYM
ijassa-1111	35	46	=	=	SYM
ijassa-1111	35	47	1	1	NUM
ijassa-1111	35	48	,	,	PUNCT
ijassa-1111	35	49	106	106	NUM
ijassa-1111	35	50	v.p	v.p	PROPN
ijassa-1111	35	51	.	.	PROPN
ijassa-1111	35	52	korneenko	korneenko	PROPN
ijassa-1111	35	53	copyright	copyright	NOUN
ijassa-1111	35	54	©	©	PROPN
ijassa-1111	35	55	2024	2024	NUM
ijassa-1111	35	56	assa	assa	PROPN
ijassa-1111	35	57	adv	adv	PROPN
ijassa-1111	35	58	.	.	PUNCT
ijassa-1111	36	1	in	in	ADP
ijassa-1111	36	2	systems	system	NOUN
ijassa-1111	36	3	science	science	NOUN
ijassa-1111	36	4	and	and	CCONJ
ijassa-1111	36	5	appl	appl	NOUN
ijassa-1111	36	6	.	.	PUNCT
ijassa-1111	37	1	(	(	PUNCT
ijassa-1111	37	2	2024	2024	NUM
ijassa-1111	37	3	)	)	PUNCT
ijassa-1111	37	4	where	where	SCONJ
ijassa-1111	37	5	𝑓	𝑓	PRON
ijassa-1111	37	6	(	(	PUNCT
ijassa-1111	37	7	𝑎	𝑎	NOUN
ijassa-1111	37	8	)	)	PUNCT
ijassa-1111	37	9	is	be	AUX
ijassa-1111	37	10	the	the	DET
ijassa-1111	37	11	object	object	NOUN
ijassa-1111	37	12	score	score	NOUN
ijassa-1111	37	13	𝑎	𝑎	NOUN
ijassa-1111	37	14	in	in	ADP
ijassa-1111	37	15	the	the	DET
ijassa-1111	37	16	resulting	result	VERB
ijassa-1111	37	17	scale	scale	NOUN
ijassa-1111	37	18	according	accord	VERB
ijassa-1111	37	19	to	to	ADP
ijassa-1111	37	20	the	the	DET
ijassa-1111	37	21	criterion	criterion	NOUN
ijassa-1111	37	22	𝑓	𝑓	PRON
ijassa-1111	37	23	,	,	PUNCT
ijassa-1111	37	24	𝑗	𝑗	PROPN
ijassa-1111	37	25	=	=	SYM
ijassa-1111	37	26	1	1	NUM
ijassa-1111	37	27	,	,	PUNCT
ijassa-1111	37	28	𝑛	𝑛	NOUN
ijassa-1111	37	29	;	;	PUNCT
ijassa-1111	37	30	𝑤	𝑤	ADP
ijassa-1111	37	31	=	=	SYM
ijassa-1111	37	32	𝑤	𝑤	PROPN
ijassa-1111	37	33	(	(	PUNCT
ijassa-1111	37	34	𝑓	𝑓	X
ijassa-1111	37	35	)	)	PUNCT
ijassa-1111	37	36	is	be	AUX
ijassa-1111	37	37	the	the	DET
ijassa-1111	37	38	quantitative	quantitative	ADJ
ijassa-1111	37	39	(	(	PUNCT
ijassa-1111	37	40	normalized	normalize	VERB
ijassa-1111	37	41	)	)	PUNCT
ijassa-1111	37	42	weight	weight	NOUN
ijassa-1111	37	43	𝑓	𝑓	PRON
ijassa-1111	37	44	of	of	ADP
ijassa-1111	37	45	the	the	DET
ijassa-1111	37	46	criterion	criterion	NOUN
ijassa-1111	37	47	.	.	PUNCT
ijassa-1111	38	1	let	let	VERB
ijassa-1111	38	2	us	we	PRON
ijassa-1111	38	3	consider	consider	VERB
ijassa-1111	38	4	the	the	DET
ijassa-1111	38	5	formulation	formulation	NOUN
ijassa-1111	38	6	of	of	ADP
ijassa-1111	38	7	the	the	DET
ijassa-1111	38	8	formation	formation	NOUN
ijassa-1111	38	9	of	of	ADP
ijassa-1111	38	10	object	object	NOUN
ijassa-1111	38	11	weights	weight	NOUN
ijassa-1111	38	12	by	by	ADP
ijassa-1111	38	13	the	the	DET
ijassa-1111	38	14	criterion	criterion	NOUN
ijassa-1111	38	15	of	of	ADP
ijassa-1111	38	16	proximity	proximity	NOUN
ijassa-1111	38	17	to	to	ADP
ijassa-1111	38	18	the	the	DET
ijassa-1111	38	19	original	original	ADJ
ijassa-1111	38	20	matrix	matrix	NOUN
ijassa-1111	38	21	of	of	ADP
ijassa-1111	38	22	paired	pair	VERB
ijassa-1111	38	23	comparisons	comparison	NOUN
ijassa-1111	38	24	of	of	ADP
ijassa-1111	38	25	a	a	DET
ijassa-1111	38	26	multiplicative	multiplicative	ADJ
ijassa-1111	38	27	matrix	matrix	NOUN
ijassa-1111	38	28	.	.	PUNCT
ijassa-1111	39	1	let	let	VERB
ijassa-1111	39	2	us	we	PRON
ijassa-1111	39	3	have	have	VERB
ijassa-1111	39	4	as	as	ADP
ijassa-1111	39	5	initial	initial	ADJ
ijassa-1111	39	6	data	datum	NOUN
ijassa-1111	39	7	:	:	PUNCT
ijassa-1111	39	8	𝑉	𝑉	PROPN
ijassa-1111	39	9	=	=	PUNCT
ijassa-1111	40	1	[	[	X
ijassa-1111	40	2	𝑣	𝑣	X
ijassa-1111	40	3	]	]	PUNCT
ijassa-1111	40	4	–	–	PUNCT
ijassa-1111	40	5	the	the	DET
ijassa-1111	40	6	initial	initial	ADJ
ijassa-1111	40	7	expert	expert	NOUN
ijassa-1111	40	8	matrix	matrix	NOUN
ijassa-1111	40	9	of	of	ADP
ijassa-1111	40	10	judgments	judgment	NOUN
ijassa-1111	40	11	about	about	ADP
ijassa-1111	40	12	the	the	DET
ijassa-1111	40	13	relative	relative	ADJ
ijassa-1111	40	14	importance	importance	NOUN
ijassa-1111	40	15	of	of	ADP
ijassa-1111	40	16	objects	object	NOUN
ijassa-1111	40	17	(	(	PUNCT
ijassa-1111	40	18	criteria	criterion	NOUN
ijassa-1111	40	19	)	)	PUNCT
ijassa-1111	40	20	𝑓	𝑓	PRON
ijassa-1111	40	21	∈	∈	PROPN
ijassa-1111	40	22	𝐹	𝐹	PROPN
ijassa-1111	40	23	,	,	PUNCT
ijassa-1111	40	24	𝑖	𝑖	PROPN
ijassa-1111	40	25	,	,	PUNCT
ijassa-1111	40	26	𝑗	𝑗	NOUN
ijassa-1111	40	27	=	=	SYM
ijassa-1111	40	28	1	1	NUM
ijassa-1111	40	29	,	,	PUNCT
ijassa-1111	40	30	𝑛	𝑛	NOUN
ijassa-1111	40	31	;	;	PUNCT
ijassa-1111	40	32	𝑊	𝑊	PROPN
ijassa-1111	40	33	–	–	PUNCT
ijassa-1111	40	34	the	the	DET
ijassa-1111	40	35	set	set	NOUN
ijassa-1111	40	36	of	of	ADP
ijassa-1111	40	37	multiplicative	multiplicative	ADJ
ijassa-1111	40	38	square	square	ADJ
ijassa-1111	40	39	matrices	matrix	NOUN
ijassa-1111	40	40	n	n	ADP
ijassa-1111	40	41	of	of	ADP
ijassa-1111	40	42	the	the	DET
ijassa-1111	40	43	nth	nth	NOUN
ijassa-1111	40	44	order	order	NOUN
ijassa-1111	40	45	over	over	ADP
ijassa-1111	40	46	the	the	DET
ijassa-1111	40	47	field	field	NOUN
ijassa-1111	40	48	of	of	ADP
ijassa-1111	40	49	real	real	ADJ
ijassa-1111	40	50	numbers	number	NOUN
ijassa-1111	40	51	.	.	PUNCT
ijassa-1111	41	1	as	as	ADP
ijassa-1111	41	2	a	a	DET
ijassa-1111	41	3	measure	measure	NOUN
ijassa-1111	41	4	of	of	ADP
ijassa-1111	41	5	proximity	proximity	NOUN
ijassa-1111	41	6	𝑑(𝑉	𝑑(𝑉	NOUN
ijassa-1111	41	7	,	,	PUNCT
ijassa-1111	41	8	𝑊	𝑊	PROPN
ijassa-1111	41	9	)	)	PUNCT
ijassa-1111	41	10	between	between	ADP
ijassa-1111	41	11	the	the	DET
ijassa-1111	41	12	original	original	ADJ
ijassa-1111	41	13	𝑉	𝑉	PROPN
ijassa-1111	41	14	=	=	PUNCT
ijassa-1111	41	15	[	[	X
ijassa-1111	41	16	𝑣	𝑣	X
ijassa-1111	41	17	]	]	PUNCT
ijassa-1111	41	18	and	and	CCONJ
ijassa-1111	41	19	the	the	DET
ijassa-1111	41	20	multiplicative	multiplicative	ADJ
ijassa-1111	41	21	𝑊	𝑊	PROPN
ijassa-1111	41	22	=	=	PUNCT
ijassa-1111	41	23	𝑤	𝑤	PRON
ijassa-1111	41	24	matrix	matrix	NOUN
ijassa-1111	41	25	,	,	PUNCT
ijassa-1111	41	26	where	where	SCONJ
ijassa-1111	41	27	𝑊	𝑊	PROPN
ijassa-1111	41	28	∈	∈	PROPN
ijassa-1111	41	29	𝑊	𝑊	PROPN
ijassa-1111	41	30	,	,	PUNCT
ijassa-1111	41	31	we	we	PRON
ijassa-1111	41	32	take	take	VERB
ijassa-1111	41	33	the	the	DET
ijassa-1111	41	34	square	square	NOUN
ijassa-1111	41	35	of	of	ADP
ijassa-1111	41	36	the	the	DET
ijassa-1111	41	37	euclidean	euclidean	ADJ
ijassa-1111	41	38	l2	l2	NOUN
ijassa-1111	41	39	-	-	PUNCT
ijassa-1111	41	40	norm	norm	NOUN
ijassa-1111	41	41	equal	equal	ADJ
ijassa-1111	41	42	to	to	ADP
ijassa-1111	41	43	the	the	DET
ijassa-1111	41	44	difference	difference	NOUN
ijassa-1111	41	45	of	of	ADP
ijassa-1111	41	46	these	these	DET
ijassa-1111	41	47	matrices	matrix	NOUN
ijassa-1111	41	48	[	[	X
ijassa-1111	41	49	9	9	NUM
ijassa-1111	41	50	]	]	SYM
ijassa-1111	41	51	:	:	PUNCT
ijassa-1111	41	52	𝑑(𝑉	𝑑(𝑉	NOUN
ijassa-1111	41	53	,	,	PUNCT
ijassa-1111	41	54	𝑊	𝑊	NOUN
ijassa-1111	41	55	)	)	PUNCT
ijassa-1111	41	56	=	=	SYM
ijassa-1111	41	57	‖𝑉	‖𝑉	NOUN
ijassa-1111	41	58	−	−	PROPN
ijassa-1111	41	59	𝑊‖	𝑊‖	NOUN
ijassa-1111	42	1	=	=	SYM
ijassa-1111	42	2	(	(	PUNCT
ijassa-1111	42	3	𝑣	𝑣	DET
ijassa-1111	42	4	−	−	NOUN
ijassa-1111	42	5	𝑤	𝑤	PROPN
ijassa-1111	42	6	)	)	PUNCT
ijassa-1111	42	7	.	.	PUNCT
ijassa-1111	43	1	(	(	PUNCT
ijassa-1111	43	2	2.1	2.1	NUM
ijassa-1111	43	3	)	)	PUNCT
ijassa-1111	43	4	then	then	ADV
ijassa-1111	43	5	the	the	DET
ijassa-1111	43	6	mathematical	mathematical	ADJ
ijassa-1111	43	7	formulation	formulation	NOUN
ijassa-1111	43	8	of	of	ADP
ijassa-1111	43	9	the	the	DET
ijassa-1111	43	10	problem	problem	NOUN
ijassa-1111	43	11	of	of	ADP
ijassa-1111	43	12	choosing	choose	VERB
ijassa-1111	43	13	a	a	DET
ijassa-1111	43	14	multiplicative	multiplicative	ADJ
ijassa-1111	43	15	matrix	matrix	NOUN
ijassa-1111	43	16	w	w	NOUN
ijassa-1111	43	17	that	that	PRON
ijassa-1111	43	18	approximates	approximate	VERB
ijassa-1111	43	19	the	the	DET
ijassa-1111	43	20	original	original	ADJ
ijassa-1111	43	21	matrix	matrix	NOUN
ijassa-1111	43	22	𝑉	𝑉	NOUN
ijassa-1111	43	23	=	=	PUNCT
ijassa-1111	44	1	[	[	X
ijassa-1111	44	2	𝑣	𝑣	X
ijassa-1111	44	3	]	]	X
ijassa-1111	44	4	,	,	PUNCT
ijassa-1111	44	5	i.e.	i.e.	X
ijassa-1111	44	6	,	,	PUNCT
ijassa-1111	44	7	the	the	DET
ijassa-1111	44	8	closest	close	ADJ
ijassa-1111	44	9	approach	approach	NOUN
ijassa-1111	44	10	to	to	ADP
ijassa-1111	44	11	the	the	DET
ijassa-1111	44	12	original	original	ADJ
ijassa-1111	44	13	expert	expert	NOUN
ijassa-1111	44	14	judgment	judgment	NOUN
ijassa-1111	44	15	matrix	matrix	NOUN
ijassa-1111	44	16	,	,	PUNCT
ijassa-1111	44	17	is	be	AUX
ijassa-1111	44	18	reduced	reduce	VERB
ijassa-1111	44	19	to	to	ADP
ijassa-1111	44	20	minimizing	minimize	VERB
ijassa-1111	44	21	the	the	DET
ijassa-1111	44	22	indicator	indicator	NOUN
ijassa-1111	44	23	(	(	PUNCT
ijassa-1111	44	24	2.1	2.1	NUM
ijassa-1111	44	25	)	)	PUNCT
ijassa-1111	44	26	in	in	ADP
ijassa-1111	44	27	the	the	DET
ijassa-1111	44	28	form	form	NOUN
ijassa-1111	44	29	(	(	PUNCT
ijassa-1111	44	30	v	v	NOUN
ijassa-1111	44	31	−	−	PROPN
ijassa-1111	44	32	w	w	NOUN
ijassa-1111	44	33	)	)	PUNCT
ijassa-1111	44	34	→	→	SYM
ijassa-1111	44	35	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
ijassa-1111	44	36	∈	∈	PROPN
ijassa-1111	44	37	,	,	PUNCT
ijassa-1111	44	38	(	(	PUNCT
ijassa-1111	44	39	2.2	2.2	NUM
ijassa-1111	44	40	)	)	PUNCT
ijassa-1111	44	41	provided	provide	VERB
ijassa-1111	44	42	that	that	SCONJ
ijassa-1111	44	43	the	the	DET
ijassa-1111	44	44	matrix	matrix	NOUN
ijassa-1111	44	45	elements	element	NOUN
ijassa-1111	44	46	are	be	AUX
ijassa-1111	44	47	multiplicative	multiplicative	ADJ
ijassa-1111	44	48	𝑊	𝑊	NOUN
ijassa-1111	44	49	=	=	SYM
ijassa-1111	45	1	[	[	X
ijassa-1111	45	2	𝑤	𝑤	X
ijassa-1111	45	3	]	]	X
ijassa-1111	45	4	:	:	PUNCT
ijassa-1111	45	5	w	w	X
ijassa-1111	45	6	=	=	SYM
ijassa-1111	45	7	w	w	PROPN
ijassa-1111	45	8	w	w	PROPN
ijassa-1111	45	9	,	,	PUNCT
ijassa-1111	45	10	∀	∀	VERB
ijassa-1111	46	1	i	i	PROPN
ijassa-1111	46	2	,	,	PUNCT
ijassa-1111	46	3	j	j	PROPN
ijassa-1111	46	4	,	,	PUNCT
ijassa-1111	46	5	k	k	PROPN
ijassa-1111	46	6	=	=	SYM
ijassa-1111	46	7	1	1	NUM
ijassa-1111	46	8	,	,	PUNCT
ijassa-1111	46	9	n.	n.	NOUN
ijassa-1111	46	10	(	(	PUNCT
ijassa-1111	46	11	2.3	2.3	NUM
ijassa-1111	46	12	)	)	PUNCT
ijassa-1111	46	13	due	due	ADP
ijassa-1111	46	14	to	to	ADP
ijassa-1111	46	15	condition	condition	NOUN
ijassa-1111	46	16	(	(	PUNCT
ijassa-1111	46	17	2.3	2.3	NUM
ijassa-1111	46	18	)	)	PUNCT
ijassa-1111	46	19	,	,	PUNCT
ijassa-1111	46	20	it	it	PRON
ijassa-1111	46	21	is	be	AUX
ijassa-1111	46	22	not	not	PART
ijassa-1111	46	23	analytically	analytically	ADV
ijassa-1111	46	24	possible	possible	ADJ
ijassa-1111	46	25	to	to	PART
ijassa-1111	46	26	obtain	obtain	VERB
ijassa-1111	46	27	a	a	DET
ijassa-1111	46	28	solution	solution	NOUN
ijassa-1111	46	29	to	to	ADP
ijassa-1111	46	30	the	the	DET
ijassa-1111	46	31	original	original	ADJ
ijassa-1111	46	32	problem	problem	NOUN
ijassa-1111	46	33	using	use	VERB
ijassa-1111	46	34	one	one	NUM
ijassa-1111	46	35	of	of	ADP
ijassa-1111	46	36	the	the	DET
ijassa-1111	46	37	classical	classical	ADJ
ijassa-1111	46	38	optimization	optimization	NOUN
ijassa-1111	46	39	methods	method	NOUN
ijassa-1111	46	40	,	,	PUNCT
ijassa-1111	46	41	for	for	ADP
ijassa-1111	46	42	example	example	NOUN
ijassa-1111	46	43	,	,	PUNCT
ijassa-1111	46	44	the	the	DET
ijassa-1111	46	45	lagrange	lagrange	ADJ
ijassa-1111	46	46	multiplier	multipli	ADJ
ijassa-1111	46	47	method	method	NOUN
ijassa-1111	46	48	.	.	PUNCT
ijassa-1111	47	1	let	let	VERB
ijassa-1111	47	2	us	we	PRON
ijassa-1111	47	3	use	use	VERB
ijassa-1111	47	4	the	the	DET
ijassa-1111	47	5	properties	property	NOUN
ijassa-1111	47	6	of	of	ADP
ijassa-1111	47	7	the	the	DET
ijassa-1111	47	8	multiplicative	multiplicative	ADJ
ijassa-1111	47	9	matrix	matrix	NOUN
ijassa-1111	47	10	and	and	CCONJ
ijassa-1111	47	11	solve	solve	VERB
ijassa-1111	47	12	this	this	DET
ijassa-1111	47	13	problem	problem	NOUN
ijassa-1111	47	14	by	by	ADP
ijassa-1111	47	15	reducing	reduce	VERB
ijassa-1111	47	16	the	the	DET
ijassa-1111	47	17	original	original	ADJ
ijassa-1111	47	18	problem	problem	NOUN
ijassa-1111	47	19	to	to	ADP
ijassa-1111	47	20	an	an	DET
ijassa-1111	47	21	equivalent	equivalent	ADJ
ijassa-1111	47	22	problem	problem	NOUN
ijassa-1111	47	23	.	.	PUNCT
ijassa-1111	48	1	3	3	X
ijassa-1111	48	2	.	.	X
ijassa-1111	48	3	special	special	ADJ
ijassa-1111	48	4	linear	linear	PROPN
ijassa-1111	48	5	properties	property	NOUN
ijassa-1111	48	6	of	of	ADP
ijassa-1111	48	7	a	a	DET
ijassa-1111	48	8	multiplicative	multiplicative	ADJ
ijassa-1111	48	9	matrix	matrix	NOUN
ijassa-1111	48	10	to	to	PART
ijassa-1111	48	11	solve	solve	VERB
ijassa-1111	48	12	the	the	DET
ijassa-1111	48	13	original	original	ADJ
ijassa-1111	48	14	problem	problem	NOUN
ijassa-1111	48	15	(	(	PUNCT
ijassa-1111	48	16	2.2)–(2.3	2.2)–(2.3	NUM
ijassa-1111	48	17	)	)	PUNCT
ijassa-1111	48	18	,	,	PUNCT
ijassa-1111	48	19	it	it	PRON
ijassa-1111	48	20	is	be	AUX
ijassa-1111	48	21	necessary	necessary	ADJ
ijassa-1111	48	22	to	to	PART
ijassa-1111	48	23	find	find	VERB
ijassa-1111	48	24	elements	element	NOUN
ijassa-1111	48	25	of	of	ADP
ijassa-1111	48	26	the	the	DET
ijassa-1111	48	27	multiplicative	multiplicative	ADJ
ijassa-1111	48	28	𝑊	𝑊	PROPN
ijassa-1111	48	29	=	=	PUNCT
ijassa-1111	48	30	𝑤	𝑤	PROPN
ijassa-1111	48	31	,	,	PUNCT
ijassa-1111	48	32	∀𝑖	∀𝑖	PROPN
ijassa-1111	48	33	,	,	PUNCT
ijassa-1111	48	34	𝑗	𝑗	NOUN
ijassa-1111	48	35	=	=	SYM
ijassa-1111	48	36	1	1	NUM
ijassa-1111	48	37	,	,	PUNCT
ijassa-1111	48	38	𝑛	𝑛	ADJ
ijassa-1111	48	39	,	,	PUNCT
ijassa-1111	48	40	matrix	matrix	NOUN
ijassa-1111	48	41	,	,	PUNCT
ijassa-1111	48	42	that	that	PRON
ijassa-1111	48	43	provides	provide	VERB
ijassa-1111	48	44	a	a	DET
ijassa-1111	48	45	minimum	minimum	NOUN
ijassa-1111	48	46	for	for	ADP
ijassa-1111	48	47	the	the	DET
ijassa-1111	48	48	quadratic	quadratic	ADJ
ijassa-1111	48	49	criterion	criterion	NOUN
ijassa-1111	48	50	𝑑(𝑉	𝑑(𝑉	NOUN
ijassa-1111	48	51	,	,	PUNCT
ijassa-1111	48	52	𝑊	𝑊	PROPN
ijassa-1111	48	53	)	)	PUNCT
ijassa-1111	48	54	(	(	PUNCT
ijassa-1111	48	55	2.1	2.1	NUM
ijassa-1111	48	56	)	)	PUNCT
ijassa-1111	48	57	under	under	ADP
ijassa-1111	48	58	condition	condition	NOUN
ijassa-1111	48	59	(	(	PUNCT
ijassa-1111	48	60	2.3	2.3	NUM
ijassa-1111	48	61	)	)	PUNCT
ijassa-1111	48	62	.	.	PUNCT
ijassa-1111	49	1	it	it	PRON
ijassa-1111	49	2	turns	turn	VERB
ijassa-1111	49	3	out	out	ADP
ijassa-1111	49	4	that	that	SCONJ
ijassa-1111	49	5	for	for	ADP
ijassa-1111	49	6	a	a	DET
ijassa-1111	49	7	multiplicative	multiplicative	ADJ
ijassa-1111	49	8	matrix	matrix	NOUN
ijassa-1111	49	9	,	,	PUNCT
ijassa-1111	49	10	the	the	DET
ijassa-1111	49	11	relationship	relationship	NOUN
ijassa-1111	49	12	between	between	ADP
ijassa-1111	49	13	the	the	DET
ijassa-1111	49	14	elements	element	NOUN
ijassa-1111	49	15	of	of	ADP
ijassa-1111	49	16	the	the	DET
ijassa-1111	49	17	columns	column	NOUN
ijassa-1111	49	18	of	of	ADP
ijassa-1111	49	19	the	the	DET
ijassa-1111	49	20	matrix	matrix	NOUN
ijassa-1111	49	21	and	and	CCONJ
ijassa-1111	49	22	the	the	DET
ijassa-1111	49	23	elements	element	NOUN
ijassa-1111	49	24	of	of	ADP
ijassa-1111	49	25	the	the	DET
ijassa-1111	49	26	right	right	ADJ
ijassa-1111	49	27	eigenvector	eigenvector	NOUN
ijassa-1111	49	28	is	be	AUX
ijassa-1111	49	29	valid	valid	ADJ
ijassa-1111	49	30	.	.	PUNCT
ijassa-1111	50	1	to	to	PART
ijassa-1111	50	2	do	do	VERB
ijassa-1111	50	3	this	this	PRON
ijassa-1111	50	4	,	,	PUNCT
ijassa-1111	50	5	consider	consider	VERB
ijassa-1111	50	6	two	two	NUM
ijassa-1111	50	7	statements	statement	NOUN
ijassa-1111	50	8	.	.	PUNCT
ijassa-1111	51	1	the	the	DET
ijassa-1111	51	2	work	work	NOUN
ijassa-1111	51	3	of	of	ADP
ijassa-1111	51	4	b.g	b.g	PROPN
ijassa-1111	51	5	.	.	PUNCT
ijassa-1111	51	6	mirkin	mirkin	PROPN
ijassa-1111	51	7	[	[	X
ijassa-1111	51	8	17	17	NUM
ijassa-1111	51	9	,	,	PUNCT
ijassa-1111	51	10	p.	p.	NOUN
ijassa-1111	51	11	183–184	183–184	NUM
ijassa-1111	51	12	]	]	PUNCT
ijassa-1111	51	13	provided	provide	VERB
ijassa-1111	51	14	that	that	SCONJ
ijassa-1111	51	15	the	the	DET
ijassa-1111	51	16	matrix	matrix	NOUN
ijassa-1111	51	17	𝐵	𝐵	NOUN
ijassa-1111	51	18	=	=	SYM
ijassa-1111	51	19	𝑏	𝑏	PROPN
ijassa-1111	51	20	,	,	PUNCT
ijassa-1111	51	21	∀	∀	NOUN
ijassa-1111	51	22	𝑖	𝑖	NOUN
ijassa-1111	51	23	,	,	PUNCT
ijassa-1111	51	24	𝑗	𝑗	NOUN
ijassa-1111	51	25	=	=	SYM
ijassa-1111	51	26	1	1	NUM
ijassa-1111	51	27	,	,	PUNCT
ijassa-1111	51	28	𝑛	𝑛	PRON
ijassa-1111	51	29	is	be	AUX
ijassa-1111	51	30	over	over	ADP
ijassa-1111	51	31	traditional	traditional	ADJ
ijassa-1111	51	32	if	if	SCONJ
ijassa-1111	51	33	there	there	PRON
ijassa-1111	51	34	exists	exist	VERB
ijassa-1111	51	35	a	a	DET
ijassa-1111	51	36	positive	positive	ADJ
ijassa-1111	51	37	vector	vector	NOUN
ijassa-1111	51	38	𝑥	𝑥	NOUN
ijassa-1111	51	39	=	=	PUNCT
ijassa-1111	51	40	(	(	PUNCT
ijassa-1111	51	41	𝑥	𝑥	INTJ
ijassa-1111	51	42	,	,	PUNCT
ijassa-1111	51	43	.	.	PUNCT
ijassa-1111	51	44	.	.	PUNCT
ijassa-1111	51	45	.	.	PUNCT
ijassa-1111	52	1	,	,	PUNCT
ijassa-1111	52	2	𝑥	𝑥	X
ijassa-1111	52	3	)	)	PUNCT
ijassa-1111	52	4	such	such	ADJ
ijassa-1111	52	5	that	that	SCONJ
ijassa-1111	52	6	that	that	SCONJ
ijassa-1111	52	7	𝑏	𝑏	PROPN
ijassa-1111	52	8	=	=	PUNCT
ijassa-1111	52	9	and	and	CCONJ
ijassa-1111	52	10	the	the	DET
ijassa-1111	52	11	vector	vector	NOUN
ijassa-1111	52	12	𝑥	𝑥	PROPN
ijassa-1111	52	13	is	be	AUX
ijassa-1111	52	14	a	a	DET
ijassa-1111	52	15	point	point	NOUN
ijassa-1111	52	16	of	of	ADP
ijassa-1111	52	17	equilibrium	equilibrium	NOUN
ijassa-1111	52	18	process	process	NOUN
ijassa-1111	52	19	:	:	PUNCT
ijassa-1111	52	20	𝑞	𝑞	X
ijassa-1111	52	21	=	=	SYM
ijassa-1111	52	22	𝐵𝑞	𝐵𝑞	PROPN
ijassa-1111	52	23	,	,	PUNCT
ijassa-1111	52	24	𝑡	𝑡	PROPN
ijassa-1111	52	25	=	=	NOUN
ijassa-1111	52	26	1	1	NUM
ijassa-1111	52	27	,	,	PUNCT
ijassa-1111	52	28	2	2	NUM
ijassa-1111	52	29	,	,	PUNCT
ijassa-1111	52	30	.	.	PUNCT
ijassa-1111	52	31	.	.	PUNCT
ijassa-1111	53	1	.	.	PUNCT
ijassa-1111	54	1	,	,	PUNCT
ijassa-1111	54	2	which	which	PRON
ijassa-1111	54	3	in	in	ADP
ijassa-1111	54	4	the	the	DET
ijassa-1111	54	5	limit	limit	NOUN
ijassa-1111	54	6	leads	lead	VERB
ijassa-1111	54	7	to	to	ADP
ijassa-1111	54	8	a	a	DET
ijassa-1111	54	9	private	private	ADJ
ijassa-1111	54	10	vector	vector	NOUN
ijassa-1111	54	11	𝑞	𝑞	X
ijassa-1111	54	12	=	=	PROPN
ijassa-1111	54	13	lim	lim	PROPN
ijassa-1111	54	14	⟶	⟶	PROPN
ijassa-1111	54	15	𝑞	𝑞	X
ijassa-1111	54	16	.	.	PUNCT
ijassa-1111	55	1	we	we	PRON
ijassa-1111	55	2	show	show	VERB
ijassa-1111	55	3	that	that	SCONJ
ijassa-1111	55	4	the	the	DET
ijassa-1111	55	5	multiplicative	multiplicative	ADJ
ijassa-1111	55	6	matrix	matrix	NOUN
ijassa-1111	55	7	has	have	VERB
ijassa-1111	55	8	several	several	ADJ
ijassa-1111	55	9	other	other	ADJ
ijassa-1111	55	10	properties	property	NOUN
ijassa-1111	55	11	that	that	PRON
ijassa-1111	55	12	will	will	AUX
ijassa-1111	55	13	be	be	AUX
ijassa-1111	55	14	useful	useful	ADJ
ijassa-1111	55	15	in	in	ADP
ijassa-1111	55	16	reducing	reduce	VERB
ijassa-1111	55	17	the	the	DET
ijassa-1111	55	18	original	original	ADJ
ijassa-1111	55	19	,	,	PUNCT
ijassa-1111	55	20	analytically	analytically	ADV
ijassa-1111	55	21	unsolvable	unsolvable	ADJ
ijassa-1111	55	22	problem	problem	NOUN
ijassa-1111	55	23	(	(	PUNCT
ijassa-1111	55	24	2.2)–(2.3	2.2)–(2.3	NUM
ijassa-1111	55	25	)	)	PUNCT
ijassa-1111	55	26	in	in	ADP
ijassa-1111	55	27	the	the	DET
ijassa-1111	55	28	framework	framework	NOUN
ijassa-1111	55	29	of	of	ADP
ijassa-1111	55	30	classical	classical	ADJ
ijassa-1111	55	31	optimization	optimization	NOUN
ijassa-1111	55	32	methods	method	NOUN
ijassa-1111	55	33	to	to	ADP
ijassa-1111	55	34	an	an	DET
ijassa-1111	55	35	equivalent	equivalent	ADJ
ijassa-1111	55	36	one	one	NUM
ijassa-1111	55	37	.	.	PUNCT
ijassa-1111	56	1	3.1	3.1	NUM
ijassa-1111	56	2	.	.	PUNCT
ijassa-1111	57	1	the	the	DET
ijassa-1111	57	2	relationship	relationship	NOUN
ijassa-1111	57	3	between	between	ADP
ijassa-1111	57	4	normalized	normalize	VERB
ijassa-1111	57	5	column	column	NOUN
ijassa-1111	57	6	elements	element	NOUN
ijassa-1111	57	7	of	of	ADP
ijassa-1111	57	8	a	a	DET
ijassa-1111	57	9	multiplicative	multiplicative	ADJ
ijassa-1111	57	10	matrix	matrix	NOUN
ijassa-1111	57	11	and	and	CCONJ
ijassa-1111	57	12	elements	element	NOUN
ijassa-1111	57	13	of	of	ADP
ijassa-1111	57	14	the	the	DET
ijassa-1111	57	15	right	right	PROPN
ijassa-1111	57	16	eigenvector	eigenvector	NOUN
ijassa-1111	57	17	theorem	theorem	ADJ
ijassa-1111	57	18	3.1	3.1	NUM
ijassa-1111	57	19	:	:	SYM
ijassa-1111	57	20	1	1	NUM
ijassa-1111	57	21	.	.	PUNCT
ijassa-1111	57	22	between	between	ADP
ijassa-1111	57	23	the	the	DET
ijassa-1111	57	24	elements	element	NOUN
ijassa-1111	57	25	𝑤	𝑤	ADP
ijassa-1111	57	26	of	of	ADP
ijassa-1111	57	27	a	a	DET
ijassa-1111	57	28	multiplicative	multiplicative	ADJ
ijassa-1111	57	29	matrix	matrix	NOUN
ijassa-1111	57	30	𝑊	𝑊	NOUN
ijassa-1111	57	31	=	=	PUNCT
ijassa-1111	57	32	𝑤	𝑤	PROPN
ijassa-1111	57	33	,	,	PUNCT
ijassa-1111	57	34	∀𝑖	∀𝑖	PROPN
ijassa-1111	57	35	,	,	PUNCT
ijassa-1111	57	36	𝑗	𝑗	NOUN
ijassa-1111	57	37	=	=	SYM
ijassa-1111	57	38	1	1	NUM
ijassa-1111	57	39	,	,	PUNCT
ijassa-1111	57	40	𝑛	𝑛	NOUN
ijassa-1111	57	41	,	,	PUNCT
ijassa-1111	57	42	and	and	CCONJ
ijassa-1111	57	43	any	any	DET
ijassa-1111	57	44	pair	pair	NOUN
ijassa-1111	57	45	(	(	PUNCT
ijassa-1111	57	46	𝑤	𝑤	INTJ
ijassa-1111	57	47	,	,	PUNCT
ijassa-1111	57	48	𝑤	𝑤	NOUN
ijassa-1111	57	49	)	)	PUNCT
ijassa-1111	57	50	component	component	NOUN
ijassa-1111	57	51	of	of	ADP
ijassa-1111	57	52	the	the	DET
ijassa-1111	57	53	right	right	PROPN
ijassa-1111	57	54	eigenvector	eigenvector	PROPN
ijassa-1111	57	55	�	�	PROPN
ijassa-1111	57	56	⃗	⃗	PROPN
ijassa-1111	57	57	�	�	NOUN
ijassa-1111	57	58	=	=	SYM
ijassa-1111	57	59	(	(	PUNCT
ijassa-1111	57	60	𝑤	𝑤	INTJ
ijassa-1111	57	61	,	,	PUNCT
ijassa-1111	57	62	.	.	PUNCT
ijassa-1111	57	63	.	.	PUNCT
ijassa-1111	58	1	.	.	PUNCT
ijassa-1111	59	1	,	,	PUNCT
ijassa-1111	59	2	𝑤	𝑤	X
ijassa-1111	59	3	)	)	PUNCT
ijassa-1111	59	4	true	true	ADJ
ijassa-1111	59	5	bijective	bijective	ADJ
ijassa-1111	59	6	mapping	mapping	NOUN
ijassa-1111	59	7	↦	↦	NOUN
ijassa-1111	59	8	𝑤	𝑤	ADP
ijassa-1111	59	9	,	,	PUNCT
ijassa-1111	59	10	whose	whose	DET
ijassa-1111	59	11	every	every	DET
ijassa-1111	59	12	attitude	attitude	NOUN
ijassa-1111	59	13	to	to	ADP
ijassa-1111	59	14	one	one	NUM
ijassa-1111	59	15	mapping	mapping	NOUN
ijassa-1111	59	16	element	element	NOUN
ijassa-1111	59	17	𝑤	𝑤	PROPN
ijassa-1111	59	18	of	of	ADP
ijassa-1111	59	19	the	the	DET
ijassa-1111	59	20	matrix	matrix	NOUN
ijassa-1111	59	21	w	w	NOUN
ijassa-1111	59	22	and	and	CCONJ
ijassa-1111	59	23	back	back	VERB
ijassa-1111	59	24	the	the	DET
ijassa-1111	59	25	approximation	approximation	NOUN
ijassa-1111	59	26	matrix	matrix	NOUN
ijassa-1111	59	27	method	method	NOUN
ijassa-1111	59	28	and	and	CCONJ
ijassa-1111	59	29	its	its	PRON
ijassa-1111	59	30	comparison	comparison	NOUN
ijassa-1111	59	31	…	…	PUNCT
ijassa-1111	59	32	107	107	NUM
ijassa-1111	59	33	copyright	copyright	NOUN
ijassa-1111	59	34	©	©	PROPN
ijassa-1111	59	35	2024	2024	NUM
ijassa-1111	59	36	assa	assa	PROPN
ijassa-1111	59	37	adv	adv	PROPN
ijassa-1111	59	38	.	.	PUNCT
ijassa-1111	60	1	in	in	ADP
ijassa-1111	60	2	systems	system	NOUN
ijassa-1111	60	3	science	science	NOUN
ijassa-1111	60	4	and	and	CCONJ
ijassa-1111	60	5	appl	appl	NOUN
ijassa-1111	60	6	.	.	PUNCT
ijassa-1111	61	1	(	(	PUNCT
ijassa-1111	61	2	2024	2024	NUM
ijassa-1111	61	3	)	)	PUNCT
ijassa-1111	61	4	𝑤	𝑤	ADP
ijassa-1111	61	5	↦	↦	PROPN
ijassa-1111	61	6	𝑤	𝑤	ADP
ijassa-1111	61	7	𝑤	𝑤	ADP
ijassa-1111	61	8	,	,	PUNCT
ijassa-1111	61	9	provided	provide	VERB
ijassa-1111	61	10	this	this	PRON
ijassa-1111	61	11	is	be	AUX
ijassa-1111	61	12	true	true	ADJ
ijassa-1111	61	13	equality	equality	NOUN
ijassa-1111	61	14	:	:	PUNCT
ijassa-1111	61	15	𝑤	𝑤	X
ijassa-1111	61	16	=	=	SYM
ijassa-1111	61	17	𝑤	𝑤	PART
ijassa-1111	61	18	𝑤	𝑤	NOUN
ijassa-1111	61	19	,	,	PUNCT
ijassa-1111	61	20	∀	∀	X
ijassa-1111	61	21	𝑖	𝑖	NOUN
ijassa-1111	61	22	,	,	PUNCT
ijassa-1111	61	23	𝑗	𝑗	NOUN
ijassa-1111	61	24	=	=	SYM
ijassa-1111	61	25	1	1	NUM
ijassa-1111	61	26	,	,	PUNCT
ijassa-1111	61	27	𝑛.	𝑛.	NOUN
ijassa-1111	61	28	(	(	PUNCT
ijassa-1111	61	29	3.4	3.4	NUM
ijassa-1111	61	30	)	)	PUNCT
ijassa-1111	61	31	2	2	NUM
ijassa-1111	61	32	.	.	PUNCT
ijassa-1111	62	1	the	the	DET
ijassa-1111	62	2	normalized	normalize	VERB
ijassa-1111	62	3	elements	element	NOUN
ijassa-1111	62	4	𝑤	𝑤	ADP
ijassa-1111	62	5	of	of	ADP
ijassa-1111	62	6	the	the	DET
ijassa-1111	62	7	columns	column	NOUN
ijassa-1111	62	8	�	�	NOUN
ijassa-1111	62	9	⃗	⃗	NOUN
ijassa-1111	62	10	�	�	NOUN
ijassa-1111	62	11	=	=	SYM
ijassa-1111	62	12	(	(	PUNCT
ijassa-1111	62	13	𝑤	𝑤	INTJ
ijassa-1111	62	14	,	,	PUNCT
ijassa-1111	62	15	…	…	PUNCT
ijassa-1111	62	16	,	,	PUNCT
ijassa-1111	62	17	𝑤	𝑤	X
ijassa-1111	62	18	)	)	PUNCT
ijassa-1111	62	19	,	,	PUNCT
ijassa-1111	62	20	𝑗	𝑗	NOUN
ijassa-1111	62	21	=	=	SYM
ijassa-1111	62	22	1	1	NUM
ijassa-1111	62	23	,	,	PUNCT
ijassa-1111	62	24	𝑛	𝑛	NOUN
ijassa-1111	62	25	,	,	PUNCT
ijassa-1111	62	26	coincide	coincide	NOUN
ijassa-1111	62	27	with	with	ADP
ijassa-1111	62	28	each	each	DET
ijassa-1111	62	29	other	other	ADJ
ijassa-1111	62	30	and	and	CCONJ
ijassa-1111	62	31	are	be	AUX
ijassa-1111	62	32	equal	equal	ADJ
ijassa-1111	62	33	to	to	ADP
ijassa-1111	62	34	the	the	DET
ijassa-1111	62	35	normalized	normalize	VERB
ijassa-1111	62	36	right	right	ADJ
ijassa-1111	62	37	eigenvector	eigenvector	NOUN
ijassa-1111	62	38	,	,	PUNCT
ijassa-1111	62	39	i.e.	i.e.	X
ijassa-1111	62	40	�	�	PROPN
ijassa-1111	62	41	⃗	⃗	NOUN
ijassa-1111	62	42	�	�	NOUN
ijassa-1111	62	43	=	=	SYM
ijassa-1111	62	44	𝑤	𝑤	PART
ijassa-1111	62	45	…	…	PUNCT
ijassa-1111	62	46	𝑤	𝑤	X
ijassa-1111	62	47	=	=	SYM
ijassa-1111	62	48	𝑤	𝑤	PART
ijassa-1111	62	49	…	…	PUNCT
ijassa-1111	62	50	𝑤	𝑤	X
ijassa-1111	62	51	=	=	PUNCT
ijassa-1111	62	52	�	�	PROPN
ijassa-1111	62	53	⃗	⃗	NOUN
ijassa-1111	62	54	�	�	PROPN
ijassa-1111	62	55	,	,	PUNCT
ijassa-1111	62	56	∀	∀	X
ijassa-1111	62	57	𝑗	𝑗	NOUN
ijassa-1111	62	58	=	=	SYM
ijassa-1111	62	59	1	1	NUM
ijassa-1111	62	60	,	,	PUNCT
ijassa-1111	62	61	𝑛	𝑛	PROPN
ijassa-1111	62	62	,	,	PUNCT
ijassa-1111	62	63	(	(	PUNCT
ijassa-1111	62	64	3.5	3.5	NUM
ijassa-1111	62	65	)	)	PUNCT
ijassa-1111	62	66	where	where	SCONJ
ijassa-1111	62	67	𝑤	𝑤	ADP
ijassa-1111	62	68	=	=	PRON
ijassa-1111	62	69	∑	∑	PROPN
ijassa-1111	62	70	is	be	AUX
ijassa-1111	62	71	the	the	DET
ijassa-1111	62	72	normalized	normalize	VERB
ijassa-1111	62	73	element	element	NOUN
ijassa-1111	62	74	𝑗	𝑗	PROPN
ijassa-1111	62	75	of	of	ADP
ijassa-1111	62	76	the	the	DET
ijassa-1111	62	77	j	j	PROPN
ijassa-1111	62	78	-	-	PUNCT
ijassa-1111	62	79	th	th	VERB
ijassa-1111	62	80	column	column	NOUN
ijassa-1111	62	81	of	of	ADP
ijassa-1111	62	82	�	�	PROPN
ijassa-1111	62	83	⃗	⃗	NOUN
ijassa-1111	62	84	�	�	NOUN
ijassa-1111	62	85	;	;	PUNCT
ijassa-1111	62	86	𝑤	𝑤	X
ijassa-1111	62	87	=	=	PUNCT
ijassa-1111	62	88	∑	∑	PROPN
ijassa-1111	62	89	is	be	AUX
ijassa-1111	62	90	the	the	DET
ijassa-1111	62	91	normalized	normalize	VERB
ijassa-1111	62	92	element	element	NOUN
ijassa-1111	62	93	of	of	ADP
ijassa-1111	62	94	the	the	DET
ijassa-1111	62	95	i	i	PROPN
ijassa-1111	62	96	-	-	PUNCT
ijassa-1111	62	97	th	th	X
ijassa-1111	62	98	row	row	NOUN
ijassa-1111	62	99	of	of	ADP
ijassa-1111	62	100	the	the	DET
ijassa-1111	62	101	right	right	PROPN
ijassa-1111	62	102	eigenvector	eigenvector	PROPN
ijassa-1111	62	103	�	�	PROPN
ijassa-1111	62	104	⃗	⃗	PROPN
ijassa-1111	62	105	�	�	PROPN
ijassa-1111	62	106	.	.	PUNCT
ijassa-1111	63	1	3	3	NUM
ijassa-1111	63	2	.	.	PUNCT
ijassa-1111	64	1	the	the	DET
ijassa-1111	64	2	multiplicative	multiplicative	ADJ
ijassa-1111	64	3	matrix	matrix	NOUN
ijassa-1111	64	4	has	have	VERB
ijassa-1111	64	5	one	one	NUM
ijassa-1111	64	6	basis	basis	NOUN
ijassa-1111	64	7	row	row	NOUN
ijassa-1111	64	8	.	.	PUNCT
ijassa-1111	65	1	proof	proof	NOUN
ijassa-1111	65	2	.	.	PUNCT
ijassa-1111	66	1	1	1	X
ijassa-1111	66	2	.	.	X
ijassa-1111	66	3	since	since	SCONJ
ijassa-1111	66	4	by	by	ADP
ijassa-1111	66	5	hypothesis	hypothesis	NOUN
ijassa-1111	66	6	the	the	DET
ijassa-1111	66	7	matrix	matrix	NOUN
ijassa-1111	66	8	𝑊	𝑊	NOUN
ijassa-1111	66	9	=	=	PUNCT
ijassa-1111	66	10	𝑤	𝑤	X
ijassa-1111	66	11	multiplicative	multiplicative	NOUN
ijassa-1111	66	12	then	then	ADV
ijassa-1111	66	13	will	will	AUX
ijassa-1111	66	14	provide	provide	VERB
ijassa-1111	66	15	that	that	SCONJ
ijassa-1111	66	16	,	,	PUNCT
ijassa-1111	66	17	if	if	SCONJ
ijassa-1111	66	18	for	for	ADP
ijassa-1111	66	19	any	any	DET
ijassa-1111	66	20	pair	pair	NOUN
ijassa-1111	66	21	of	of	ADP
ijassa-1111	66	22	numbers	number	NOUN
ijassa-1111	66	23	from	from	ADP
ijassa-1111	66	24	{	{	PUNCT
ijassa-1111	66	25	𝑤	𝑤	INTJ
ijassa-1111	66	26	,	,	PUNCT
ijassa-1111	66	27	.	.	PUNCT
ijassa-1111	66	28	.	.	PUNCT
ijassa-1111	67	1	.	.	PUNCT
ijassa-1111	68	1	,	,	PUNCT
ijassa-1111	68	2	𝑤	𝑤	X
ijassa-1111	68	3	}	}	PUNCT
ijassa-1111	68	4	the	the	DET
ijassa-1111	68	5	validity	validity	NOUN
ijassa-1111	68	6	of	of	ADP
ijassa-1111	68	7	the	the	DET
ijassa-1111	68	8	equation	equation	NOUN
ijassa-1111	68	9	(	(	PUNCT
ijassa-1111	68	10	3.4	3.4	NUM
ijassa-1111	68	11	)	)	PUNCT
ijassa-1111	68	12	,	,	PUNCT
ijassa-1111	68	13	then	then	ADV
ijassa-1111	68	14	in	in	ADP
ijassa-1111	68	15	this	this	DET
ijassa-1111	68	16	case	case	NOUN
ijassa-1111	68	17	the	the	DET
ijassa-1111	68	18	condition	condition	NOUN
ijassa-1111	68	19	of	of	ADP
ijassa-1111	68	20	multiplicative	multiplicative	ADJ
ijassa-1111	68	21	between	between	ADP
ijassa-1111	68	22	the	the	DET
ijassa-1111	68	23	elements	element	NOUN
ijassa-1111	68	24	of	of	ADP
ijassa-1111	68	25	the	the	DET
ijassa-1111	68	26	matrix	matrix	NOUN
ijassa-1111	68	27	𝑊	𝑊	NOUN
ijassa-1111	68	28	=	=	SYM
ijassa-1111	68	29	,	,	PUNCT
ijassa-1111	68	30	i.e.	i.e.	X
ijassa-1111	68	31	thus	thus	ADV
ijassa-1111	68	32	there	there	PRON
ijassa-1111	68	33	exists	exist	VERB
ijassa-1111	68	34	a	a	DET
ijassa-1111	68	35	one	one	NUM
ijassa-1111	68	36	-	-	PUNCT
ijassa-1111	68	37	to	to	ADP
ijassa-1111	68	38	-	-	PUNCT
ijassa-1111	68	39	one	one	NUM
ijassa-1111	68	40	mapping	mapping	NOUN
ijassa-1111	68	41	between	between	ADP
ijassa-1111	68	42	the	the	DET
ijassa-1111	68	43	elements	element	NOUN
ijassa-1111	68	44	:	:	PUNCT
ijassa-1111	68	45	𝑤	𝑤	ADP
ijassa-1111	68	46	↔	↔	PROPN
ijassa-1111	68	47	.	.	PUNCT
ijassa-1111	69	1	indeed	indeed	ADV
ijassa-1111	69	2	,	,	PUNCT
ijassa-1111	69	3	if	if	SCONJ
ijassa-1111	69	4	𝑤	𝑤	VERB
ijassa-1111	69	5	=	=	PUNCT
ijassa-1111	69	6	and	and	CCONJ
ijassa-1111	69	7	𝑤	𝑤	X
ijassa-1111	69	8	=	=	PRON
ijassa-1111	69	9	,	,	PUNCT
ijassa-1111	69	10	then	then	ADV
ijassa-1111	69	11	we	we	PRON
ijassa-1111	69	12	have	have	VERB
ijassa-1111	69	13	𝑤	𝑤	ADP
ijassa-1111	69	14	𝑤	𝑤	NOUN
ijassa-1111	69	15	=	=	SYM
ijassa-1111	69	16	×	×	NOUN
ijassa-1111	69	17	=	=	PUNCT
ijassa-1111	69	18	=	=	SYM
ijassa-1111	69	19	𝑤	𝑤	PROPN
ijassa-1111	69	20	,	,	PUNCT
ijassa-1111	69	21	that	that	ADV
ijassa-1111	69	22	is	is	ADV
ijassa-1111	69	23	,	,	PUNCT
ijassa-1111	69	24	for	for	ADP
ijassa-1111	69	25	all	all	PRON
ijassa-1111	69	26	𝑖	𝑖	SYM
ijassa-1111	69	27	,	,	PUNCT
ijassa-1111	69	28	𝑗	𝑗	INTJ
ijassa-1111	69	29	,	,	PUNCT
ijassa-1111	69	30	𝑘	𝑘	X
ijassa-1111	69	31	=	=	SYM
ijassa-1111	69	32	1	1	NUM
ijassa-1111	69	33	,	,	PUNCT
ijassa-1111	69	34	𝑛	𝑛	PRON
ijassa-1111	69	35	,	,	PUNCT
ijassa-1111	69	36	the	the	DET
ijassa-1111	69	37	multiplicativity	multiplicativity	NOUN
ijassa-1111	69	38	condition	condition	NOUN
ijassa-1111	69	39	is	be	AUX
ijassa-1111	69	40	satisfied	satisfied	ADJ
ijassa-1111	69	41	.	.	PUNCT
ijassa-1111	70	1	2	2	X
ijassa-1111	70	2	.	.	X
ijassa-1111	70	3	let	let	VERB
ijassa-1111	70	4	the	the	DET
ijassa-1111	70	5	elements	element	NOUN
ijassa-1111	70	6	of	of	ADP
ijassa-1111	70	7	the	the	DET
ijassa-1111	70	8	vector	vector	PROPN
ijassa-1111	70	9	�	�	PROPN
ijassa-1111	70	10	⃗	⃗	NOUN
ijassa-1111	70	11	�	�	NOUN
ijassa-1111	70	12	=	=	SYM
ijassa-1111	70	13	(	(	PUNCT
ijassa-1111	70	14	𝑤	𝑤	INTJ
ijassa-1111	70	15	,	,	PUNCT
ijassa-1111	70	16	…	…	PUNCT
ijassa-1111	70	17	,	,	PUNCT
ijassa-1111	70	18	𝑤	𝑤	PART
ijassa-1111	70	19	)	)	PUNCT
ijassa-1111	70	20	satisfy	satisfy	VERB
ijassa-1111	70	21	equality	equality	NOUN
ijassa-1111	70	22	(	(	PUNCT
ijassa-1111	70	23	3.4	3.4	NUM
ijassa-1111	70	24	)	)	PUNCT
ijassa-1111	70	25	.	.	PUNCT
ijassa-1111	71	1	we	we	PRON
ijassa-1111	71	2	show	show	VERB
ijassa-1111	71	3	that	that	SCONJ
ijassa-1111	71	4	�	�	NOUN
ijassa-1111	71	5	⃗	⃗	NOUN
ijassa-1111	71	6	�	�	NOUN
ijassa-1111	71	7	=	=	SYM
ijassa-1111	71	8	(	(	PUNCT
ijassa-1111	71	9	𝑤1	𝑤1	VERB
ijassa-1111	71	10	,	,	PUNCT
ijassa-1111	71	11	.	.	PUNCT
ijassa-1111	71	12	.	.	PUNCT
ijassa-1111	72	1	.	.	PUNCT
ijassa-1111	73	1	,	,	PUNCT
ijassa-1111	73	2	𝑤	𝑤	X
ijassa-1111	73	3	𝑤𝑛	𝑤𝑛	NOUN
ijassa-1111	73	4	)	)	PUNCT
ijassa-1111	73	5	is	be	AUX
ijassa-1111	73	6	the	the	DET
ijassa-1111	73	7	right	right	ADJ
ijassa-1111	73	8	eigenvector	eigenvector	NOUN
ijassa-1111	73	9	of	of	ADP
ijassa-1111	73	10	the	the	DET
ijassa-1111	73	11	matrix	matrix	NOUN
ijassa-1111	73	12	𝑊	𝑊	NOUN
ijassa-1111	73	13	=	=	SYM
ijassa-1111	73	14	,	,	PUNCT
ijassa-1111	73	15	∀𝑖	∀𝑖	PROPN
ijassa-1111	73	16	,	,	PUNCT
ijassa-1111	73	17	𝑗	𝑗	PROPN
ijassa-1111	73	18	=	=	SYM
ijassa-1111	73	19	1	1	NUM
ijassa-1111	73	20	,	,	PUNCT
ijassa-1111	73	21	𝑛.	𝑛.	NOUN
ijassa-1111	73	22	let	let	VERB
ijassa-1111	73	23	us	we	PRON
ijassa-1111	73	24	verify	verify	VERB
ijassa-1111	73	25	that	that	SCONJ
ijassa-1111	73	26	𝑊	𝑊	PROPN
ijassa-1111	73	27	�	�	NOUN
ijassa-1111	73	28	⃗	⃗	NOUN
ijassa-1111	73	29	�	�	PROPN
ijassa-1111	73	30	=	=	SYM
ijassa-1111	73	31	λ	λ	PROPN
ijassa-1111	73	32	�	�	PROPN
ijassa-1111	73	33	⃗	⃗	NOUN
ijassa-1111	73	34	�	�	PROPN
ijassa-1111	73	35	is	be	AUX
ijassa-1111	73	36	valid	valid	ADJ
ijassa-1111	73	37	:	:	PUNCT
ijassa-1111	73	38	𝑊	𝑊	PROPN
ijassa-1111	73	39	�	�	NOUN
ijassa-1111	73	40	⃗	⃗	NOUN
ijassa-1111	73	41	�	�	NOUN
ijassa-1111	73	42	=	=	SYM
ijassa-1111	73	43	𝑤	𝑤	PART
ijassa-1111	73	44	/𝑤	/𝑤	PUNCT
ijassa-1111	73	45	𝑤	𝑤	NOUN
ijassa-1111	73	46	/𝑤	/𝑤	PUNCT
ijassa-1111	73	47	…	…	PUNCT
ijassa-1111	73	48	𝑤	𝑤	X
ijassa-1111	73	49	/𝑤	/𝑤	PUNCT
ijassa-1111	73	50	𝑤	𝑤	NOUN
ijassa-1111	73	51	/𝑤	/𝑤	PUNCT
ijassa-1111	73	52	…	…	PUNCT
ijassa-1111	73	53	𝑤	𝑤	X
ijassa-1111	73	54	/𝑤	/𝑤	NUM
ijassa-1111	73	55	…	…	PUNCT
ijassa-1111	73	56	…	…	PUNCT
ijassa-1111	73	57	…	…	PUNCT
ijassa-1111	73	58	𝑤	𝑤	X
ijassa-1111	73	59	/𝑤	/𝑤	SYM
ijassa-1111	73	60	…	…	PUNCT
ijassa-1111	73	61	𝑤	𝑤	X
ijassa-1111	73	62	/𝑤	/𝑤	PUNCT
ijassa-1111	73	63	𝑤	𝑤	NOUN
ijassa-1111	73	64	/𝑤	/𝑤	PUNCT
ijassa-1111	73	65	…	…	PUNCT
ijassa-1111	73	66	𝑤	𝑤	X
ijassa-1111	73	67	/𝑤	/𝑤	PUNCT
ijassa-1111	73	68	𝑤	𝑤	NOUN
ijassa-1111	73	69	𝑤	𝑤	PART
ijassa-1111	73	70	…	…	PUNCT
ijassa-1111	73	71	𝑤	𝑤	X
ijassa-1111	73	72	=	=	VERB
ijassa-1111	73	73	𝑛𝑤	𝑛𝑤	NOUN
ijassa-1111	73	74	𝑛𝑤	𝑛𝑤	ADV
ijassa-1111	73	75	…	…	PUNCT
ijassa-1111	74	1	𝑛𝑤	𝑛𝑤	VERB
ijassa-1111	74	2	=	=	NOUN
ijassa-1111	74	3	𝑛	𝑛	PART
ijassa-1111	74	4	𝑤	𝑤	PART
ijassa-1111	74	5	𝑤	𝑤	PART
ijassa-1111	74	6	…	…	PUNCT
ijassa-1111	74	7	𝑤	𝑤	X
ijassa-1111	74	8	=	=	SYM
ijassa-1111	74	9	𝑛	𝑛	PROPN
ijassa-1111	74	10	�	�	PROPN
ijassa-1111	74	11	⃗	⃗	NOUN
ijassa-1111	74	12	�	�	PROPN
ijassa-1111	74	13	,	,	PUNCT
ijassa-1111	74	14	where	where	SCONJ
ijassa-1111	74	15	λ	λ	NOUN
ijassa-1111	74	16	=	=	PRON
ijassa-1111	74	17	𝑛	𝑛	PROPN
ijassa-1111	74	18	is	be	AUX
ijassa-1111	74	19	the	the	DET
ijassa-1111	74	20	maximum	maximum	ADJ
ijassa-1111	74	21	eigenvalue	eigenvalue	NOUN
ijassa-1111	74	22	.	.	PUNCT
ijassa-1111	75	1	for	for	ADP
ijassa-1111	75	2	arbitrary	arbitrary	ADJ
ijassa-1111	75	3	columns	column	NOUN
ijassa-1111	75	4	�	�	NOUN
ijassa-1111	75	5	⃗	⃗	PROPN
ijassa-1111	75	6	�	�	PROPN
ijassa-1111	75	7	и	и	PROPN
ijassa-1111	75	8	�	�	PROPN
ijassa-1111	75	9	⃗	⃗	NOUN
ijassa-1111	75	10	�	�	PROPN
ijassa-1111	75	11	𝑤𝑘	𝑤𝑘	ADP
ijassa-1111	75	12	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
ijassa-1111	75	13	𝑤𝑞	𝑤𝑞	ADP
ijassa-1111	75	14	(	(	PUNCT
ijassa-1111	75	15	1	1	NUM
ijassa-1111	75	16	≤	≤	NUM
ijassa-1111	75	17	𝑘	𝑘	X
ijassa-1111	75	18	,	,	PUNCT
ijassa-1111	75	19	𝑞	𝑞	PROPN
ijassa-1111	75	20	≤	≤	PROPN
ijassa-1111	75	21	𝑛	𝑛	NOUN
ijassa-1111	75	22	)	)	PUNCT
ijassa-1111	75	23	of	of	ADP
ijassa-1111	75	24	the	the	DET
ijassa-1111	75	25	matrice	matrice	PROPN
ijassa-1111	75	26	w	w	PROPN
ijassa-1111	75	27	,	,	PUNCT
ijassa-1111	75	28	whose	whose	DET
ijassa-1111	75	29	elements	element	NOUN
ijassa-1111	75	30	satisfy	satisfy	VERB
ijassa-1111	75	31	the	the	DET
ijassa-1111	75	32	multiplicativity	multiplicativity	NOUN
ijassa-1111	75	33	condition	condition	NOUN
ijassa-1111	75	34	𝑤	𝑤	ADP
ijassa-1111	75	35	(	(	PUNCT
ijassa-1111	75	36	2.3	2.3	NUM
ijassa-1111	75	37	)	)	PUNCT
ijassa-1111	75	38	,	,	PUNCT
ijassa-1111	75	39	we	we	PRON
ijassa-1111	75	40	normalize	normalize	VERB
ijassa-1111	75	41	the	the	DET
ijassa-1111	75	42	elements	element	NOUN
ijassa-1111	75	43	.	.	PUNCT
ijassa-1111	76	1	since	since	SCONJ
ijassa-1111	76	2	𝑤	𝑤	DET
ijassa-1111	76	3	=	=	SYM
ijassa-1111	76	4	𝑤	𝑤	PART
ijassa-1111	76	5	𝑤	𝑤	NOUN
ijassa-1111	76	6	,	,	PUNCT
ijassa-1111	76	7	then	then	ADV
ijassa-1111	76	8	𝑤	𝑤	ADP
ijassa-1111	76	9	=	=	SYM
ijassa-1111	76	10	𝑤	𝑤	PROPN
ijassa-1111	76	11	/𝑤	/𝑤	PUNCT
ijassa-1111	76	12	,	,	PUNCT
ijassa-1111	76	13	whence	whence	NOUN
ijassa-1111	76	14	for	for	ADP
ijassa-1111	76	15	any	any	DET
ijassa-1111	76	16	column	column	NOUN
ijassa-1111	76	17	numbers	number	NOUN
ijassa-1111	76	18	𝑘	𝑘	PROPN
ijassa-1111	76	19	,	,	PUNCT
ijassa-1111	76	20	𝑞	𝑞	X
ijassa-1111	76	21	we	we	PRON
ijassa-1111	76	22	have	have	VERB
ijassa-1111	76	23	:	:	PUNCT
ijassa-1111	76	24	𝑤	𝑤	X
ijassa-1111	76	25	=	=	PUNCT
ijassa-1111	76	26	∑	∑	PUNCT
ijassa-1111	76	27	=	=	PUNCT
ijassa-1111	76	28	/	/	SYM
ijassa-1111	76	29	∑	∑	PUNCT
ijassa-1111	76	30	=	=	PUNCT
ijassa-1111	76	31	∑	∑	PUNCT
ijassa-1111	76	32	=	=	PUNCT
ijassa-1111	76	33	∑	∑	PUNCT
ijassa-1111	76	34	=	=	SYM
ijassa-1111	76	35	𝑤	𝑤	PROPN
ijassa-1111	76	36	,	,	PUNCT
ijassa-1111	76	37	∀	∀	NOUN
ijassa-1111	76	38	𝑖	𝑖	NOUN
ijassa-1111	76	39	=	=	SYM
ijassa-1111	76	40	1	1	NUM
ijassa-1111	76	41	,	,	PUNCT
ijassa-1111	76	42	𝑛	𝑛	ADJ
ijassa-1111	76	43	,	,	PUNCT
ijassa-1111	76	44	i.e.	i.e.	X
ijassa-1111	76	45	,	,	PUNCT
ijassa-1111	76	46	the	the	DET
ijassa-1111	76	47	normalized	normalize	VERB
ijassa-1111	76	48	components	component	NOUN
ijassa-1111	76	49	of	of	ADP
ijassa-1111	76	50	the	the	DET
ijassa-1111	76	51	columns	column	NOUN
ijassa-1111	76	52	of	of	ADP
ijassa-1111	76	53	the	the	DET
ijassa-1111	76	54	matrix	matrix	NOUN
ijassa-1111	76	55	coincide	coincide	NOUN
ijassa-1111	76	56	with	with	ADP
ijassa-1111	76	57	each	each	DET
ijassa-1111	76	58	other	other	ADJ
ijassa-1111	76	59	.	.	PUNCT
ijassa-1111	77	1	on	on	ADP
ijassa-1111	77	2	the	the	DET
ijassa-1111	77	3	other	other	ADJ
ijassa-1111	77	4	hand	hand	NOUN
ijassa-1111	77	5	:	:	PUNCT
ijassa-1111	77	6	𝑤	𝑤	X
ijassa-1111	77	7	=	=	SYM
ijassa-1111	77	8	𝑤	𝑤	PART
ijassa-1111	77	9	∑	∑	PUNCT
ijassa-1111	77	10	𝑤	𝑤	SYM
ijassa-1111	77	11	=	=	PUNCT
ijassa-1111	77	12	𝑤	𝑤	PART
ijassa-1111	77	13	/𝑤	/𝑤	PUNCT
ijassa-1111	77	14	∑	∑	ADV
ijassa-1111	77	15	𝑤	𝑤	PART
ijassa-1111	77	16	/𝑤	/𝑤	SYM
ijassa-1111	77	17	=	=	PUNCT
ijassa-1111	77	18	𝑤	𝑤	PART
ijassa-1111	77	19	∑	∑	PUNCT
ijassa-1111	77	20	𝑤	𝑤	PROPN
ijassa-1111	77	21	=	=	PUNCT
ijassa-1111	77	22	𝑤	𝑤	PROPN
ijassa-1111	77	23	,	,	PUNCT
ijassa-1111	77	24	∀	∀	NOUN
ijassa-1111	77	25	𝑖	𝑖	NOUN
ijassa-1111	77	26	=	=	SYM
ijassa-1111	77	27	1	1	NUM
ijassa-1111	77	28	,	,	PUNCT
ijassa-1111	77	29	𝑛.	𝑛.	NOUN
ijassa-1111	77	30	thus	thus	ADV
ijassa-1111	77	31	,	,	PUNCT
ijassa-1111	77	32	the	the	DET
ijassa-1111	77	33	normalized	normalize	VERB
ijassa-1111	77	34	components	component	NOUN
ijassa-1111	77	35	of	of	ADP
ijassa-1111	77	36	the	the	DET
ijassa-1111	77	37	matrix	matrix	NOUN
ijassa-1111	77	38	columns	column	NOUN
ijassa-1111	77	39	are	be	AUX
ijassa-1111	77	40	also	also	ADV
ijassa-1111	77	41	equal	equal	ADJ
ijassa-1111	77	42	to	to	ADP
ijassa-1111	77	43	the	the	DET
ijassa-1111	77	44	normalized	normalize	VERB
ijassa-1111	77	45	elements	element	NOUN
ijassa-1111	77	46	of	of	ADP
ijassa-1111	77	47	the	the	DET
ijassa-1111	77	48	right	right	ADJ
ijassa-1111	77	49	vector	vector	NOUN
ijassa-1111	77	50	of	of	ADP
ijassa-1111	77	51	the	the	DET
ijassa-1111	77	52	multiplicative	multiplicative	ADJ
ijassa-1111	77	53	matrix	matrix	NOUN
ijassa-1111	77	54	.	.	PUNCT
ijassa-1111	78	1	3	3	X
ijassa-1111	78	2	.	.	X
ijassa-1111	78	3	since	since	SCONJ
ijassa-1111	78	4	the	the	DET
ijassa-1111	78	5	matrix	matrix	NOUN
ijassa-1111	78	6	𝑊	𝑊	NOUN
ijassa-1111	78	7	=	=	PUNCT
ijassa-1111	78	8	by	by	ADP
ijassa-1111	78	9	linear	linear	ADJ
ijassa-1111	78	10	transformations	transformation	NOUN
ijassa-1111	78	11	is	be	AUX
ijassa-1111	78	12	reduced	reduce	VERB
ijassa-1111	78	13	to	to	ADP
ijassa-1111	78	14	the	the	DET
ijassa-1111	78	15	form	form	NOUN
ijassa-1111	78	16	:	:	PUNCT
ijassa-1111	78	17	108	108	NUM
ijassa-1111	78	18	v.p	v.p	PROPN
ijassa-1111	78	19	.	.	PROPN
ijassa-1111	78	20	korneenko	korneenko	PROPN
ijassa-1111	78	21	copyright	copyright	NOUN
ijassa-1111	78	22	©	©	PROPN
ijassa-1111	78	23	2024	2024	NUM
ijassa-1111	78	24	assa	assa	PROPN
ijassa-1111	78	25	adv	adv	PROPN
ijassa-1111	78	26	.	.	PUNCT
ijassa-1111	79	1	in	in	ADP
ijassa-1111	79	2	systems	system	NOUN
ijassa-1111	79	3	science	science	NOUN
ijassa-1111	79	4	and	and	CCONJ
ijassa-1111	79	5	appl	appl	NOUN
ijassa-1111	79	6	.	.	PUNCT
ijassa-1111	80	1	(	(	PUNCT
ijassa-1111	80	2	2024	2024	NUM
ijassa-1111	80	3	)	)	PUNCT
ijassa-1111	80	4	𝑤	𝑤	PART
ijassa-1111	80	5	/𝑤	/𝑤	PUNCT
ijassa-1111	80	6	𝑤	𝑤	NOUN
ijassa-1111	80	7	/𝑤	/𝑤	PUNCT
ijassa-1111	80	8	.	.	PUNCT
ijassa-1111	80	9	.	.	PUNCT
ijassa-1111	80	10	.	.	PUNCT
ijassa-1111	81	1	𝑤	𝑤	AUX
ijassa-1111	81	2	/𝑤	/𝑤	SYM
ijassa-1111	81	3	𝑤	𝑤	NOUN
ijassa-1111	81	4	/𝑤	/𝑤	PUNCT
ijassa-1111	81	5	.	.	PUNCT
ijassa-1111	81	6	.	.	PUNCT
ijassa-1111	81	7	.	.	PUNCT
ijassa-1111	82	1	𝑤	𝑤	X
ijassa-1111	82	2	/𝑤	/𝑤	PUNCT
ijassa-1111	82	3	.	.	PUNCT
ijassa-1111	82	4	.	.	PUNCT
ijassa-1111	82	5	.	.	PUNCT
ijassa-1111	82	6	.	.	PUNCT
ijassa-1111	82	7	.	.	PUNCT
ijassa-1111	82	8	.	.	PUNCT
ijassa-1111	82	9	.	.	PUNCT
ijassa-1111	82	10	.	.	PUNCT
ijassa-1111	82	11	.	.	PUNCT
ijassa-1111	83	1	𝑤	𝑤	X
ijassa-1111	83	2	/𝑤	/𝑤	PUNCT
ijassa-1111	83	3	.	.	PUNCT
ijassa-1111	83	4	.	.	PUNCT
ijassa-1111	83	5	.	.	PUNCT
ijassa-1111	84	1	𝑤	𝑤	AUX
ijassa-1111	84	2	/𝑤	/𝑤	SYM
ijassa-1111	84	3	𝑤	𝑤	NOUN
ijassa-1111	84	4	/𝑤	/𝑤	PUNCT
ijassa-1111	84	5	.	.	PUNCT
ijassa-1111	84	6	.	.	PUNCT
ijassa-1111	84	7	.	.	PUNCT
ijassa-1111	85	1	𝑤	𝑤	X
ijassa-1111	85	2	/𝑤	/𝑤	PUNCT
ijassa-1111	85	3	~	~	PUNCT
ijassa-1111	85	4	∏	∏	PROPN
ijassa-1111	85	5	𝑤	𝑤	ADP
ijassa-1111	85	6	1/𝑤	1/𝑤	NUM
ijassa-1111	85	7	1/𝑤	1/𝑤	NUM
ijassa-1111	85	8	.	.	PUNCT
ijassa-1111	85	9	.	.	PUNCT
ijassa-1111	85	10	.	.	PUNCT
ijassa-1111	86	1	1/𝑤	1/𝑤	NUM
ijassa-1111	86	2	1/𝑤	1/𝑤	NUM
ijassa-1111	86	3	.	.	PUNCT
ijassa-1111	86	4	.	.	PUNCT
ijassa-1111	87	1	.	.	PUNCT
ijassa-1111	88	1	1/𝑤	1/𝑤	NUM
ijassa-1111	88	2	.	.	PUNCT
ijassa-1111	88	3	.	.	PUNCT
ijassa-1111	88	4	.	.	PUNCT
ijassa-1111	88	5	.	.	PUNCT
ijassa-1111	88	6	.	.	PUNCT
ijassa-1111	88	7	.	.	PUNCT
ijassa-1111	88	8	.	.	PUNCT
ijassa-1111	88	9	.	.	PUNCT
ijassa-1111	88	10	.	.	PUNCT
ijassa-1111	89	1	1/𝑤	1/𝑤	NUM
ijassa-1111	89	2	.	.	PUNCT
ijassa-1111	89	3	.	.	PUNCT
ijassa-1111	89	4	.	.	PUNCT
ijassa-1111	90	1	1/𝑤	1/𝑤	NUM
ijassa-1111	90	2	1/𝑤	1/𝑤	NUM
ijassa-1111	90	3	.	.	PUNCT
ijassa-1111	90	4	.	.	PUNCT
ijassa-1111	90	5	.	.	PUNCT
ijassa-1111	91	1	1/𝑤	1/𝑤	NUM
ijassa-1111	92	1	~	~	PUNCT
ijassa-1111	92	2	∏	∏	PROPN
ijassa-1111	92	3	𝑤	𝑤	ADP
ijassa-1111	92	4	1/𝑤	1/𝑤	NUM
ijassa-1111	92	5	0	0	NUM
ijassa-1111	92	6	.	.	PUNCT
ijassa-1111	92	7	.	.	PUNCT
ijassa-1111	92	8	.	.	PUNCT
ijassa-1111	93	1	0	0	NUM
ijassa-1111	93	2	1/𝑤	1/𝑤	NUM
ijassa-1111	93	3	.	.	PUNCT
ijassa-1111	93	4	.	.	PUNCT
ijassa-1111	93	5	.	.	PUNCT
ijassa-1111	94	1	0	0	X
ijassa-1111	94	2	.	.	PUNCT
ijassa-1111	94	3	.	.	PUNCT
ijassa-1111	94	4	.	.	PUNCT
ijassa-1111	94	5	.	.	PUNCT
ijassa-1111	94	6	.	.	PUNCT
ijassa-1111	94	7	.	.	PUNCT
ijassa-1111	94	8	.	.	PUNCT
ijassa-1111	94	9	.	.	PUNCT
ijassa-1111	95	1	.	.	PUNCT
ijassa-1111	96	1	0	0	X
ijassa-1111	96	2	.	.	PUNCT
ijassa-1111	96	3	.	.	PUNCT
ijassa-1111	96	4	.	.	PUNCT
ijassa-1111	97	1	1/𝑤	1/𝑤	NUM
ijassa-1111	97	2	0	0	NUM
ijassa-1111	97	3	.	.	PUNCT
ijassa-1111	97	4	.	.	PUNCT
ijassa-1111	98	1	.	.	PUNCT
ijassa-1111	99	1	0	0	NUM
ijassa-1111	100	1	,	,	PUNCT
ijassa-1111	100	2	the	the	DET
ijassa-1111	100	3	rank	rank	NOUN
ijassa-1111	100	4	of	of	ADP
ijassa-1111	100	5	the	the	DET
ijassa-1111	100	6	multiplicative	multiplicative	ADJ
ijassa-1111	100	7	matrix	matrix	NOUN
ijassa-1111	100	8	is	be	AUX
ijassa-1111	100	9	equal	equal	ADJ
ijassa-1111	100	10	to	to	ADP
ijassa-1111	100	11	one	one	NUM
ijassa-1111	100	12	:	:	PUNCT
ijassa-1111	100	13	rg	rg	PROPN
ijassa-1111	100	14	𝑊	𝑊	PROPN
ijassa-1111	100	15	=	=	SYM
ijassa-1111	100	16	1	1	NUM
ijassa-1111	100	17	,	,	PUNCT
ijassa-1111	100	18	i.e.	i.e.	X
ijassa-1111	100	19	,	,	PUNCT
ijassa-1111	100	20	the	the	DET
ijassa-1111	100	21	multiplicative	multiplicative	ADJ
ijassa-1111	100	22	matrix	matrix	NOUN
ijassa-1111	100	23	has	have	VERB
ijassa-1111	100	24	one	one	NUM
ijassa-1111	100	25	basic	basic	ADJ
ijassa-1111	100	26	row	row	NOUN
ijassa-1111	100	27	.	.	PUNCT
ijassa-1111	101	1	the	the	DET
ijassa-1111	101	2	theorem	theorem	NOUN
ijassa-1111	101	3	is	be	AUX
ijassa-1111	101	4	proved	prove	VERB
ijassa-1111	101	5	.	.	PUNCT
ijassa-1111	102	1	∎	∎	ADV
ijassa-1111	102	2	3.2	3.2	NUM
ijassa-1111	102	3	.	.	PUNCT
ijassa-1111	103	1	reducing	reduce	VERB
ijassa-1111	103	2	the	the	DET
ijassa-1111	103	3	elements	element	NOUN
ijassa-1111	103	4	of	of	ADP
ijassa-1111	103	5	the	the	DET
ijassa-1111	103	6	matrix	matrix	NOUN
ijassa-1111	103	7	columns	column	NOUN
ijassa-1111	103	8	to	to	ADP
ijassa-1111	103	9	integer	integer	NOUN
ijassa-1111	103	10	values	value	NOUN
ijassa-1111	103	11	and	and	CCONJ
ijassa-1111	103	12	equality	equality	NOUN
ijassa-1111	103	13	to	to	ADP
ijassa-1111	103	14	the	the	DET
ijassa-1111	103	15	right	right	ADJ
ijassa-1111	103	16	eigenvector	eigenvector	NOUN
ijassa-1111	103	17	theorem	theorem	NOUN
ijassa-1111	103	18	3.2	3.2	NUM
ijassa-1111	103	19	:	:	PUNCT
ijassa-1111	103	20	let	let	VERB
ijassa-1111	103	21	the	the	DET
ijassa-1111	103	22	elements	element	NOUN
ijassa-1111	103	23	𝑞	𝑞	X
ijassa-1111	103	24	,	,	PUNCT
ijassa-1111	103	25	𝑖	𝑖	PROPN
ijassa-1111	103	26	,	,	PUNCT
ijassa-1111	103	27	𝑘	𝑘	X
ijassa-1111	103	28	=	=	SYM
ijassa-1111	103	29	1	1	NUM
ijassa-1111	103	30	,	,	PUNCT
ijassa-1111	103	31	𝑛	𝑛	PROPN
ijassa-1111	103	32	,	,	PUNCT
ijassa-1111	103	33	of	of	ADP
ijassa-1111	103	34	the	the	DET
ijassa-1111	103	35	multiplicative	multiplicative	ADJ
ijassa-1111	103	36	matrix	matrix	NOUN
ijassa-1111	103	37	𝑊	𝑊	NOUN
ijassa-1111	103	38	=	=	PUNCT
ijassa-1111	104	1	[	[	X
ijassa-1111	104	2	𝑞	𝑞	X
ijassa-1111	104	3	]	]	X
ijassa-1111	104	4	,	,	PUNCT
ijassa-1111	104	5	∀	∀	X
ijassa-1111	104	6	𝑖	𝑖	NOUN
ijassa-1111	104	7	,	,	PUNCT
ijassa-1111	104	8	𝑘	𝑘	X
ijassa-1111	104	9	=	=	SYM
ijassa-1111	104	10	1	1	NUM
ijassa-1111	104	11	,	,	PUNCT
ijassa-1111	104	12	𝑛	𝑛	VERB
ijassa-1111	104	13	,	,	PUNCT
ijassa-1111	104	14	be	be	AUX
ijassa-1111	104	15	represented	represent	VERB
ijassa-1111	104	16	in	in	ADP
ijassa-1111	104	17	general	general	ADJ
ijassa-1111	104	18	by	by	ADP
ijassa-1111	104	19	integers	integer	NOUN
ijassa-1111	104	20	and	and	CCONJ
ijassa-1111	104	21	rational	rational	ADJ
ijassa-1111	104	22	numbers	number	NOUN
ijassa-1111	104	23	in	in	ADP
ijassa-1111	104	24	the	the	DET
ijassa-1111	104	25	form	form	NOUN
ijassa-1111	104	26	of	of	ADP
ijassa-1111	104	27	irregular	irregular	ADJ
ijassa-1111	104	28	fractions	fraction	NOUN
ijassa-1111	104	29	.	.	PUNCT
ijassa-1111	105	1	then	then	ADV
ijassa-1111	105	2	,	,	PUNCT
ijassa-1111	105	3	if	if	SCONJ
ijassa-1111	105	4	the	the	DET
ijassa-1111	105	5	elements	element	NOUN
ijassa-1111	105	6	of	of	ADP
ijassa-1111	105	7	𝑞	𝑞	PROPN
ijassa-1111	105	8	any	any	DET
ijassa-1111	105	9	column	column	NOUN
ijassa-1111	105	10	�	�	PROPN
ijassa-1111	105	11	⃗	⃗	PROPN
ijassa-1111	105	12	�	�	PROPN
ijassa-1111	105	13	,	,	PUNCT
ijassa-1111	105	14	𝑘	𝑘	X
ijassa-1111	105	15	=	=	SYM
ijassa-1111	105	16	1	1	NUM
ijassa-1111	105	17	,	,	PUNCT
ijassa-1111	105	18	𝑛	𝑛	PROPN
ijassa-1111	105	19	,	,	PUNCT
ijassa-1111	105	20	of	of	ADP
ijassa-1111	105	21	the	the	DET
ijassa-1111	105	22	matrix	matrix	NOUN
ijassa-1111	105	23	is	be	AUX
ijassa-1111	105	24	multiplied	multiply	VERB
ijassa-1111	105	25	by	by	ADP
ijassa-1111	105	26	the	the	DET
ijassa-1111	105	27	least	least	ADV
ijassa-1111	105	28	common	common	ADJ
ijassa-1111	105	29	multiple	multiple	ADJ
ijassa-1111	105	30	𝑛	𝑛	DET
ijassa-1111	105	31	denominators	denominator	NOUN
ijassa-1111	105	32	of	of	ADP
ijassa-1111	105	33	the	the	DET
ijassa-1111	105	34	rational	rational	ADJ
ijassa-1111	105	35	elements	element	NOUN
ijassa-1111	105	36	of	of	ADP
ijassa-1111	105	37	the	the	DET
ijassa-1111	105	38	column	column	NOUN
ijassa-1111	105	39	,	,	PUNCT
ijassa-1111	105	40	obtained	obtain	VERB
ijassa-1111	105	41	in	in	ADP
ijassa-1111	105	42	the	the	DET
ijassa-1111	105	43	result	result	NOUN
ijassa-1111	105	44	of	of	ADP
ijassa-1111	105	45	this	this	DET
ijassa-1111	105	46	procedure	procedure	NOUN
ijassa-1111	105	47	,	,	PUNCT
ijassa-1111	105	48	the	the	DET
ijassa-1111	105	49	integer	integer	NOUN
ijassa-1111	105	50	elements	element	NOUN
ijassa-1111	105	51	𝑧	𝑧	PRON
ijassa-1111	105	52	=	=	VERB
ijassa-1111	105	53	𝑛	𝑛	PRON
ijassa-1111	105	54	𝑞	𝑞	PROPN
ijassa-1111	105	55	,	,	PUNCT
ijassa-1111	105	56	∀	∀	X
ijassa-1111	105	57	𝑘	𝑘	X
ijassa-1111	105	58	=	=	SYM
ijassa-1111	105	59	1	1	NUM
ijassa-1111	105	60	,	,	PUNCT
ijassa-1111	105	61	𝑛	𝑛	PROPN
ijassa-1111	105	62	,	,	PUNCT
ijassa-1111	105	63	the	the	DET
ijassa-1111	105	64	columns	column	NOUN
ijassa-1111	105	65	of	of	ADP
ijassa-1111	105	66	the	the	DET
ijassa-1111	105	67	matrix	matrix	NOUN
ijassa-1111	105	68	coincide	coincide	NOUN
ijassa-1111	105	69	with	with	ADP
ijassa-1111	105	70	each	each	DET
ijassa-1111	105	71	other	other	ADJ
ijassa-1111	105	72	on	on	ADP
ijassa-1111	105	73	any	any	DET
ijassa-1111	105	74	line	line	NOUN
ijassa-1111	105	75	number	number	NOUN
ijassa-1111	105	76	,	,	PUNCT
ijassa-1111	105	77	and	and	CCONJ
ijassa-1111	105	78	will	will	AUX
ijassa-1111	105	79	be	be	AUX
ijassa-1111	105	80	equal	equal	ADJ
ijassa-1111	105	81	to	to	ADP
ijassa-1111	105	82	the	the	DET
ijassa-1111	105	83	integer	integer	NOUN
ijassa-1111	105	84	elements	element	NOUN
ijassa-1111	105	85	𝑤	𝑤	ADP
ijassa-1111	105	86	right	right	ADJ
ijassa-1111	105	87	eigenvector	eigenvector	PROPN
ijassa-1111	105	88	�	�	PROPN
ijassa-1111	105	89	⃗	⃗	PROPN
ijassa-1111	105	90	�	�	NOUN
ijassa-1111	105	91	=	=	SYM
ijassa-1111	105	92	(	(	PUNCT
ijassa-1111	105	93	𝑤	𝑤	INTJ
ijassa-1111	105	94	,	,	PUNCT
ijassa-1111	105	95	.	.	PUNCT
ijassa-1111	105	96	.	.	PUNCT
ijassa-1111	106	1	.	.	PUNCT
ijassa-1111	107	1	,	,	PUNCT
ijassa-1111	107	2	𝑤	𝑤	X
ijassa-1111	107	3	,	,	PUNCT
ijassa-1111	107	4	…	…	PUNCT
ijassa-1111	107	5	𝑤	𝑤	X
ijassa-1111	107	6	)	)	PUNCT
ijassa-1111	107	7	corresponding	correspond	VERB
ijassa-1111	107	8	to	to	ADP
ijassa-1111	107	9	its	its	PRON
ijassa-1111	107	10	own	own	ADJ
ijassa-1111	107	11	maximum	maximum	ADJ
ijassa-1111	107	12	eigenvalue	eigenvalue	NOUN
ijassa-1111	107	13	𝜆	𝜆	NOUN
ijassa-1111	107	14	=	=	SYM
ijassa-1111	107	15	𝑛	𝑛	NOUN
ijassa-1111	107	16	:	:	PUNCT
ijassa-1111	107	17	z	z	NOUN
ijassa-1111	107	18	…	…	PUNCT
ijassa-1111	107	19	z	z	X
ijassa-1111	107	20	=	=	SYM
ijassa-1111	107	21	𝑤	𝑤	PART
ijassa-1111	107	22	…	…	PUNCT
ijassa-1111	107	23	𝑤	𝑤	INTJ
ijassa-1111	107	24	,	,	PUNCT
ijassa-1111	107	25	1	1	NUM
ijassa-1111	107	26	≤	≤	NOUN
ijassa-1111	107	27	𝑘	𝑘	DET
ijassa-1111	107	28	≤	≤	ADJ
ijassa-1111	107	29	𝑛.	𝑛.	NOUN
ijassa-1111	107	30	(	(	PUNCT
ijassa-1111	107	31	3.6	3.6	NUM
ijassa-1111	107	32	)	)	PUNCT
ijassa-1111	107	33	proof	proof	NOUN
ijassa-1111	107	34	.	.	PUNCT
ijassa-1111	108	1	by	by	ADP
ijassa-1111	108	2	theorem	theorem	NOUN
ijassa-1111	108	3	1	1	NUM
ijassa-1111	108	4	,	,	PUNCT
ijassa-1111	108	5	the	the	DET
ijassa-1111	108	6	elements	element	NOUN
ijassa-1111	108	7	of	of	ADP
ijassa-1111	108	8	any	any	DET
ijassa-1111	108	9	multiplicative	multiplicative	ADJ
ijassa-1111	108	10	inverse	inverse	NOUN
ijassa-1111	108	11	-	-	PUNCT
ijassa-1111	108	12	symmetric	symmetric	NOUN
ijassa-1111	108	13	matrix	matrix	NOUN
ijassa-1111	108	14	can	can	AUX
ijassa-1111	108	15	be	be	AUX
ijassa-1111	108	16	brought	bring	VERB
ijassa-1111	108	17	to	to	ADP
ijassa-1111	108	18	mind	mind	NOUN
ijassa-1111	108	19	(	(	PUNCT
ijassa-1111	108	20	3.4	3.4	NUM
ijassa-1111	108	21	)	)	PUNCT
ijassa-1111	108	22	,	,	PUNCT
ijassa-1111	108	23	namely	namely	ADV
ijassa-1111	108	24	:	:	PUNCT
ijassa-1111	108	25	𝑞	𝑞	X
ijassa-1111	108	26	=	=	X
ijassa-1111	108	27	,	,	PUNCT
ijassa-1111	108	28	where	where	SCONJ
ijassa-1111	108	29	𝑤	𝑤	PART
ijassa-1111	108	30	are	be	AUX
ijassa-1111	108	31	positive	positive	ADJ
ijassa-1111	108	32	integer	integer	NOUN
ijassa-1111	108	33	numbers	number	NOUN
ijassa-1111	108	34	–	–	PUNCT
ijassa-1111	108	35	the	the	DET
ijassa-1111	108	36	elements	element	NOUN
ijassa-1111	108	37	of	of	ADP
ijassa-1111	108	38	the	the	DET
ijassa-1111	108	39	right	right	ADJ
ijassa-1111	108	40	eigenvector	eigenvector	NOUN
ijassa-1111	108	41	,	,	PUNCT
ijassa-1111	108	42	the	the	DET
ijassa-1111	108	43	least	least	ADV
ijassa-1111	108	44	common	common	ADJ
ijassa-1111	108	45	multiple	multiple	NOUN
ijassa-1111	108	46	of	of	ADP
ijassa-1111	108	47	positive	positive	ADJ
ijassa-1111	108	48	integers	integer	NOUN
ijassa-1111	108	49	to	to	ADP
ijassa-1111	108	50	rational	rational	ADJ
ijassa-1111	108	51	denominators	denominator	NOUN
ijassa-1111	108	52	of	of	ADP
ijassa-1111	108	53	the	the	DET
ijassa-1111	108	54	elements	element	NOUN
ijassa-1111	108	55	of	of	ADP
ijassa-1111	108	56	such	such	DET
ijassa-1111	108	57	a	a	DET
ijassa-1111	108	58	multiplicative	multiplicative	ADJ
ijassa-1111	108	59	matrix	matrix	NOUN
ijassa-1111	108	60	is	be	AUX
ijassa-1111	108	61	equal	equal	ADJ
ijassa-1111	108	62	to	to	ADP
ijassa-1111	108	63	𝑛	𝑛	PROPN
ijassa-1111	108	64	=	=	SYM
ijassa-1111	108	65	𝑤	𝑤	PROPN
ijassa-1111	108	66	,	,	PUNCT
ijassa-1111	108	67	∀	∀	X
ijassa-1111	108	68	𝑘	𝑘	X
ijassa-1111	108	69	=	=	SYM
ijassa-1111	108	70	1	1	NUM
ijassa-1111	108	71	,	,	PUNCT
ijassa-1111	108	72	𝑛.	𝑛.	NOUN
ijassa-1111	108	73	as	as	ADP
ijassa-1111	108	74	a	a	DET
ijassa-1111	108	75	result	result	NOUN
ijassa-1111	108	76	,	,	PUNCT
ijassa-1111	108	77	for	for	ADP
ijassa-1111	108	78	k	k	PROPN
ijassa-1111	108	79	-	-	PUNCT
ijassa-1111	108	80	th	th	VERB
ijassa-1111	108	81	column	column	NOUN
ijassa-1111	108	82	�	�	PROPN
ijassa-1111	108	83	⃗	⃗	PROPN
ijassa-1111	108	84	�	�	PROPN
ijassa-1111	108	85	=	=	SYM
ijassa-1111	108	86	,	,	PUNCT
ijassa-1111	108	87	.	.	PUNCT
ijassa-1111	108	88	.	.	PUNCT
ijassa-1111	108	89	.	.	PUNCT
ijassa-1111	109	1	,	,	PUNCT
ijassa-1111	109	2	,	,	PUNCT
ijassa-1111	109	3	we	we	PRON
ijassa-1111	109	4	find	find	VERB
ijassa-1111	109	5	𝑛	𝑛	DET
ijassa-1111	109	6	�	�	NOUN
ijassa-1111	109	7	⃗	⃗	NOUN
ijassa-1111	109	8	�	�	NOUN
ijassa-1111	109	9	=	=	SYM
ijassa-1111	109	10	𝑛	𝑛	PRON
ijassa-1111	109	11	×	×	NOUN
ijassa-1111	109	12	𝑤	𝑤	X
ijassa-1111	109	13	/𝑛	/𝑛	SYM
ijassa-1111	109	14	…	…	PUNCT
ijassa-1111	109	15	𝑤	𝑤	X
ijassa-1111	109	16	/𝑛	/𝑛	PUNCT
ijassa-1111	109	17	=	=	NOUN
ijassa-1111	109	18	𝑤	𝑤	PART
ijassa-1111	109	19	×	×	NOUN
ijassa-1111	109	20	𝑤	𝑤	ADP
ijassa-1111	109	21	/𝑤	/𝑤	PUNCT
ijassa-1111	109	22	…	…	PUNCT
ijassa-1111	109	23	𝑤	𝑤	X
ijassa-1111	109	24	/𝑤	/𝑤	SYM
ijassa-1111	109	25	=	=	NOUN
ijassa-1111	109	26	𝑤	𝑤	PART
ijassa-1111	109	27	…	…	PUNCT
ijassa-1111	109	28	𝑤	𝑤	X
ijassa-1111	109	29	=	=	PUNCT
ijassa-1111	109	30	�	�	PROPN
ijassa-1111	109	31	⃗	⃗	NOUN
ijassa-1111	109	32	�	�	PROPN
ijassa-1111	109	33	,	,	PUNCT
ijassa-1111	109	34	∀	∀	X
ijassa-1111	109	35	𝑘	𝑘	X
ijassa-1111	109	36	=	=	SYM
ijassa-1111	109	37	1	1	NUM
ijassa-1111	109	38	,	,	PUNCT
ijassa-1111	109	39	𝑛	𝑛	PROPN
ijassa-1111	109	40	,	,	PUNCT
ijassa-1111	109	41	that	that	ADV
ijassa-1111	109	42	is	is	ADV
ijassa-1111	109	43	,	,	PUNCT
ijassa-1111	109	44	we	we	PRON
ijassa-1111	109	45	proved	prove	VERB
ijassa-1111	109	46	the	the	DET
ijassa-1111	109	47	correctness	correctness	NOUN
ijassa-1111	109	48	of	of	ADP
ijassa-1111	109	49	(	(	PUNCT
ijassa-1111	109	50	3.6	3.6	NUM
ijassa-1111	109	51	)	)	PUNCT
ijassa-1111	109	52	.	.	PUNCT
ijassa-1111	110	1	it	it	PRON
ijassa-1111	110	2	is	be	AUX
ijassa-1111	110	3	easy	easy	ADJ
ijassa-1111	110	4	to	to	PART
ijassa-1111	110	5	verify	verify	VERB
ijassa-1111	110	6	that	that	SCONJ
ijassa-1111	110	7	�	�	NOUN
ijassa-1111	110	8	⃗	⃗	NOUN
ijassa-1111	110	9	�	�	PROPN
ijassa-1111	110	10	is	be	AUX
ijassa-1111	110	11	the	the	DET
ijassa-1111	110	12	right	right	ADJ
ijassa-1111	110	13	eigenvector	eigenvector	NOUN
ijassa-1111	110	14	of	of	ADP
ijassa-1111	110	15	the	the	DET
ijassa-1111	110	16	matrix	matrix	NOUN
ijassa-1111	110	17	𝑊	𝑊	PROPN
ijassa-1111	110	18	,	,	PUNCT
ijassa-1111	110	19	which	which	PRON
ijassa-1111	110	20	was	be	AUX
ijassa-1111	110	21	required	require	VERB
ijassa-1111	110	22	to	to	PART
ijassa-1111	110	23	prove	prove	VERB
ijassa-1111	110	24	.	.	PUNCT
ijassa-1111	111	1	the	the	DET
ijassa-1111	111	2	theorem	theorem	NOUN
ijassa-1111	111	3	is	be	AUX
ijassa-1111	111	4	proved	prove	VERB
ijassa-1111	111	5	.	.	PUNCT
ijassa-1111	112	1	∎	∎	PROPN
ijassa-1111	112	2	example	example	NOUN
ijassa-1111	112	3	1	1	X
ijassa-1111	112	4	.	.	X
ijassa-1111	112	5	consider	consider	VERB
ijassa-1111	112	6	a	a	DET
ijassa-1111	112	7	multiplicative	multiplicative	ADJ
ijassa-1111	112	8	matrix	matrix	NOUN
ijassa-1111	112	9	𝑊	𝑊	NOUN
ijassa-1111	112	10	=	=	SYM
ijassa-1111	112	11	⎝	⎝	PROPN
ijassa-1111	112	12	⎜	⎜	PROPN
ijassa-1111	112	13	⎜	⎜	PROPN
ijassa-1111	112	14	⎜	⎜	PROPN
ijassa-1111	112	15	⎛	⎛	NOUN
ijassa-1111	113	1	1	1	NUM
ijassa-1111	113	2	1	1	NUM
ijassa-1111	113	3	2	2	NUM
ijassa-1111	113	4	1	1	NUM
ijassa-1111	113	5	3	3	NUM
ijassa-1111	113	6	1	1	NUM
ijassa-1111	113	7	5	5	NUM
ijassa-1111	113	8	2	2	NUM
ijassa-1111	113	9	1	1	NUM
ijassa-1111	113	10	2	2	NUM
ijassa-1111	113	11	3	3	NUM
ijassa-1111	113	12	2	2	NUM
ijassa-1111	113	13	5	5	NUM
ijassa-1111	113	14	3	3	NUM
ijassa-1111	113	15	3	3	NUM
ijassa-1111	113	16	2	2	NUM
ijassa-1111	113	17	1	1	NUM
ijassa-1111	113	18	3	3	NUM
ijassa-1111	113	19	5	5	NUM
ijassa-1111	113	20	5	5	NUM
ijassa-1111	113	21	5	5	NUM
ijassa-1111	113	22	2	2	NUM
ijassa-1111	113	23	5	5	NUM
ijassa-1111	113	24	3	3	NUM
ijassa-1111	113	25	1⎠	1⎠	NUM
ijassa-1111	113	26	⎟	⎟	X
ijassa-1111	113	27	⎟	⎟	X
ijassa-1111	113	28	⎟	⎟	PROPN
ijassa-1111	113	29	⎞	⎞	PROPN
ijassa-1111	113	30	(	(	PUNCT
ijassa-1111	113	31	3.7	3.7	NUM
ijassa-1111	113	32	)	)	PUNCT
ijassa-1111	113	33	for	for	ADP
ijassa-1111	113	34	the	the	DET
ijassa-1111	113	35	columns	column	NOUN
ijassa-1111	113	36	of	of	ADP
ijassa-1111	113	37	the	the	DET
ijassa-1111	113	38	matrix	matrix	NOUN
ijassa-1111	113	39	,	,	PUNCT
ijassa-1111	113	40	the	the	DET
ijassa-1111	113	41	lowest	low	ADJ
ijassa-1111	113	42	common	common	ADJ
ijassa-1111	113	43	multiples	multiple	NOUN
ijassa-1111	113	44	are	be	AUX
ijassa-1111	113	45	:	:	PUNCT
ijassa-1111	113	46	𝑛	𝑛	PROPN
ijassa-1111	113	47	=	=	PUNCT
ijassa-1111	113	48	𝑤	𝑤	SYM
ijassa-1111	113	49	=	=	SYM
ijassa-1111	113	50	2	2	NUM
ijassa-1111	113	51	×	×	NOUN
ijassa-1111	113	52	3	3	NUM
ijassa-1111	113	53	×	×	NOUN
ijassa-1111	113	54	5	5	NUM
ijassa-1111	113	55	=	=	SYM
ijassa-1111	113	56	30	30	NUM
ijassa-1111	113	57	,	,	PUNCT
ijassa-1111	113	58	𝑛	𝑛	PROPN
ijassa-1111	113	59	=	=	PUNCT
ijassa-1111	113	60	𝑤	𝑤	SYM
ijassa-1111	113	61	=	=	SYM
ijassa-1111	113	62	3	3	NUM
ijassa-1111	113	63	×	×	NOUN
ijassa-1111	113	64	5	5	NUM
ijassa-1111	113	65	=	=	SYM
ijassa-1111	113	66	15	15	NUM
ijassa-1111	113	67	,	,	PUNCT
ijassa-1111	113	68	𝑛	𝑛	PROPN
ijassa-1111	113	69	=	=	PUNCT
ijassa-1111	113	70	𝑤	𝑤	SYM
ijassa-1111	113	71	=	=	SYM
ijassa-1111	113	72	2	2	NUM
ijassa-1111	113	73	×	×	NOUN
ijassa-1111	113	74	5	5	NUM
ijassa-1111	113	75	=	=	SYM
ijassa-1111	113	76	10	10	NUM
ijassa-1111	113	77	,	,	PUNCT
ijassa-1111	113	78	𝑛	𝑛	NOUN
ijassa-1111	113	79	=	=	SYM
ijassa-1111	113	80	2	2	NUM
ijassa-1111	113	81	×	×	NOUN
ijassa-1111	113	82	3	3	NUM
ijassa-1111	113	83	=	=	SYM
ijassa-1111	113	84	6	6	NUM
ijassa-1111	113	85	.	.	PUNCT
ijassa-1111	114	1	from	from	ADP
ijassa-1111	114	2	here	here	ADV
ijassa-1111	114	3	we	we	PRON
ijassa-1111	114	4	come	come	VERB
ijassa-1111	114	5	to	to	ADP
ijassa-1111	114	6	the	the	DET
ijassa-1111	114	7	matrix	matrix	NOUN
ijassa-1111	114	8	:	:	PUNCT
ijassa-1111	114	9	𝑊	𝑊	NOUN
ijassa-1111	114	10	=	=	SYM
ijassa-1111	114	11	30	30	NUM
ijassa-1111	114	12	15	15	NUM
ijassa-1111	114	13	10	10	NUM
ijassa-1111	114	14	6	6	NUM
ijassa-1111	114	15	30	30	NUM
ijassa-1111	114	16	15	15	NUM
ijassa-1111	114	17	10	10	NUM
ijassa-1111	114	18	6	6	NUM
ijassa-1111	114	19	30	30	NUM
ijassa-1111	114	20	15	15	NUM
ijassa-1111	114	21	10	10	NUM
ijassa-1111	114	22	6	6	NUM
ijassa-1111	114	23	30	30	NUM
ijassa-1111	114	24	15	15	NUM
ijassa-1111	114	25	10	10	NUM
ijassa-1111	114	26	6	6	NUM
ijassa-1111	114	27	.	.	PUNCT
ijassa-1111	115	1	it	it	PRON
ijassa-1111	115	2	is	be	AUX
ijassa-1111	115	3	easy	easy	ADJ
ijassa-1111	115	4	to	to	PART
ijassa-1111	115	5	verify	verify	VERB
ijassa-1111	115	6	that	that	SCONJ
ijassa-1111	115	7	the	the	DET
ijassa-1111	115	8	right	right	NOUN
ijassa-1111	115	9	the	the	DET
ijassa-1111	115	10	approximation	approximation	NOUN
ijassa-1111	115	11	matrix	matrix	NOUN
ijassa-1111	115	12	method	method	NOUN
ijassa-1111	115	13	and	and	CCONJ
ijassa-1111	115	14	its	its	PRON
ijassa-1111	115	15	comparison	comparison	NOUN
ijassa-1111	115	16	…	…	PUNCT
ijassa-1111	115	17	109	109	NUM
ijassa-1111	115	18	copyright	copyright	NOUN
ijassa-1111	115	19	©	©	PROPN
ijassa-1111	115	20	2024	2024	NUM
ijassa-1111	115	21	assa	assa	PROPN
ijassa-1111	115	22	adv	adv	PROPN
ijassa-1111	115	23	.	.	PUNCT
ijassa-1111	116	1	in	in	ADP
ijassa-1111	116	2	systems	system	NOUN
ijassa-1111	116	3	science	science	NOUN
ijassa-1111	116	4	and	and	CCONJ
ijassa-1111	116	5	appl	appl	NOUN
ijassa-1111	116	6	.	.	PUNCT
ijassa-1111	117	1	(	(	PUNCT
ijassa-1111	117	2	2024	2024	NUM
ijassa-1111	117	3	)	)	PUNCT
ijassa-1111	117	4	eigenvector	eigenvector	PROPN
ijassa-1111	117	5	�	�	PROPN
ijassa-1111	117	6	⃗	⃗	PROPN
ijassa-1111	117	7	�	�	NOUN
ijassa-1111	117	8	=	=	SYM
ijassa-1111	117	9	(	(	PUNCT
ijassa-1111	117	10	30	30	NUM
ijassa-1111	117	11	,	,	PUNCT
ijassa-1111	117	12	15	15	NUM
ijassa-1111	117	13	,	,	PUNCT
ijassa-1111	117	14	10	10	NUM
ijassa-1111	117	15	,	,	PUNCT
ijassa-1111	117	16	6	6	NUM
ijassa-1111	117	17	)	)	PUNCT
ijassa-1111	117	18	of	of	ADP
ijassa-1111	117	19	the	the	DET
ijassa-1111	117	20	matrix	matrix	NOUN
ijassa-1111	117	21	w	w	NOUN
ijassa-1111	117	22	(	(	PUNCT
ijassa-1111	117	23	3.7	3.7	NUM
ijassa-1111	117	24	)	)	PUNCT
ijassa-1111	117	25	,	,	PUNCT
ijassa-1111	117	26	corresponding	correspond	VERB
ijassa-1111	117	27	to	to	ADP
ijassa-1111	117	28	the	the	DET
ijassa-1111	117	29	eigenvalue	eigenvalue	PROPN
ijassa-1111	117	30	𝜆	𝜆	NOUN
ijassa-1111	117	31	=	=	SYM
ijassa-1111	117	32	4	4	NUM
ijassa-1111	117	33	and	and	CCONJ
ijassa-1111	117	34	the	the	DET
ijassa-1111	117	35	normalized	normalize	VERB
ijassa-1111	117	36	elements	element	NOUN
ijassa-1111	117	37	of	of	ADP
ijassa-1111	117	38	the	the	DET
ijassa-1111	117	39	columns	column	NOUN
ijassa-1111	117	40	of	of	ADP
ijassa-1111	117	41	the	the	DET
ijassa-1111	117	42	matrix	matrix	NOUN
ijassa-1111	117	43	coincide	coincide	NOUN
ijassa-1111	117	44	with	with	ADP
ijassa-1111	117	45	each	each	DET
ijassa-1111	117	46	other	other	ADJ
ijassa-1111	117	47	and	and	CCONJ
ijassa-1111	117	48	are	be	AUX
ijassa-1111	117	49	equal	equal	ADJ
ijassa-1111	117	50	to	to	ADP
ijassa-1111	117	51	the	the	DET
ijassa-1111	117	52	elements	element	NOUN
ijassa-1111	117	53	of	of	ADP
ijassa-1111	117	54	the	the	DET
ijassa-1111	117	55	normalized	normalize	VERB
ijassa-1111	117	56	right	right	ADJ
ijassa-1111	117	57	vector	vector	NOUN
ijassa-1111	117	58	of	of	ADP
ijassa-1111	117	59	the	the	DET
ijassa-1111	117	60	matrix	matrix	NOUN
ijassa-1111	117	61	:	:	PUNCT
ijassa-1111	117	62	�	�	PROPN
ijassa-1111	117	63	⃗	⃗	NOUN
ijassa-1111	117	64	�	�	NOUN
ijassa-1111	117	65	=	=	SYM
ijassa-1111	117	66	30	30	NUM
ijassa-1111	117	67	61	61	NUM
ijassa-1111	117	68	,	,	PUNCT
ijassa-1111	117	69	15	15	NUM
ijassa-1111	117	70	61	61	NUM
ijassa-1111	117	71	,	,	PUNCT
ijassa-1111	117	72	10	10	NUM
ijassa-1111	117	73	61	61	NUM
ijassa-1111	117	74	,	,	PUNCT
ijassa-1111	117	75	6	6	NUM
ijassa-1111	117	76	61	61	NUM
ijassa-1111	117	77	.	.	PUNCT
ijassa-1111	118	1	the	the	DET
ijassa-1111	118	2	original	original	ADJ
ijassa-1111	118	3	matrix	matrix	NOUN
ijassa-1111	118	4	can	can	AUX
ijassa-1111	118	5	also	also	ADV
ijassa-1111	118	6	be	be	AUX
ijassa-1111	118	7	represented	represent	VERB
ijassa-1111	118	8	as	as	ADP
ijassa-1111	118	9	𝑊	𝑊	PROPN
ijassa-1111	118	10	=	=	NOUN
ijassa-1111	118	11	:	:	PUNCT
ijassa-1111	118	12	𝑊	𝑊	NOUN
ijassa-1111	118	13	=	=	SYM
ijassa-1111	118	14	30/30	30/30	NUM
ijassa-1111	119	1	15/30	15/30	NUM
ijassa-1111	119	2	10/30	10/30	NUM
ijassa-1111	119	3	6/30	6/30	NUM
ijassa-1111	119	4	30/15	30/15	NUM
ijassa-1111	119	5	15/15	15/15	NUM
ijassa-1111	119	6	10/15	10/15	NUM
ijassa-1111	119	7	6/15	6/15	NUM
ijassa-1111	119	8	30/10	30/10	NUM
ijassa-1111	119	9	15/10	15/10	NUM
ijassa-1111	119	10	10/10	10/10	NUM
ijassa-1111	119	11	6/10	6/10	NUM
ijassa-1111	119	12	30/6	30/6	NUM
ijassa-1111	119	13	15/6	15/6	NUM
ijassa-1111	119	14	10/6	10/6	NUM
ijassa-1111	119	15	6/6	6/6	NUM
ijassa-1111	119	16	.	.	PUNCT
ijassa-1111	120	1	4	4	X
ijassa-1111	120	2	.	.	X
ijassa-1111	120	3	reducing	reduce	VERB
ijassa-1111	120	4	the	the	DET
ijassa-1111	120	5	original	original	ADJ
ijassa-1111	120	6	problem	problem	NOUN
ijassa-1111	120	7	to	to	ADP
ijassa-1111	120	8	an	an	DET
ijassa-1111	120	9	equivalent	equivalent	ADJ
ijassa-1111	120	10	one	one	NOUN
ijassa-1111	120	11	since	since	SCONJ
ijassa-1111	120	12	,	,	PUNCT
ijassa-1111	120	13	following	follow	VERB
ijassa-1111	120	14	(	(	PUNCT
ijassa-1111	120	15	3.5	3.5	NUM
ijassa-1111	120	16	)	)	PUNCT
ijassa-1111	120	17	,	,	PUNCT
ijassa-1111	120	18	the	the	DET
ijassa-1111	120	19	elements	element	NOUN
ijassa-1111	120	20	of	of	ADP
ijassa-1111	120	21	the	the	DET
ijassa-1111	120	22	𝑖-th	𝑖-th	PROPN
ijassa-1111	120	23	rows	row	NOUN
ijassa-1111	120	24	of	of	ADP
ijassa-1111	120	25	the	the	DET
ijassa-1111	120	26	normalized	normalize	VERB
ijassa-1111	120	27	vector	vector	NOUN
ijassa-1111	120	28	columns	column	NOUN
ijassa-1111	120	29	of	of	ADP
ijassa-1111	120	30	the	the	DET
ijassa-1111	120	31	multiplier	multipli	ADJ
ijassa-1111	120	32	and	and	CCONJ
ijassa-1111	120	33	vector	vector	NOUN
ijassa-1111	120	34	matrix	matrix	NOUN
ijassa-1111	120	35	are	be	AUX
ijassa-1111	120	36	equal	equal	ADJ
ijassa-1111	120	37	to	to	ADP
ijassa-1111	120	38	the	the	DET
ijassa-1111	120	39	𝑖-th	𝑖-th	PROPN
ijassa-1111	120	40	normalized	normalize	VERB
ijassa-1111	120	41	component	component	NOUN
ijassa-1111	120	42	of	of	ADP
ijassa-1111	120	43	the	the	DET
ijassa-1111	120	44	right	right	ADJ
ijassa-1111	120	45	proper	proper	ADJ
ijassa-1111	120	46	vector	vector	NOUN
ijassa-1111	120	47	,	,	PUNCT
ijassa-1111	120	48	namely	namely	ADV
ijassa-1111	120	49	:	:	PUNCT
ijassa-1111	120	50	𝑤	𝑤	X
ijassa-1111	120	51	=	=	PUNCT
ijassa-1111	120	52	⋯	⋯	NOUN
ijassa-1111	120	53	=	=	SYM
ijassa-1111	120	54	𝑤	𝑤	NOUN
ijassa-1111	120	55	=	=	PUNCT
ijassa-1111	120	56	⋯	⋯	NOUN
ijassa-1111	120	57	=	=	SYM
ijassa-1111	120	58	𝑤	𝑤	PROPN
ijassa-1111	120	59	=	=	PUNCT
ijassa-1111	120	60	𝑤	𝑤	PROPN
ijassa-1111	120	61	,	,	PUNCT
ijassa-1111	120	62	(	(	PUNCT
ijassa-1111	120	63	4.8	4.8	NUM
ijassa-1111	120	64	)	)	PUNCT
ijassa-1111	120	65	where	where	SCONJ
ijassa-1111	120	66	∑	∑	ADP
ijassa-1111	120	67	𝑤	𝑤	SYM
ijassa-1111	120	68	=	=	SYM
ijassa-1111	120	69	1	1	NUM
ijassa-1111	120	70	,	,	PUNCT
ijassa-1111	120	71	to	to	ADP
ijassa-1111	120	72	we	we	PRON
ijassa-1111	120	73	have	have	VERB
ijassa-1111	120	74	:	:	PUNCT
ijassa-1111	120	75	𝑤	𝑤	ADP
ijassa-1111	120	76	=	=	SYM
ijassa-1111	120	77	=	=	PUNCT
ijassa-1111	120	78	/	/	SYM
ijassa-1111	120	79	∑	∑	PROPN
ijassa-1111	120	80	/	/	SYM
ijassa-1111	120	81	∑	∑	PROPN
ijassa-1111	120	82	=	=	SYM
ijassa-1111	120	83	,	,	PUNCT
ijassa-1111	120	84	∀𝑖	∀𝑖	PROPN
ijassa-1111	120	85	,	,	PUNCT
ijassa-1111	120	86	𝑗	𝑗	PROPN
ijassa-1111	120	87	=	=	SYM
ijassa-1111	120	88	1	1	NUM
ijassa-1111	120	89	,	,	PUNCT
ijassa-1111	120	90	𝑛.	𝑛.	NOUN
ijassa-1111	120	91	we	we	PRON
ijassa-1111	120	92	show	show	VERB
ijassa-1111	120	93	that	that	SCONJ
ijassa-1111	120	94	the	the	DET
ijassa-1111	120	95	multiplicativity	multiplicativity	NOUN
ijassa-1111	120	96	condition	condition	NOUN
ijassa-1111	120	97	(	(	PUNCT
ijassa-1111	120	98	2.3	2.3	NUM
ijassa-1111	120	99	)	)	PUNCT
ijassa-1111	120	100	for	for	ADP
ijassa-1111	120	101	the	the	DET
ijassa-1111	120	102	normalized	normalize	VERB
ijassa-1111	120	103	row	row	NOUN
ijassa-1111	120	104	elements	element	NOUN
ijassa-1111	120	105	(	(	PUNCT
ijassa-1111	120	106	4.8	4.8	NUM
ijassa-1111	120	107	)	)	PUNCT
ijassa-1111	120	108	of	of	ADP
ijassa-1111	120	109	the	the	DET
ijassa-1111	120	110	matrix	matrix	NOUN
ijassa-1111	120	111	is	be	AUX
ijassa-1111	120	112	satisfied	satisfied	ADJ
ijassa-1111	120	113	:	:	PUNCT
ijassa-1111	120	114	𝑤	𝑤	PART
ijassa-1111	120	115	𝑤	𝑤	X
ijassa-1111	120	116	=	=	NOUN
ijassa-1111	120	117	𝑤	𝑤	PART
ijassa-1111	120	118	𝑤	𝑤	PART
ijassa-1111	120	119	×	×	NOUN
ijassa-1111	120	120	𝑤	𝑤	ADP
ijassa-1111	120	121	𝑤	𝑤	NOUN
ijassa-1111	120	122	=	=	NOUN
ijassa-1111	120	123	𝑤	𝑤	PART
ijassa-1111	120	124	𝑤	𝑤	NOUN
ijassa-1111	120	125	=	=	SYM
ijassa-1111	120	126	𝑤	𝑤	PROPN
ijassa-1111	120	127	,	,	PUNCT
ijassa-1111	120	128	𝑖	𝑖	SYM
ijassa-1111	120	129	,	,	PUNCT
ijassa-1111	120	130	𝑗	𝑗	INTJ
ijassa-1111	120	131	,	,	PUNCT
ijassa-1111	120	132	𝑘	𝑘	X
ijassa-1111	120	133	=	=	SYM
ijassa-1111	120	134	1	1	NUM
ijassa-1111	120	135	,	,	PUNCT
ijassa-1111	120	136	𝑛.	𝑛.	NOUN
ijassa-1111	120	137	thus	thus	ADV
ijassa-1111	120	138	,	,	PUNCT
ijassa-1111	120	139	finding	find	VERB
ijassa-1111	120	140	the	the	DET
ijassa-1111	120	141	elements	element	NOUN
ijassa-1111	120	142	of	of	ADP
ijassa-1111	120	143	the	the	DET
ijassa-1111	120	144	approximating	approximate	VERB
ijassa-1111	120	145	matrix	matrix	NOUN
ijassa-1111	120	146	𝑊	𝑊	NOUN
ijassa-1111	120	147	=	=	PUNCT
ijassa-1111	121	1	[	[	X
ijassa-1111	121	2	𝑤	𝑤	X
ijassa-1111	121	3	]	]	PUNCT
ijassa-1111	121	4	of	of	ADP
ijassa-1111	121	5	the	the	DET
ijassa-1111	121	6	problem	problem	NOUN
ijassa-1111	121	7	(	(	PUNCT
ijassa-1111	121	8	2.2	2.2	NUM
ijassa-1111	121	9	)	)	PUNCT
ijassa-1111	121	10	–	–	PUNCT
ijassa-1111	121	11	(	(	PUNCT
ijassa-1111	121	12	2.3	2.3	NUM
ijassa-1111	121	13	)	)	PUNCT
ijassa-1111	121	14	is	be	AUX
ijassa-1111	121	15	equivalent	equivalent	ADJ
ijassa-1111	121	16	to	to	ADP
ijassa-1111	121	17	finding	find	VERB
ijassa-1111	121	18	the	the	DET
ijassa-1111	121	19	elements	element	NOUN
ijassa-1111	121	20	of	of	ADP
ijassa-1111	121	21	a	a	DET
ijassa-1111	121	22	normalized	normalize	VERB
ijassa-1111	121	23	column	column	NOUN
ijassa-1111	121	24	vector	vector	NOUN
ijassa-1111	121	25	:	:	PUNCT
ijassa-1111	121	26	�	�	PROPN
ijassa-1111	121	27	⃗	⃗	NOUN
ijassa-1111	121	28	�	�	NOUN
ijassa-1111	121	29	=	=	SYM
ijassa-1111	121	30	(	(	PUNCT
ijassa-1111	121	31	𝑤	𝑤	INTJ
ijassa-1111	121	32	,	,	PUNCT
ijassa-1111	121	33	…	…	PUNCT
ijassa-1111	121	34	,	,	PUNCT
ijassa-1111	121	35	𝑤	𝑤	PART
ijassa-1111	121	36	,	,	PUNCT
ijassa-1111	121	37	…	…	PUNCT
ijassa-1111	121	38	,	,	PUNCT
ijassa-1111	121	39	𝑤	𝑤	X
ijassa-1111	121	40	)	)	PUNCT
ijassa-1111	121	41	.	.	PUNCT
ijassa-1111	122	1	as	as	ADP
ijassa-1111	122	2	the	the	DET
ijassa-1111	122	3	target	target	NOUN
ijassa-1111	122	4	indicator	indicator	NOUN
ijassa-1111	122	5	of	of	ADP
ijassa-1111	122	6	the	the	DET
ijassa-1111	122	7	approximation	approximation	NOUN
ijassa-1111	122	8	problem	problem	NOUN
ijassa-1111	122	9	,	,	PUNCT
ijassa-1111	122	10	we	we	PRON
ijassa-1111	122	11	take	take	VERB
ijassa-1111	122	12	the	the	DET
ijassa-1111	122	13	square	square	NOUN
ijassa-1111	122	14	of	of	ADP
ijassa-1111	122	15	the	the	DET
ijassa-1111	122	16	difference	difference	NOUN
ijassa-1111	122	17	between	between	ADP
ijassa-1111	122	18	the	the	DET
ijassa-1111	122	19	normalized	normalize	VERB
ijassa-1111	122	20	elements	element	NOUN
ijassa-1111	122	21	of	of	ADP
ijassa-1111	122	22	the	the	DET
ijassa-1111	122	23	original	original	ADJ
ijassa-1111	122	24	and	and	CCONJ
ijassa-1111	122	25	multiplicative	multiplicative	ADJ
ijassa-1111	122	26	matrices	matrix	NOUN
ijassa-1111	122	27	in	in	ADP
ijassa-1111	122	28	the	the	DET
ijassa-1111	122	29	form	form	NOUN
ijassa-1111	122	30	:	:	PUNCT
ijassa-1111	122	31	𝜌	𝜌	X
ijassa-1111	122	32	𝑉	𝑉	PROPN
ijassa-1111	122	33	,	,	PUNCT
ijassa-1111	122	34	𝑊	𝑊	PROPN
ijassa-1111	122	35	=	=	SYM
ijassa-1111	122	36	𝑣	𝑣	PRON
ijassa-1111	122	37	−	−	PROPN
ijassa-1111	122	38	𝑤	𝑤	SYM
ijassa-1111	122	39	(	(	PUNCT
ijassa-1111	122	40	4.9	4.9	NUM
ijassa-1111	122	41	)	)	PUNCT
ijassa-1111	122	42	then	then	ADV
ijassa-1111	122	43	the	the	DET
ijassa-1111	122	44	mathematical	mathematical	ADJ
ijassa-1111	122	45	formulation	formulation	NOUN
ijassa-1111	122	46	of	of	ADP
ijassa-1111	122	47	the	the	DET
ijassa-1111	122	48	original	original	ADJ
ijassa-1111	122	49	problem	problem	NOUN
ijassa-1111	122	50	is	be	AUX
ijassa-1111	122	51	reduced	reduce	VERB
ijassa-1111	122	52	to	to	ADP
ijassa-1111	122	53	finding	find	VERB
ijassa-1111	122	54	the	the	DET
ijassa-1111	122	55	normalized	normalize	VERB
ijassa-1111	122	56	right	right	ADJ
ijassa-1111	122	57	column	column	NOUN
ijassa-1111	122	58	vector	vector	NOUN
ijassa-1111	122	59	of	of	ADP
ijassa-1111	122	60	the	the	DET
ijassa-1111	122	61	approximating	approximate	VERB
ijassa-1111	122	62	matrix	matrix	NOUN
ijassa-1111	122	63	and	and	CCONJ
ijassa-1111	122	64	providing	provide	VERB
ijassa-1111	122	65	the	the	DET
ijassa-1111	122	66	minimum	minimum	ADJ
ijassa-1111	122	67	criterion	criterion	NOUN
ijassa-1111	122	68	(	(	PUNCT
ijassa-1111	122	69	4.9	4.9	NUM
ijassa-1111	122	70	):	):	PUNCT
ijassa-1111	122	71	𝑣	𝑣	PRON
ijassa-1111	122	72	−	−	PROPN
ijassa-1111	122	73	𝑤	𝑤	PROPN
ijassa-1111	122	74	→	→	SYM
ijassa-1111	122	75	min	min	PROPN
ijassa-1111	122	76	(	(	PUNCT
ijassa-1111	122	77	,	,	PUNCT
ijassa-1111	122	78	…	…	PUNCT
ijassa-1111	122	79	,	,	PUNCT
ijassa-1111	122	80	)	)	PUNCT
ijassa-1111	122	81	,	,	PUNCT
ijassa-1111	122	82	(	(	PUNCT
ijassa-1111	122	83	4.10	4.10	NUM
ijassa-1111	122	84	)	)	PUNCT
ijassa-1111	122	85	where	where	SCONJ
ijassa-1111	122	86	𝑣	𝑣	X
ijassa-1111	122	87	=	=	PUNCT
ijassa-1111	122	88	∑	∑	PUNCT
ijassa-1111	122	89	are	be	AUX
ijassa-1111	122	90	the	the	DET
ijassa-1111	122	91	normalized	normalize	VERB
ijassa-1111	122	92	elements	element	NOUN
ijassa-1111	122	93	of	of	ADP
ijassa-1111	122	94	the	the	DET
ijassa-1111	122	95	matrix	matrix	NOUN
ijassa-1111	122	96	𝑉	𝑉	NOUN
ijassa-1111	123	1	=	=	PUNCT
ijassa-1111	124	1	[	[	X
ijassa-1111	124	2	𝑣	𝑣	X
ijassa-1111	124	3	]	]	PUNCT
ijassa-1111	124	4	of	of	ADP
ijassa-1111	124	5	judgments	judgment	NOUN
ijassa-1111	124	6	,	,	PUNCT
ijassa-1111	124	7	𝑗	𝑗	NOUN
ijassa-1111	124	8	=	=	SYM
ijassa-1111	124	9	1	1	NUM
ijassa-1111	124	10	,	,	PUNCT
ijassa-1111	124	11	𝑛.	𝑛.	NOUN
ijassa-1111	124	12	the	the	DET
ijassa-1111	124	13	reasonableness	reasonableness	NOUN
ijassa-1111	124	14	of	of	ADP
ijassa-1111	124	15	the	the	DET
ijassa-1111	124	16	transition	transition	NOUN
ijassa-1111	124	17	from	from	ADP
ijassa-1111	124	18	the	the	DET
ijassa-1111	124	19	original	original	ADJ
ijassa-1111	124	20	perturbed	perturb	VERB
ijassa-1111	124	21	matrix	matrix	NOUN
ijassa-1111	124	22	𝑉	𝑉	NOUN
ijassa-1111	124	23	=	=	PUNCT
ijassa-1111	125	1	[	[	X
ijassa-1111	125	2	𝑣	𝑣	X
ijassa-1111	125	3	]	]	PUNCT
ijassa-1111	125	4	to	to	ADP
ijassa-1111	125	5	the	the	DET
ijassa-1111	125	6	normalized	normalize	VERB
ijassa-1111	125	7	𝑉	𝑉	PROPN
ijassa-1111	125	8	=	=	PUNCT
ijassa-1111	126	1	[	[	X
ijassa-1111	126	2	𝑣	𝑣	X
ijassa-1111	126	3	]	]	PUNCT
ijassa-1111	126	4	is	be	AUX
ijassa-1111	126	5	based	base	VERB
ijassa-1111	126	6	on	on	ADP
ijassa-1111	126	7	the	the	DET
ijassa-1111	126	8	fact	fact	NOUN
ijassa-1111	126	9	that	that	SCONJ
ijassa-1111	126	10	the	the	DET
ijassa-1111	126	11	rank	rank	NOUN
ijassa-1111	126	12	and	and	CCONJ
ijassa-1111	126	13	magnitude	magnitude	NOUN
ijassa-1111	126	14	of	of	ADP
ijassa-1111	126	15	the	the	DET
ijassa-1111	126	16	relation	relation	NOUN
ijassa-1111	126	17	between	between	ADP
ijassa-1111	126	18	the	the	DET
ijassa-1111	126	19	elements	element	NOUN
ijassa-1111	126	20	of	of	ADP
ijassa-1111	126	21	the	the	DET
ijassa-1111	126	22	same	same	ADJ
ijassa-1111	126	23	vector	vector	NOUN
ijassa-1111	126	24	column	column	NOUN
ijassa-1111	126	25	are	be	AUX
ijassa-1111	126	26	preserved	preserve	VERB
ijassa-1111	126	27	for	for	ADP
ijassa-1111	126	28	the	the	DET
ijassa-1111	126	29	original	original	ADJ
ijassa-1111	126	30	and	and	CCONJ
ijassa-1111	126	31	normalized	normalize	VERB
ijassa-1111	126	32	matrix	matrix	NOUN
ijassa-1111	126	33	.	.	PUNCT
ijassa-1111	127	1	110	110	NUM
ijassa-1111	127	2	v.p	v.p	PROPN
ijassa-1111	127	3	.	.	PROPN
ijassa-1111	127	4	korneenko	korneenko	PROPN
ijassa-1111	127	5	copyright	copyright	NOUN
ijassa-1111	127	6	©	©	PROPN
ijassa-1111	127	7	2024	2024	NUM
ijassa-1111	127	8	assa	assa	PROPN
ijassa-1111	127	9	adv	adv	PROPN
ijassa-1111	127	10	.	.	PUNCT
ijassa-1111	128	1	in	in	ADP
ijassa-1111	128	2	systems	system	NOUN
ijassa-1111	128	3	science	science	NOUN
ijassa-1111	128	4	and	and	CCONJ
ijassa-1111	128	5	appl	appl	NOUN
ijassa-1111	128	6	.	.	PUNCT
ijassa-1111	129	1	(	(	PUNCT
ijassa-1111	129	2	2024	2024	NUM
ijassa-1111	129	3	)	)	PUNCT
ijassa-1111	129	4	4.1	4.1	NUM
ijassa-1111	129	5	.	.	PUNCT
ijassa-1111	129	6	theorem	theorem	VERB
ijassa-1111	129	7	on	on	ADP
ijassa-1111	129	8	the	the	DET
ijassa-1111	129	9	optimal	optimal	ADJ
ijassa-1111	129	10	solution	solution	NOUN
ijassa-1111	129	11	:	:	PUNCT
ijassa-1111	129	12	theorem	theorem	VERB
ijassa-1111	129	13	4.3	4.3	NUM
ijassa-1111	129	14	:	:	PUNCT
ijassa-1111	129	15	the	the	DET
ijassa-1111	129	16	optimal	optimal	ADJ
ijassa-1111	129	17	solution	solution	NOUN
ijassa-1111	129	18	to	to	ADP
ijassa-1111	129	19	the	the	DET
ijassa-1111	129	20	problem	problem	NOUN
ijassa-1111	129	21	(	(	PUNCT
ijassa-1111	129	22	4.10	4.10	NUM
ijassa-1111	129	23	)	)	PUNCT
ijassa-1111	129	24	is	be	AUX
ijassa-1111	129	25	a	a	DET
ijassa-1111	129	26	normalized	normalize	VERB
ijassa-1111	129	27	vector	vector	NOUN
ijassa-1111	129	28	�	�	PROPN
ijassa-1111	129	29	⃗	⃗	NOUN
ijassa-1111	129	30	�	�	NOUN
ijassa-1111	129	31	∗	∗	NOUN
ijassa-1111	129	32	=	=	SYM
ijassa-1111	129	33	𝑤∗	𝑤∗	NOUN
ijassa-1111	129	34	…	…	PUNCT
ijassa-1111	129	35	𝑤∗	𝑤∗	NOUN
ijassa-1111	129	36	,	,	PUNCT
ijassa-1111	129	37	the	the	DET
ijassa-1111	129	38	components	component	NOUN
ijassa-1111	129	39	of	of	ADP
ijassa-1111	129	40	which	which	PRON
ijassa-1111	129	41	are	be	AUX
ijassa-1111	129	42	taken	take	VERB
ijassa-1111	129	43	as	as	ADP
ijassa-1111	129	44	the	the	DET
ijassa-1111	129	45	coefficients	coefficient	NOUN
ijassa-1111	129	46	of	of	ADP
ijassa-1111	129	47	the	the	DET
ijassa-1111	129	48	importance	importance	NOUN
ijassa-1111	129	49	the	the	DET
ijassa-1111	129	50	criteria	criterion	NOUN
ijassa-1111	129	51	𝑤∗	𝑤∗	PROPN
ijassa-1111	129	52	=	=	SYM
ijassa-1111	129	53	𝑤(𝑓	𝑤(𝑓	PROPN
ijassa-1111	129	54	)	)	PUNCT
ijassa-1111	129	55	and	and	CCONJ
ijassa-1111	129	56	calculated	calculate	VERB
ijassa-1111	129	57	by	by	ADP
ijassa-1111	129	58	the	the	DET
ijassa-1111	129	59	formula	formula	NOUN
ijassa-1111	129	60	:	:	PUNCT
ijassa-1111	130	1	𝑤∗	𝑤∗	NOUN
ijassa-1111	130	2	=	=	SYM
ijassa-1111	130	3	1	1	NUM
ijassa-1111	130	4	𝑛	𝑛	PRON
ijassa-1111	130	5	𝑣	𝑣	NOUN
ijassa-1111	130	6	,	,	PUNCT
ijassa-1111	130	7	∀	∀	NOUN
ijassa-1111	130	8	𝑖	𝑖	NOUN
ijassa-1111	130	9	=	=	SYM
ijassa-1111	130	10	1	1	NUM
ijassa-1111	130	11	,	,	PUNCT
ijassa-1111	130	12	𝑛	𝑛	ADJ
ijassa-1111	130	13	,	,	PUNCT
ijassa-1111	130	14	while	while	SCONJ
ijassa-1111	130	15	delivering	deliver	VERB
ijassa-1111	130	16	a	a	DET
ijassa-1111	130	17	minimum	minimum	NOUN
ijassa-1111	130	18	of	of	ADP
ijassa-1111	130	19	the	the	DET
ijassa-1111	130	20	indicator	indicator	NOUN
ijassa-1111	130	21	(	(	PUNCT
ijassa-1111	130	22	4.9	4.9	NUM
ijassa-1111	130	23	)	)	PUNCT
ijassa-1111	130	24	.	.	PUNCT
ijassa-1111	131	1	the	the	DET
ijassa-1111	131	2	elements	element	NOUN
ijassa-1111	131	3	of	of	ADP
ijassa-1111	131	4	the	the	DET
ijassa-1111	131	5	optimal	optimal	ADJ
ijassa-1111	131	6	approximation	approximation	NOUN
ijassa-1111	131	7	matrix	matrix	NOUN
ijassa-1111	131	8	𝑊∗	𝑊∗	NUM
ijassa-1111	131	9	=	=	PUNCT
ijassa-1111	131	10	𝑤∗	𝑤∗	NOUN
ijassa-1111	131	11	are	be	AUX
ijassa-1111	131	12	determined	determine	VERB
ijassa-1111	131	13	by	by	ADP
ijassa-1111	131	14	the	the	DET
ijassa-1111	131	15	formula	formula	NOUN
ijassa-1111	131	16	:	:	PUNCT
ijassa-1111	131	17	𝑤∗	𝑤∗	NOUN
ijassa-1111	131	18	=	=	SYM
ijassa-1111	131	19	𝑤∗	𝑤∗	PROPN
ijassa-1111	131	20	𝑤∗.	𝑤∗.	NOUN
ijassa-1111	131	21	as	as	ADP
ijassa-1111	131	22	an	an	DET
ijassa-1111	131	23	estimate	estimate	NOUN
ijassa-1111	131	24	of	of	ADP
ijassa-1111	131	25	the	the	DET
ijassa-1111	131	26	approximation	approximation	NOUN
ijassa-1111	131	27	matrix	matrix	NOUN
ijassa-1111	131	28	to	to	ADP
ijassa-1111	131	29	the	the	DET
ijassa-1111	131	30	original	original	ADJ
ijassa-1111	131	31	judgment	judgment	NOUN
ijassa-1111	131	32	matrix	matrix	NOUN
ijassa-1111	131	33	,	,	PUNCT
ijassa-1111	131	34	we	we	PRON
ijassa-1111	131	35	take	take	VERB
ijassa-1111	131	36	the	the	DET
ijassa-1111	131	37	euclidean	euclidean	ADJ
ijassa-1111	131	38	matrix	matrix	NOUN
ijassa-1111	131	39	norm	norm	NOUN
ijassa-1111	132	1	[	[	X
ijassa-1111	132	2	9	9	NUM
ijassa-1111	132	3	]	]	SYM
ijassa-1111	132	4	:	:	PUNCT
ijassa-1111	132	5	𝑑(𝑉	𝑑(𝑉	NOUN
ijassa-1111	132	6	,	,	PUNCT
ijassa-1111	132	7	𝑊∗	𝑊∗	NUM
ijassa-1111	132	8	)	)	PUNCT
ijassa-1111	132	9	=	=	SYM
ijassa-1111	132	10	‖𝑉	‖𝑉	NOUN
ijassa-1111	132	11	−	−	PROPN
ijassa-1111	132	12	𝑊∗‖	𝑊∗‖	NOUN
ijassa-1111	132	13	=	=	PUNCT
ijassa-1111	132	14	𝑣	𝑣	PRON
ijassa-1111	132	15	−	−	PROPN
ijassa-1111	132	16	𝑤∗	𝑤∗	PROPN
ijassa-1111	132	17	(	(	PUNCT
ijassa-1111	132	18	4.11	4.11	NUM
ijassa-1111	132	19	)	)	PUNCT
ijassa-1111	132	20	the	the	DET
ijassa-1111	132	21	proof	proof	NOUN
ijassa-1111	132	22	is	be	AUX
ijassa-1111	132	23	trivial	trivial	ADJ
ijassa-1111	132	24	and	and	CCONJ
ijassa-1111	132	25	is	be	AUX
ijassa-1111	132	26	based	base	VERB
ijassa-1111	132	27	on	on	ADP
ijassa-1111	132	28	necessary	necessary	ADJ
ijassa-1111	132	29	and	and	CCONJ
ijassa-1111	132	30	sufficient	sufficient	ADJ
ijassa-1111	132	31	conditions	condition	NOUN
ijassa-1111	132	32	for	for	ADP
ijassa-1111	132	33	the	the	DET
ijassa-1111	132	34	existence	existence	NOUN
ijassa-1111	132	35	of	of	ADP
ijassa-1111	132	36	an	an	DET
ijassa-1111	132	37	optimal	optimal	ADJ
ijassa-1111	132	38	solution	solution	NOUN
ijassa-1111	132	39	of	of	ADP
ijassa-1111	132	40	a	a	DET
ijassa-1111	132	41	function	function	NOUN
ijassa-1111	132	42	of	of	ADP
ijassa-1111	132	43	many	many	ADJ
ijassa-1111	132	44	variables	variable	NOUN
ijassa-1111	132	45	.	.	PUNCT
ijassa-1111	133	1	4.2	4.2	NUM
ijassa-1111	133	2	.	.	PUNCT
ijassa-1111	133	3	algorithm	algorithm	NOUN
ijassa-1111	133	4	for	for	ADP
ijassa-1111	133	5	generating	generate	VERB
ijassa-1111	133	6	optimal	optimal	ADJ
ijassa-1111	133	7	weights	weight	NOUN
ijassa-1111	133	8	for	for	ADP
ijassa-1111	133	9	criteria	criterion	NOUN
ijassa-1111	133	10	step	step	NOUN
ijassa-1111	133	11	1	1	NUM
ijassa-1111	133	12	.	.	PUNCT
ijassa-1111	133	13	normalization	normalization	NOUN
ijassa-1111	133	14	of	of	ADP
ijassa-1111	133	15	elements	element	NOUN
ijassa-1111	133	16	of	of	ADP
ijassa-1111	133	17	the	the	DET
ijassa-1111	133	18	original	original	ADJ
ijassa-1111	133	19	matrix	matrix	NOUN
ijassa-1111	133	20	of	of	ADP
ijassa-1111	133	21	pairwise	pairwise	NOUN
ijassa-1111	133	22	comparisons	comparison	NOUN
ijassa-1111	133	23	of	of	ADP
ijassa-1111	133	24	the	the	DET
ijassa-1111	133	25	importance	importance	NOUN
ijassa-1111	133	26	of	of	ADP
ijassa-1111	133	27	criteria	criterion	NOUN
ijassa-1111	133	28	by	by	ADP
ijassa-1111	133	29	the	the	DET
ijassa-1111	133	30	sum	sum	NOUN
ijassa-1111	133	31	∑	∑	VERB
ijassa-1111	133	32	𝑣	𝑣	PRON
ijassa-1111	133	33	of	of	ADP
ijassa-1111	133	34	elements	element	NOUN
ijassa-1111	133	35	columns	column	NOUN
ijassa-1111	133	36	of	of	ADP
ijassa-1111	133	37	the	the	DET
ijassa-1111	133	38	original	original	ADJ
ijassa-1111	133	39	matrix	matrix	NOUN
ijassa-1111	133	40	of	of	ADP
ijassa-1111	133	41	judgments	judgment	NOUN
ijassa-1111	133	42	:	:	PUNCT
ijassa-1111	133	43	𝑣	𝑣	ADP
ijassa-1111	133	44	=	=	PUNCT
ijassa-1111	133	45	∑	∑	PUNCT
ijassa-1111	133	46	are	be	AUX
ijassa-1111	133	47	the	the	DET
ijassa-1111	133	48	normalized	normalize	VERB
ijassa-1111	133	49	elements	element	NOUN
ijassa-1111	133	50	of	of	ADP
ijassa-1111	133	51	the	the	DET
ijassa-1111	133	52	judgment	judgment	NOUN
ijassa-1111	133	53	matrix	matrix	NOUN
ijassa-1111	133	54	𝑉	𝑉	NOUN
ijassa-1111	133	55	=	=	PUNCT
ijassa-1111	134	1	[	[	X
ijassa-1111	134	2	𝑣	𝑣	X
ijassa-1111	134	3	]	]	PUNCT
ijassa-1111	134	4	.	.	PUNCT
ijassa-1111	135	1	step	step	NOUN
ijassa-1111	135	2	2	2	NUM
ijassa-1111	135	3	.	.	PUNCT
ijassa-1111	136	1	the	the	DET
ijassa-1111	136	2	calculation	calculation	NOUN
ijassa-1111	136	3	for	for	ADP
ijassa-1111	136	4	each	each	DET
ijassa-1111	136	5	row	row	NOUN
ijassa-1111	136	6	of	of	ADP
ijassa-1111	136	7	the	the	DET
ijassa-1111	136	8	normalized	normalize	VERB
ijassa-1111	136	9	matrix	matrix	NOUN
ijassa-1111	136	10	𝑉	𝑉	NOUN
ijassa-1111	136	11	=	=	PUNCT
ijassa-1111	137	1	[	[	X
ijassa-1111	137	2	𝑣	𝑣	X
ijassa-1111	137	3	]	]	PUNCT
ijassa-1111	137	4	of	of	ADP
ijassa-1111	137	5	judgments	judgment	NOUN
ijassa-1111	137	6	of	of	ADP
ijassa-1111	137	7	its	its	PRON
ijassa-1111	137	8	average	average	ADJ
ijassa-1111	137	9	value	value	NOUN
ijassa-1111	137	10	,	,	PUNCT
ijassa-1111	137	11	we	we	PRON
ijassa-1111	137	12	take	take	VERB
ijassa-1111	137	13	it	it	PRON
ijassa-1111	137	14	as	as	ADP
ijassa-1111	137	15	the	the	DET
ijassa-1111	137	16	normalized	normalize	VERB
ijassa-1111	137	17	weights	weight	NOUN
ijassa-1111	137	18	of	of	ADP
ijassa-1111	137	19	the	the	DET
ijassa-1111	137	20	criteria	criterion	NOUN
ijassa-1111	137	21	,	,	PUNCT
ijassa-1111	137	22	namely	namely	ADV
ijassa-1111	137	23	:	:	PUNCT
ijassa-1111	137	24	𝑤∗	𝑤∗	NOUN
ijassa-1111	137	25	=	=	SYM
ijassa-1111	137	26	1	1	NUM
ijassa-1111	137	27	𝑛	𝑛	PRON
ijassa-1111	137	28	𝑣	𝑣	NOUN
ijassa-1111	137	29	,	,	PUNCT
ijassa-1111	137	30	𝑤∗	𝑤∗	PROPN
ijassa-1111	137	31	=	=	SYM
ijassa-1111	137	32	𝑤(𝑓	𝑤(𝑓	PROPN
ijassa-1111	137	33	)	)	PUNCT
ijassa-1111	137	34	∀	∀	PUNCT
ijassa-1111	138	1	𝑖	𝑖	NOUN
ijassa-1111	138	2	=	=	SYM
ijassa-1111	138	3	1	1	NUM
ijassa-1111	138	4	,	,	PUNCT
ijassa-1111	138	5	𝑛.	𝑛.	NOUN
ijassa-1111	138	6	step	step	NOUN
ijassa-1111	138	7	3	3	NUM
ijassa-1111	138	8	.	.	PUNCT
ijassa-1111	138	9	recovery	recovery	NOUN
ijassa-1111	138	10	of	of	ADP
ijassa-1111	138	11	the	the	DET
ijassa-1111	138	12	elements	element	NOUN
ijassa-1111	138	13	of	of	ADP
ijassa-1111	138	14	the	the	DET
ijassa-1111	138	15	multiplicative	multiplicative	ADJ
ijassa-1111	138	16	matrix	matrix	NOUN
ijassa-1111	138	17	by	by	ADP
ijassa-1111	138	18	the	the	DET
ijassa-1111	138	19	optimal	optimal	ADJ
ijassa-1111	138	20	normalized	normalize	VERB
ijassa-1111	138	21	weights	weight	NOUN
ijassa-1111	138	22	of	of	ADP
ijassa-1111	138	23	the	the	DET
ijassa-1111	138	24	criteria	criterion	NOUN
ijassa-1111	138	25	:	:	PUNCT
ijassa-1111	138	26	𝑊	𝑊	NOUN
ijassa-1111	138	27	=	=	NOUN
ijassa-1111	138	28	∗	∗	NOUN
ijassa-1111	138	29	∗	∗	NOUN
ijassa-1111	138	30	.	.	PUNCT
ijassa-1111	139	1	step	step	NOUN
ijassa-1111	139	2	4	4	NUM
ijassa-1111	139	3	.	.	PUNCT
ijassa-1111	139	4	estimation	estimation	NOUN
ijassa-1111	139	5	of	of	ADP
ijassa-1111	139	6	the	the	DET
ijassa-1111	139	7	proximity	proximity	NOUN
ijassa-1111	139	8	between	between	ADP
ijassa-1111	139	9	the	the	DET
ijassa-1111	139	10	elements	element	NOUN
ijassa-1111	139	11	of	of	ADP
ijassa-1111	139	12	the	the	DET
ijassa-1111	139	13	original	original	ADJ
ijassa-1111	139	14	matrix	matrix	NOUN
ijassa-1111	139	15	of	of	ADP
ijassa-1111	139	16	pairwise	pairwise	NOUN
ijassa-1111	139	17	comparisons	comparison	NOUN
ijassa-1111	139	18	and	and	CCONJ
ijassa-1111	139	19	the	the	DET
ijassa-1111	139	20	optimal	optimal	ADJ
ijassa-1111	139	21	multiplicative	multiplicative	ADJ
ijassa-1111	139	22	matrix	matrix	NOUN
ijassa-1111	139	23	by	by	ADP
ijassa-1111	139	24	the	the	DET
ijassa-1111	139	25	formula	formula	NOUN
ijassa-1111	139	26	𝑑(𝑉	𝑑(𝑉	NOUN
ijassa-1111	139	27	,	,	PUNCT
ijassa-1111	139	28	𝑊∗	𝑊∗	NUM
ijassa-1111	139	29	)	)	PUNCT
ijassa-1111	139	30	(	(	PUNCT
ijassa-1111	139	31	4.11	4.11	NUM
ijassa-1111	139	32	)	)	PUNCT
ijassa-1111	139	33	.	.	PUNCT
ijassa-1111	140	1	5	5	X
ijassa-1111	140	2	.	.	X
ijassa-1111	140	3	comparison	comparison	NOUN
ijassa-1111	140	4	of	of	ADP
ijassa-1111	140	5	the	the	DET
ijassa-1111	140	6	effectiveness	effectiveness	NOUN
ijassa-1111	140	7	of	of	ADP
ijassa-1111	140	8	the	the	DET
ijassa-1111	140	9	method	method	NOUN
ijassa-1111	140	10	with	with	ADP
ijassa-1111	140	11	the	the	DET
ijassa-1111	140	12	analytical	analytical	ADJ
ijassa-1111	140	13	hierarchy	hierarchy	NOUN
ijassa-1111	140	14	process	process	NOUN
ijassa-1111	140	15	by	by	ADP
ijassa-1111	140	16	t.	t.	PROPN
ijassa-1111	140	17	saaty	saaty	NOUN
ijassa-1111	140	18	let	let	VERB
ijassa-1111	140	19	us	we	PRON
ijassa-1111	140	20	compare	compare	VERB
ijassa-1111	140	21	the	the	DET
ijassa-1111	140	22	error	error	NOUN
ijassa-1111	140	23	of	of	ADP
ijassa-1111	140	24	calculating	calculate	VERB
ijassa-1111	140	25	the	the	DET
ijassa-1111	140	26	weights	weight	NOUN
ijassa-1111	140	27	of	of	ADP
ijassa-1111	140	28	the	the	DET
ijassa-1111	140	29	importance	importance	NOUN
ijassa-1111	140	30	of	of	ADP
ijassa-1111	140	31	objects	object	NOUN
ijassa-1111	140	32	(	(	PUNCT
ijassa-1111	140	33	criteria	criterion	NOUN
ijassa-1111	140	34	,	,	PUNCT
ijassa-1111	140	35	alternatives	alternative	NOUN
ijassa-1111	140	36	)	)	PUNCT
ijassa-1111	140	37	by	by	ADP
ijassa-1111	140	38	t.	t.	PROPN
ijassa-1111	140	39	saaty	saaty	PROPN
ijassa-1111	140	40	's	's	PART
ijassa-1111	140	41	method	method	NOUN
ijassa-1111	140	42	with	with	ADP
ijassa-1111	140	43	the	the	DET
ijassa-1111	140	44	optimization	optimization	NOUN
ijassa-1111	140	45	method	method	NOUN
ijassa-1111	140	46	of	of	ADP
ijassa-1111	140	47	the	the	DET
ijassa-1111	140	48	approximation	approximation	NOUN
ijassa-1111	140	49	matrix	matrix	NOUN
ijassa-1111	140	50	for	for	ADP
ijassa-1111	140	51	the	the	DET
ijassa-1111	140	52	approximation	approximation	NOUN
ijassa-1111	140	53	matrix	matrix	NOUN
ijassa-1111	140	54	method	method	NOUN
ijassa-1111	140	55	and	and	CCONJ
ijassa-1111	140	56	its	its	PRON
ijassa-1111	140	57	comparison	comparison	NOUN
ijassa-1111	140	58	…	…	PUNCT
ijassa-1111	140	59	111	111	NUM
ijassa-1111	140	60	copyright	copyright	NOUN
ijassa-1111	140	61	©	©	PROPN
ijassa-1111	140	62	2024	2024	NUM
ijassa-1111	140	63	assa	assa	PROPN
ijassa-1111	140	64	adv	adv	PROPN
ijassa-1111	140	65	.	.	PUNCT
ijassa-1111	141	1	in	in	ADP
ijassa-1111	141	2	systems	system	NOUN
ijassa-1111	141	3	science	science	NOUN
ijassa-1111	141	4	and	and	CCONJ
ijassa-1111	141	5	appl	appl	NOUN
ijassa-1111	141	6	.	.	PUNCT
ijassa-1111	142	1	(	(	PUNCT
ijassa-1111	142	2	2024	2024	NUM
ijassa-1111	142	3	)	)	PUNCT
ijassa-1111	142	4	the	the	DET
ijassa-1111	142	5	formation	formation	NOUN
ijassa-1111	142	6	of	of	ADP
ijassa-1111	142	7	object	object	NOUN
ijassa-1111	142	8	weights	weight	NOUN
ijassa-1111	142	9	in	in	ADP
ijassa-1111	142	10	multi	multi	ADJ
ijassa-1111	142	11	-	-	ADJ
ijassa-1111	142	12	criteria	criterion	NOUN
ijassa-1111	142	13	problems	problem	NOUN
ijassa-1111	142	14	.	.	PUNCT
ijassa-1111	143	1	as	as	SCONJ
ijassa-1111	143	2	multiplicative	multiplicative	ADJ
ijassa-1111	143	3	matrices	matrix	NOUN
ijassa-1111	143	4	consider	consider	VERB
ijassa-1111	143	5	the	the	DET
ijassa-1111	143	6	square	square	ADJ
ijassa-1111	143	7	matrix	matrix	NOUN
ijassa-1111	143	8	𝑊	𝑊	NOUN
ijassa-1111	143	9	=	=	NOUN
ijassa-1111	143	10	,	,	PUNCT
ijassa-1111	143	11	,	,	PUNCT
ijassa-1111	143	12	.	.	PUNCT
ijassa-1111	144	1	and	and	CCONJ
ijassa-1111	144	2	𝑊	𝑊	PROPN
ijassa-1111	144	3	=	=	NOUN
ijassa-1111	144	4	∗	∗	NOUN
ijassa-1111	144	5	∗	∗	NOUN
ijassa-1111	144	6	,	,	PUNCT
ijassa-1111	144	7	,	,	PUNCT
ijassa-1111	144	8	.	.	PUNCT
ijassa-1111	145	1	,	,	PUNCT
ijassa-1111	145	2	in	in	ADP
ijassa-1111	145	3	which	which	PRON
ijassa-1111	145	4	the	the	DET
ijassa-1111	145	5	elements	element	NOUN
ijassa-1111	145	6	are	be	AUX
ijassa-1111	145	7	determined	determine	VERB
ijassa-1111	145	8	by	by	ADP
ijassa-1111	145	9	the	the	DET
ijassa-1111	145	10	vector	vector	NOUN
ijassa-1111	145	11	of	of	ADP
ijassa-1111	145	12	priorities	priority	NOUN
ijassa-1111	145	13	,	,	PUNCT
ijassa-1111	145	14	found	find	VERB
ijassa-1111	145	15	by	by	ADP
ijassa-1111	145	16	the	the	DET
ijassa-1111	145	17	method	method	NOUN
ijassa-1111	145	18	of	of	ADP
ijassa-1111	145	19	analysis	analysis	NOUN
ijassa-1111	145	20	of	of	ADP
ijassa-1111	145	21	hierarchies	hierarchy	NOUN
ijassa-1111	145	22	and	and	CCONJ
ijassa-1111	145	23	using	use	VERB
ijassa-1111	145	24	approximate	approximate	ADJ
ijassa-1111	145	25	matrices	matrix	NOUN
ijassa-1111	145	26	.	.	PUNCT
ijassa-1111	146	1	to	to	PART
ijassa-1111	146	2	do	do	VERB
ijassa-1111	146	3	this	this	PRON
ijassa-1111	146	4	,	,	PUNCT
ijassa-1111	146	5	we	we	PRON
ijassa-1111	146	6	will	will	AUX
ijassa-1111	146	7	use	use	VERB
ijassa-1111	146	8	the	the	DET
ijassa-1111	146	9	data	datum	NOUN
ijassa-1111	146	10	from	from	ADP
ijassa-1111	146	11	the	the	DET
ijassa-1111	146	12	example	example	NOUN
ijassa-1111	146	13	of	of	ADP
ijassa-1111	146	14	buying	buy	VERB
ijassa-1111	146	15	a	a	DET
ijassa-1111	146	16	house	house	NOUN
ijassa-1111	146	17	by	by	ADP
ijassa-1111	146	18	a	a	DET
ijassa-1111	146	19	family	family	NOUN
ijassa-1111	146	20	with	with	ADP
ijassa-1111	146	21	average	average	ADJ
ijassa-1111	146	22	incomes	income	NOUN
ijassa-1111	146	23	,	,	PUNCT
ijassa-1111	146	24	given	give	VERB
ijassa-1111	146	25	in	in	ADP
ijassa-1111	146	26	the	the	DET
ijassa-1111	146	27	work	work	NOUN
ijassa-1111	146	28	of	of	ADP
ijassa-1111	146	29	t.	t.	PROPN
ijassa-1111	146	30	saaty	saaty	PROPN
ijassa-1111	146	31	(	(	PUNCT
ijassa-1111	146	32	see	see	VERB
ijassa-1111	146	33	[	[	X
ijassa-1111	146	34	6	6	NUM
ijassa-1111	146	35	,	,	PUNCT
ijassa-1111	146	36	p.	p.	NOUN
ijassa-1111	146	37	41–44	41–44	NUM
ijassa-1111	146	38	]	]	PUNCT
ijassa-1111	146	39	)	)	PUNCT
ijassa-1111	146	40	.	.	PUNCT
ijassa-1111	147	1	the	the	DET
ijassa-1111	147	2	problem	problem	NOUN
ijassa-1111	147	3	consists	consist	VERB
ijassa-1111	147	4	in	in	ADP
ijassa-1111	147	5	choosing	choose	VERB
ijassa-1111	147	6	one	one	NUM
ijassa-1111	147	7	house	house	NOUN
ijassa-1111	147	8	from	from	ADP
ijassa-1111	147	9	three	three	NUM
ijassa-1111	147	10	available	available	ADJ
ijassa-1111	147	11	alternatives	alternative	NOUN
ijassa-1111	147	12	{	{	PUNCT
ijassa-1111	147	13	a	a	DET
ijassa-1111	147	14	,	,	PUNCT
ijassa-1111	147	15	b	b	NOUN
ijassa-1111	147	16	,	,	PUNCT
ijassa-1111	147	17	c	c	NOUN
ijassa-1111	147	18	}	}	PUNCT
ijassa-1111	147	19	based	base	VERB
ijassa-1111	147	20	on	on	ADP
ijassa-1111	147	21	eight	eight	NUM
ijassa-1111	147	22	factors	factor	NOUN
ijassa-1111	147	23	that	that	PRON
ijassa-1111	147	24	serve	serve	VERB
ijassa-1111	147	25	as	as	ADP
ijassa-1111	147	26	criteria	criterion	NOUN
ijassa-1111	147	27	for	for	ADP
ijassa-1111	147	28	the	the	DET
ijassa-1111	147	29	multi	multi	ADJ
ijassa-1111	147	30	-	-	ADJ
ijassa-1111	147	31	criteria	criterion	NOUN
ijassa-1111	147	32	selection	selection	NOUN
ijassa-1111	147	33	problem	problem	NOUN
ijassa-1111	147	34	.	.	PUNCT
ijassa-1111	148	1	table	table	NOUN
ijassa-1111	148	2	5.1	5.1	NUM
ijassa-1111	148	3	shows	show	NOUN
ijassa-1111	148	4	expert	expert	NOUN
ijassa-1111	148	5	estimates	estimate	NOUN
ijassa-1111	148	6	of	of	ADP
ijassa-1111	148	7	pairwise	pairwise	NOUN
ijassa-1111	148	8	comparison	comparison	NOUN
ijassa-1111	148	9	of	of	ADP
ijassa-1111	148	10	the	the	DET
ijassa-1111	148	11	importance	importance	NOUN
ijassa-1111	148	12	of	of	ADP
ijassa-1111	148	13	criteria	criterion	NOUN
ijassa-1111	148	14	and	and	CCONJ
ijassa-1111	148	15	the	the	DET
ijassa-1111	148	16	priority	priority	NOUN
ijassa-1111	148	17	vector	vector	NOUN
ijassa-1111	148	18	calculated	calculate	VERB
ijassa-1111	148	19	from	from	ADP
ijassa-1111	148	20	the	the	DET
ijassa-1111	148	21	maximum	maximum	PROPN
ijassa-1111	148	22	eigenvalue	eigenvalue	NOUN
ijassa-1111	148	23	following	follow	VERB
ijassa-1111	148	24	the	the	DET
ijassa-1111	148	25	method	method	NOUN
ijassa-1111	148	26	of	of	ADP
ijassa-1111	148	27	hierarchy	hierarchy	NOUN
ijassa-1111	148	28	analysis	analysis	NOUN
ijassa-1111	148	29	by	by	ADP
ijassa-1111	148	30	t.	t.	PROPN
ijassa-1111	148	31	saaty	saaty	NOUN
ijassa-1111	148	32	(	(	PUNCT
ijassa-1111	148	33	𝜆	𝜆	NOUN
ijassa-1111	148	34	=	=	SYM
ijassa-1111	148	35	8,811	8,811	NUM
ijassa-1111	148	36	,	,	PUNCT
ijassa-1111	148	37	compatibility	compatibility	NOUN
ijassa-1111	148	38	index	index	NOUN
ijassa-1111	148	39	𝑆.	𝑆.	PROPN
ijassa-1111	148	40	𝐼.	𝐼.	PROPN
ijassa-1111	148	41	=	=	PUNCT
ijassa-1111	148	42	,	,	PUNCT
ijassa-1111	148	43	≈	≈	PROPN
ijassa-1111	148	44	1,101	1,101	NUM
ijassa-1111	148	45	)	)	PUNCT
ijassa-1111	148	46	.	.	PUNCT
ijassa-1111	149	1	the	the	DET
ijassa-1111	149	2	summed	sum	VERB
ijassa-1111	149	3	elements	element	NOUN
ijassa-1111	149	4	of	of	ADP
ijassa-1111	149	5	the	the	DET
ijassa-1111	149	6	judgment	judgment	NOUN
ijassa-1111	149	7	matrix	matrix	NOUN
ijassa-1111	149	8	and	and	CCONJ
ijassa-1111	149	9	the	the	DET
ijassa-1111	149	10	vector	vector	NOUN
ijassa-1111	149	11	of	of	ADP
ijassa-1111	149	12	weights	weight	NOUN
ijassa-1111	149	13	of	of	ADP
ijassa-1111	149	14	the	the	DET
ijassa-1111	149	15	importance	importance	NOUN
ijassa-1111	149	16	of	of	ADP
ijassa-1111	149	17	criteria	criterion	NOUN
ijassa-1111	149	18	found	find	VERB
ijassa-1111	149	19	from	from	ADP
ijassa-1111	149	20	these	these	DET
ijassa-1111	149	21	data	datum	NOUN
ijassa-1111	149	22	using	use	VERB
ijassa-1111	149	23	the	the	DET
ijassa-1111	149	24	approximation	approximation	NOUN
ijassa-1111	149	25	matrix	matrix	NOUN
ijassa-1111	149	26	method	method	NOUN
ijassa-1111	149	27	are	be	AUX
ijassa-1111	149	28	presented	present	VERB
ijassa-1111	149	29	in	in	ADP
ijassa-1111	149	30	table	table	NOUN
ijassa-1111	149	31	5.2	5.2	NUM
ijassa-1111	149	32	.	.	PUNCT
ijassa-1111	149	33	table	table	NOUN
ijassa-1111	149	34	5.1	5.1	NUM
ijassa-1111	149	35	.	.	PUNCT
ijassa-1111	150	1	initial	initial	ADJ
ijassa-1111	150	2	matrix	matrix	NOUN
ijassa-1111	150	3	𝑉	𝑉	PROPN
ijassa-1111	150	4	of	of	ADP
ijassa-1111	150	5	judgments	judgment	NOUN
ijassa-1111	150	6	and	and	CCONJ
ijassa-1111	150	7	priority	priority	NOUN
ijassa-1111	150	8	vector	vector	NOUN
ijassa-1111	150	9	according	accord	VERB
ijassa-1111	150	10	to	to	ADP
ijassa-1111	150	11	ahp	ahp	PROPN
ijassa-1111	150	12	[	[	X
ijassa-1111	150	13	6	6	NUM
ijassa-1111	150	14	,	,	PUNCT
ijassa-1111	150	15	p.	p.	NOUN
ijassa-1111	150	16	42	42	NUM
ijassa-1111	150	17	]	]	PUNCT
ijassa-1111	150	18	factor	factor	NOUN
ijassa-1111	150	19	(	(	PUNCT
ijassa-1111	150	20	criteria	criteria	PROPN
ijassa-1111	150	21	)	)	PUNCT
ijassa-1111	151	1	𝑓	𝑓	PRON
ijassa-1111	151	2	𝑓	𝑓	PRON
ijassa-1111	151	3	𝑓	𝑓	PRON
ijassa-1111	151	4	𝑓	𝑓	PRON
ijassa-1111	151	5	𝑓	𝑓	PRON
ijassa-1111	151	6	𝑓	𝑓	PRON
ijassa-1111	151	7	𝑓	𝑓	DET
ijassa-1111	151	8	𝑓	𝑓	DET
ijassa-1111	151	9	priority	priority	NOUN
ijassa-1111	151	10	vector	vector	NOUN
ijassa-1111	151	11	,	,	PUNCT
ijassa-1111	151	12	𝑤	𝑤	ADP
ijassa-1111	151	13	size	size	NOUN
ijassa-1111	151	14	,	,	PUNCT
ijassa-1111	151	15	𝑓	𝑓	DET
ijassa-1111	151	16	1	1	NUM
ijassa-1111	151	17	5	5	NUM
ijassa-1111	151	18	3	3	NUM
ijassa-1111	151	19	7	7	NUM
ijassa-1111	151	20	6	6	NUM
ijassa-1111	151	21	6	6	NUM
ijassa-1111	151	22	1/3	1/3	NUM
ijassa-1111	151	23	1/4	1/4	NUM
ijassa-1111	151	24	0,175	0,175	NUM
ijassa-1111	151	25	transport	transport	NOUN
ijassa-1111	151	26	,	,	PUNCT
ijassa-1111	151	27	𝑓	𝑓	PROPN
ijassa-1111	151	28	1/5	1/5	NUM
ijassa-1111	151	29	1	1	NUM
ijassa-1111	151	30	1/3	1/3	NUM
ijassa-1111	151	31	5	5	NUM
ijassa-1111	151	32	3	3	NUM
ijassa-1111	151	33	3	3	NUM
ijassa-1111	151	34	1/5	1/5	NUM
ijassa-1111	151	35	1/7	1/7	NUM
ijassa-1111	151	36	0,062	0,062	NUM
ijassa-1111	151	37	environment	environment	NOUN
ijassa-1111	151	38	,	,	PUNCT
ijassa-1111	151	39	𝑓	𝑓	PROPN
ijassa-1111	151	40	1/3	1/3	NUM
ijassa-1111	151	41	3	3	NUM
ijassa-1111	151	42	1	1	NUM
ijassa-1111	151	43	6	6	NUM
ijassa-1111	151	44	3	3	NUM
ijassa-1111	151	45	4	4	NUM
ijassa-1111	151	46	1/2	1/2	NUM
ijassa-1111	151	47	1/5	1/5	NUM
ijassa-1111	151	48	0,103	0,103	NUM
ijassa-1111	151	49	age	age	NOUN
ijassa-1111	151	50	,	,	PUNCT
ijassa-1111	151	51	𝑓	𝑓	PROPN
ijassa-1111	151	52	1/7	1/7	NUM
ijassa-1111	151	53	1/5	1/5	NUM
ijassa-1111	151	54	1/6	1/6	NUM
ijassa-1111	151	55	1	1	NUM
ijassa-1111	151	56	1/3	1/3	NUM
ijassa-1111	151	57	1/4	1/4	NUM
ijassa-1111	151	58	1/7	1/7	NUM
ijassa-1111	151	59	1/8	1/8	NUM
ijassa-1111	151	60	0,019	0,019	NUM
ijassa-1111	151	61	yard	yard	NOUN
ijassa-1111	151	62	,	,	PUNCT
ijassa-1111	151	63	𝑓	𝑓	PROPN
ijassa-1111	151	64	1/6	1/6	NUM
ijassa-1111	151	65	1/3	1/3	NUM
ijassa-1111	151	66	1/3	1/3	NUM
ijassa-1111	151	67	3	3	NUM
ijassa-1111	151	68	1	1	NUM
ijassa-1111	151	69	1/2	1/2	NUM
ijassa-1111	151	70	1/5	1/5	NUM
ijassa-1111	151	71	1/6	1/6	NUM
ijassa-1111	151	72	0,034	0,034	NUM
ijassa-1111	151	73	facilities	facility	NOUN
ijassa-1111	151	74	,	,	PUNCT
ijassa-1111	151	75	𝑓	𝑓	PROPN
ijassa-1111	151	76	1/6	1/6	NUM
ijassa-1111	151	77	1/3	1/3	NUM
ijassa-1111	151	78	1/4	1/4	NUM
ijassa-1111	151	79	4	4	NUM
ijassa-1111	151	80	2	2	NUM
ijassa-1111	151	81	1	1	NUM
ijassa-1111	151	82	1/5	1/5	NUM
ijassa-1111	151	83	1/6	1/6	NUM
ijassa-1111	151	84	0,041	0,041	NUM
ijassa-1111	151	85	state	state	NOUN
ijassa-1111	151	86	,	,	PUNCT
ijassa-1111	151	87	𝑓	𝑓	DET
ijassa-1111	151	88	3	3	NUM
ijassa-1111	151	89	5	5	NUM
ijassa-1111	151	90	2	2	NUM
ijassa-1111	151	91	7	7	NUM
ijassa-1111	151	92	5	5	NUM
ijassa-1111	151	93	5	5	NUM
ijassa-1111	151	94	1	1	NUM
ijassa-1111	151	95	1/2	1/2	NUM
ijassa-1111	151	96	0,221	0,221	NUM
ijassa-1111	151	97	finance	finance	NOUN
ijassa-1111	151	98	,	,	PUNCT
ijassa-1111	151	99	𝑓	𝑓	DET
ijassa-1111	151	100	4	4	NUM
ijassa-1111	151	101	7	7	NUM
ijassa-1111	151	102	5	5	NUM
ijassa-1111	151	103	8	8	NUM
ijassa-1111	151	104	6	6	NUM
ijassa-1111	151	105	6	6	NUM
ijassa-1111	151	106	2	2	NUM
ijassa-1111	151	107	1	1	NUM
ijassa-1111	151	108	0,348	0,348	NUM
ijassa-1111	151	109	table	table	NOUN
ijassa-1111	151	110	5.2	5.2	NUM
ijassa-1111	151	111	.	.	PUNCT
ijassa-1111	152	1	normalized	normalize	VERB
ijassa-1111	152	2	matrix	matrix	NOUN
ijassa-1111	152	3	𝑉	𝑉	NOUN
ijassa-1111	152	4	=	=	PUNCT
ijassa-1111	152	5	∑	∑	PROPN
ijassa-1111	152	6	of	of	ADP
ijassa-1111	152	7	judgments	judgment	NOUN
ijassa-1111	152	8	and	and	CCONJ
ijassa-1111	152	9	a	a	DET
ijassa-1111	152	10	vector	vector	NOUN
ijassa-1111	152	11	of	of	ADP
ijassa-1111	152	12	priorities	priority	NOUN
ijassa-1111	152	13	by	by	ADP
ijassa-1111	152	14	mam	mam	PROPN
ijassa-1111	152	15	factor	factor	NOUN
ijassa-1111	152	16	(	(	PUNCT
ijassa-1111	152	17	criteria	criteria	PROPN
ijassa-1111	152	18	)	)	PUNCT
ijassa-1111	152	19	𝑓	𝑓	PRON
ijassa-1111	152	20	𝑓	𝑓	PRON
ijassa-1111	152	21	𝑓	𝑓	PRON
ijassa-1111	152	22	𝑓	𝑓	PRON
ijassa-1111	152	23	𝑓	𝑓	PRON
ijassa-1111	152	24	𝑓	𝑓	PRON
ijassa-1111	152	25	𝑓	𝑓	DET
ijassa-1111	152	26	𝑓	𝑓	DET
ijassa-1111	152	27	priority	priority	NOUN
ijassa-1111	152	28	vector	vector	NOUN
ijassa-1111	152	29	,	,	PUNCT
ijassa-1111	152	30	𝑤	𝑤	ADP
ijassa-1111	152	31	size	size	NOUN
ijassa-1111	152	32	,	,	PUNCT
ijassa-1111	152	33	𝑓	𝑓	PRON
ijassa-1111	152	34	0,11	0,11	NOUN
ijassa-1111	152	35	0,23	0,23	NUM
ijassa-1111	152	36	0,25	0,25	NUM
ijassa-1111	152	37	0,17	0,17	NUM
ijassa-1111	152	38	0,23	0,23	NUM
ijassa-1111	152	39	0,23	0,23	NUM
ijassa-1111	152	40	0,07	0,07	NUM
ijassa-1111	153	1	0,10	0,10	NOUN
ijassa-1111	153	2	0,174	0,174	NUM
ijassa-1111	153	3	transport	transport	NOUN
ijassa-1111	153	4	,	,	PUNCT
ijassa-1111	153	5	𝑓	𝑓	DET
ijassa-1111	153	6	0,02	0,02	NUM
ijassa-1111	153	7	0,05	0,05	NUM
ijassa-1111	153	8	0,03	0,03	NUM
ijassa-1111	153	9	0,12	0,12	NUM
ijassa-1111	153	10	0,11	0,11	NOUN
ijassa-1111	154	1	0,12	0,12	X
ijassa-1111	155	1	0,04	0,04	NUM
ijassa-1111	155	2	0,06	0,06	PROPN
ijassa-1111	155	3	0,068	0,068	NUM
ijassa-1111	155	4	environment	environment	NOUN
ijassa-1111	155	5	,	,	PUNCT
ijassa-1111	155	6	𝑓	𝑓	PRON
ijassa-1111	155	7	0,04	0,04	NUM
ijassa-1111	155	8	0,14	0,14	ADP
ijassa-1111	155	9	0,08	0,08	NUM
ijassa-1111	155	10	0,15	0,15	NOUN
ijassa-1111	155	11	0,11	0,11	NOUN
ijassa-1111	156	1	0,16	0,16	NUM
ijassa-1111	156	2	0,11	0,11	NOUN
ijassa-1111	156	3	0,08	0,08	NUM
ijassa-1111	156	4	0,108	0,108	NUM
ijassa-1111	156	5	age	age	NOUN
ijassa-1111	156	6	,	,	PUNCT
ijassa-1111	156	7	𝑓	𝑓	DET
ijassa-1111	156	8	0,02	0,02	NUM
ijassa-1111	156	9	0,01	0,01	NUM
ijassa-1111	156	10	0,01	0,01	NUM
ijassa-1111	156	11	0,02	0,02	NUM
ijassa-1111	156	12	0,01	0,01	NUM
ijassa-1111	156	13	0,01	0,01	NUM
ijassa-1111	156	14	0,03	0,03	NUM
ijassa-1111	156	15	0,05	0,05	NUM
ijassa-1111	156	16	0,021	0,021	NUM
ijassa-1111	156	17	yard	yard	NOUN
ijassa-1111	156	18	,	,	PUNCT
ijassa-1111	156	19	𝑓	𝑓	PROPN
ijassa-1111	156	20	0,02	0,02	PROPN
ijassa-1111	156	21	0,02	0,02	NUM
ijassa-1111	156	22	0,03	0,03	NUM
ijassa-1111	156	23	0,07	0,07	PROPN
ijassa-1111	157	1	0,04	0,04	PROPN
ijassa-1111	157	2	0,02	0,02	NUM
ijassa-1111	157	3	0,04	0,04	NUM
ijassa-1111	157	4	0,07	0,07	PROPN
ijassa-1111	157	5	0,038	0,038	NUM
ijassa-1111	157	6	facilities	facility	NOUN
ijassa-1111	157	7	,	,	PUNCT
ijassa-1111	157	8	𝑓	𝑓	PROPN
ijassa-1111	157	9	0,02	0,02	PROPN
ijassa-1111	157	10	0,02	0,02	PROPN
ijassa-1111	157	11	0,02	0,02	PROPN
ijassa-1111	157	12	0,10	0,10	NUM
ijassa-1111	157	13	0,08	0,08	NUM
ijassa-1111	158	1	0,04	0,04	PROPN
ijassa-1111	158	2	0,04	0,04	PROPN
ijassa-1111	158	3	0,07	0,07	PROPN
ijassa-1111	159	1	0,047	0,047	NUM
ijassa-1111	159	2	state	state	NOUN
ijassa-1111	159	3	,	,	PUNCT
ijassa-1111	159	4	𝑓	𝑓	PRON
ijassa-1111	159	5	0,33	0,33	PROPN
ijassa-1111	159	6	0,23	0,23	NOUN
ijassa-1111	159	7	0,17	0,17	NOUN
ijassa-1111	159	8	0,17	0,17	NUM
ijassa-1111	159	9	0,19	0,19	NUM
ijassa-1111	159	10	0,19	0,19	NOUN
ijassa-1111	159	11	0,22	0,22	X
ijassa-1111	159	12	0,20	0,20	NUM
ijassa-1111	159	13	0,212	0,212	NUM
ijassa-1111	159	14	finance	finance	NOUN
ijassa-1111	159	15	,	,	PUNCT
ijassa-1111	159	16	𝑓	𝑓	PRON
ijassa-1111	159	17	0,44	0,44	NOUN
ijassa-1111	159	18	0,32	0,32	PUNCT
ijassa-1111	159	19	0,41	0,41	PUNCT
ijassa-1111	159	20	0,20	0,20	NOUN
ijassa-1111	159	21	0,23	0,23	PUNCT
ijassa-1111	159	22	0,23	0,23	NOUN
ijassa-1111	159	23	0,44	0,44	PUNCT
ijassa-1111	160	1	0,39	0,39	ADV
ijassa-1111	160	2	0,333	0,333	NUM
ijassa-1111	160	3	to	to	PART
ijassa-1111	160	4	evaluate	evaluate	VERB
ijassa-1111	160	5	the	the	DET
ijassa-1111	160	6	accuracy	accuracy	NOUN
ijassa-1111	160	7	,	,	PUNCT
ijassa-1111	160	8	we	we	PRON
ijassa-1111	160	9	restore	restore	VERB
ijassa-1111	160	10	multiplicative	multiplicative	ADJ
ijassa-1111	160	11	matrices	matrix	NOUN
ijassa-1111	160	12	of	of	ADP
ijassa-1111	160	13	pairwise	pairwise	NOUN
ijassa-1111	160	14	relations	relation	NOUN
ijassa-1111	160	15	by	by	ADP
ijassa-1111	160	16	priority	priority	NOUN
ijassa-1111	160	17	vectors	vector	NOUN
ijassa-1111	160	18	:	:	PUNCT
ijassa-1111	160	19	�	�	PROPN
ijassa-1111	160	20	⃗	⃗	NOUN
ijassa-1111	160	21	�	�	NOUN
ijassa-1111	160	22	=	=	SYM
ijassa-1111	160	23	(	(	PUNCT
ijassa-1111	160	24	0,175	0,175	NUM
ijassa-1111	160	25	;	;	PUNCT
ijassa-1111	160	26	0,062	0,062	NUM
ijassa-1111	160	27	;	;	PUNCT
ijassa-1111	160	28	0,103	0,103	NUM
ijassa-1111	160	29	;	;	PUNCT
ijassa-1111	160	30	0,019	0,019	NUM
ijassa-1111	160	31	;	;	PUNCT
ijassa-1111	160	32	0,034	0,034	NUM
ijassa-1111	160	33	;	;	PUNCT
ijassa-1111	160	34	0,041	0,041	NUM
ijassa-1111	160	35	;	;	PUNCT
ijassa-1111	160	36	0,221	0,221	NUM
ijassa-1111	160	37	;	;	PUNCT
ijassa-1111	160	38	0,348	0,348	NUM
ijassa-1111	160	39	)	)	PUNCT
ijassa-1111	160	40	,	,	PUNCT
ijassa-1111	160	41	(	(	PUNCT
ijassa-1111	160	42	5.12	5.12	NUM
ijassa-1111	160	43	)	)	PUNCT
ijassa-1111	160	44	�	�	PROPN
ijassa-1111	160	45	⃗	⃗	NOUN
ijassa-1111	160	46	�	�	NOUN
ijassa-1111	160	47	=	=	SYM
ijassa-1111	160	48	(	(	PUNCT
ijassa-1111	160	49	0,174	0,174	NUM
ijassa-1111	160	50	;	;	PUNCT
ijassa-1111	160	51	0,068	0,068	NUM
ijassa-1111	160	52	;	;	PUNCT
ijassa-1111	160	53	0,108	0,108	NUM
ijassa-1111	160	54	;	;	PUNCT
ijassa-1111	160	55	0,021	0,021	NUM
ijassa-1111	160	56	;	;	PUNCT
ijassa-1111	160	57	0,038	0,038	NUM
ijassa-1111	160	58	;	;	PUNCT
ijassa-1111	160	59	0,047	0,047	NUM
ijassa-1111	160	60	;	;	PUNCT
ijassa-1111	160	61	0,212	0,212	NUM
ijassa-1111	160	62	;	;	PUNCT
ijassa-1111	160	63	0,333	0,333	NUM
ijassa-1111	160	64	)	)	PUNCT
ijassa-1111	160	65	,	,	PUNCT
ijassa-1111	160	66	(	(	PUNCT
ijassa-1111	160	67	5.13	5.13	NUM
ijassa-1111	160	68	)	)	PUNCT
ijassa-1111	160	69	obtained	obtain	VERB
ijassa-1111	160	70	by	by	ADP
ijassa-1111	160	71	the	the	DET
ijassa-1111	160	72	method	method	NOUN
ijassa-1111	160	73	of	of	ADP
ijassa-1111	160	74	calculating	calculate	VERB
ijassa-1111	160	75	the	the	DET
ijassa-1111	160	76	eigenvector	eigenvector	NOUN
ijassa-1111	160	77	and	and	CCONJ
ijassa-1111	160	78	the	the	DET
ijassa-1111	160	79	method	method	NOUN
ijassa-1111	160	80	of	of	ADP
ijassa-1111	160	81	approximating	approximate	VERB
ijassa-1111	160	82	the	the	DET
ijassa-1111	160	83	matrix	matrix	NOUN
ijassa-1111	160	84	of	of	ADP
ijassa-1111	160	85	pairwise	pairwise	NOUN
ijassa-1111	160	86	comparisons	comparison	NOUN
ijassa-1111	160	87	using	use	VERB
ijassa-1111	160	88	the	the	DET
ijassa-1111	160	89	minimum	minimum	ADJ
ijassa-1111	160	90	distance	distance	NOUN
ijassa-1111	160	91	criterion	criterion	NOUN
ijassa-1111	160	92	,	,	PUNCT
ijassa-1111	160	93	and	and	CCONJ
ijassa-1111	160	94	compare	compare	VERB
ijassa-1111	160	95	the	the	DET
ijassa-1111	160	96	results	result	NOUN
ijassa-1111	160	97	.	.	PUNCT
ijassa-1111	161	1	tables	table	VERB
ijassa-1111	161	2	5.3	5.3	NUM
ijassa-1111	161	3	and	and	CCONJ
ijassa-1111	161	4	5.4	5.4	NUM
ijassa-1111	161	5	present	present	ADJ
ijassa-1111	161	6	multiplicative	multiplicative	ADJ
ijassa-1111	161	7	matrices	matrix	NOUN
ijassa-1111	161	8	�	�	NOUN
ijassa-1111	161	9	⃗	⃗	PROPN
ijassa-1111	161	10	�	�	PROPN
ijassa-1111	161	11	,	,	PUNCT
ijassa-1111	161	12	�	�	PROPN
ijassa-1111	161	13	⃗	⃗	NOUN
ijassa-1111	161	14	�	�	PROPN
ijassa-1111	161	15	,	,	PUNCT
ijassa-1111	161	16	with	with	ADP
ijassa-1111	161	17	priority	priority	NOUN
ijassa-1111	161	18	vectors	vector	NOUN
ijassa-1111	161	19	�	�	NOUN
ijassa-1111	161	20	⃗	⃗	PROPN
ijassa-1111	161	21	�	�	PROPN
ijassa-1111	161	22	(	(	PUNCT
ijassa-1111	161	23	5.12	5.12	NUM
ijassa-1111	161	24	)	)	PUNCT
ijassa-1111	161	25	and	and	CCONJ
ijassa-1111	161	26	�	�	PROPN
ijassa-1111	161	27	⃗	⃗	PROPN
ijassa-1111	161	28	�	�	PROPN
ijassa-1111	161	29	(	(	PUNCT
ijassa-1111	161	30	5.13	5.13	NUM
ijassa-1111	161	31	)	)	PUNCT
ijassa-1111	161	32	formed	form	VERB
ijassa-1111	161	33	from	from	ADP
ijassa-1111	161	34	normalized	normalize	VERB
ijassa-1111	161	35	weights	weight	NOUN
ijassa-1111	161	36	.	.	PUNCT
ijassa-1111	161	37	table	table	NOUN
ijassa-1111	161	38	5.3	5.3	NUM
ijassa-1111	161	39	.	.	PUNCT
ijassa-1111	162	1	multiplicative	multiplicative	ADJ
ijassa-1111	162	2	matrix	matrix	NOUN
ijassa-1111	162	3	w	w	NOUN
ijassa-1111	162	4	,	,	PUNCT
ijassa-1111	162	5	formed	form	VERB
ijassa-1111	162	6	from	from	ADP
ijassa-1111	162	7	normalized	normalize	VERB
ijassa-1111	162	8	weights	weight	NOUN
ijassa-1111	162	9	of	of	ADP
ijassa-1111	162	10	the	the	DET
ijassa-1111	162	11	priority	priority	NOUN
ijassa-1111	162	12	vector	vector	NOUN
ijassa-1111	162	13	𝑤	𝑤	ADP
ijassa-1111	162	14	factor	factor	NOUN
ijassa-1111	162	15	(	(	PUNCT
ijassa-1111	162	16	criteria	criterion	NOUN
ijassa-1111	162	17	)	)	PUNCT
ijassa-1111	162	18	𝑓	𝑓	PRON
ijassa-1111	162	19	𝑓	𝑓	PRON
ijassa-1111	162	20	𝑓	𝑓	PRON
ijassa-1111	162	21	𝑓	𝑓	PRON
ijassa-1111	162	22	𝑓	𝑓	PRON
ijassa-1111	162	23	𝑓	𝑓	PRON
ijassa-1111	162	24	𝑓	𝑓	DET
ijassa-1111	162	25	𝑓	𝑓	DET
ijassa-1111	162	26	size	size	NOUN
ijassa-1111	162	27	,	,	PUNCT
ijassa-1111	162	28	𝑓	𝑓	DET
ijassa-1111	162	29	1,00	1,00	NUM
ijassa-1111	162	30	2,82	2,82	NUM
ijassa-1111	163	1	1,70	1,70	NUM
ijassa-1111	163	2	9,21	9,21	NUM
ijassa-1111	163	3	5,15	5,15	NUM
ijassa-1111	163	4	4,27	4,27	NUM
ijassa-1111	163	5	0,79	0,79	NOUN
ijassa-1111	164	1	0,50	0,50	PROPN
ijassa-1111	164	2	transport	transport	NOUN
ijassa-1111	164	3	,	,	PUNCT
ijassa-1111	164	4	𝑓	𝑓	DET
ijassa-1111	164	5	0,35	0,35	X
ijassa-1111	164	6	1,00	1,00	NUM
ijassa-1111	164	7	0,60	0,60	NUM
ijassa-1111	164	8	3,26	3,26	NUM
ijassa-1111	165	1	1,2	1,2	NUM
ijassa-1111	165	2	1,51	1,51	NUM
ijassa-1111	165	3	0,28	0,28	NUM
ijassa-1111	165	4	0,18	0,18	PUNCT
ijassa-1111	166	1	environment	environment	NOUN
ijassa-1111	166	2	,	,	PUNCT
ijassa-1111	166	3	𝑓	𝑓	DET
ijassa-1111	166	4	0,59	0,59	ADJ
ijassa-1111	166	5	1,66	1,66	NUM
ijassa-1111	166	6	1,00	1,00	NUM
ijassa-1111	166	7	5,42	5,42	NUM
ijassa-1111	166	8	3,03	3,03	NUM
ijassa-1111	166	9	2,51	2,51	NUM
ijassa-1111	166	10	0,47	0,47	NUM
ijassa-1111	166	11	0,30	0,30	NUM
ijassa-1111	166	12	age	age	NOUN
ijassa-1111	166	13	,	,	PUNCT
ijassa-1111	166	14	𝑓	𝑓	DET
ijassa-1111	166	15	0,11	0,11	NUM
ijassa-1111	166	16	0,31	0,31	NOUN
ijassa-1111	166	17	0,18	0,18	PUNCT
ijassa-1111	167	1	1,00	1,00	NUM
ijassa-1111	167	2	0,56	0,56	PROPN
ijassa-1111	167	3	0,46	0,46	NOUN
ijassa-1111	167	4	0,09	0,09	PUNCT
ijassa-1111	168	1	0,05	0,05	NUM
ijassa-1111	168	2	yard	yard	NOUN
ijassa-1111	168	3	,	,	PUNCT
ijassa-1111	168	4	𝑓	𝑓	PRON
ijassa-1111	168	5	0,19	0,19	NOUN
ijassa-1111	168	6	0,55	0,55	PUNCT
ijassa-1111	169	1	0,33	0,33	PROPN
ijassa-1111	169	2	1,79	1,79	PROPN
ijassa-1111	169	3	1,00	1,00	NUM
ijassa-1111	169	4	0,83	0,83	NUM
ijassa-1111	170	1	0,15	0,15	NUM
ijassa-1111	170	2	0,10	0,10	NOUN
ijassa-1111	171	1	112	112	NUM
ijassa-1111	171	2	v.p	v.p	PROPN
ijassa-1111	171	3	.	.	PROPN
ijassa-1111	171	4	korneenko	korneenko	PROPN
ijassa-1111	171	5	copyright	copyright	NOUN
ijassa-1111	171	6	©	©	PROPN
ijassa-1111	171	7	2024	2024	NUM
ijassa-1111	171	8	assa	assa	PROPN
ijassa-1111	171	9	adv	adv	PROPN
ijassa-1111	171	10	.	.	PUNCT
ijassa-1111	172	1	in	in	ADP
ijassa-1111	172	2	systems	system	NOUN
ijassa-1111	172	3	science	science	NOUN
ijassa-1111	172	4	and	and	CCONJ
ijassa-1111	172	5	appl	appl	NOUN
ijassa-1111	172	6	.	.	PUNCT
ijassa-1111	173	1	(	(	PUNCT
ijassa-1111	173	2	2024	2024	NUM
ijassa-1111	173	3	)	)	PUNCT
ijassa-1111	173	4	facilities	facility	NOUN
ijassa-1111	173	5	,	,	PUNCT
ijassa-1111	173	6	𝑓	𝑓	DET
ijassa-1111	173	7	0,23	0,23	NOUN
ijassa-1111	173	8	0,66	0,66	NUM
ijassa-1111	173	9	0,40	0,40	NUM
ijassa-1111	174	1	2,16	2,16	NUM
ijassa-1111	174	2	1,21	1,21	NUM
ijassa-1111	175	1	1,00	1,00	PROPN
ijassa-1111	175	2	0,19	0,19	NUM
ijassa-1111	176	1	0,12	0,12	NUM
ijassa-1111	176	2	state	state	NOUN
ijassa-1111	176	3	,	,	PUNCT
ijassa-1111	176	4	𝑓	𝑓	PRON
ijassa-1111	176	5	1,26	1,26	NUM
ijassa-1111	176	6	3,56	3,56	PROPN
ijassa-1111	176	7	2,15	2,15	NUM
ijassa-1111	176	8	11,63	11,63	NUM
ijassa-1111	176	9	6,50	6,50	NUM
ijassa-1111	176	10	5,39	5,39	NOUN
ijassa-1111	176	11	1,00	1,00	NUM
ijassa-1111	176	12	0,64	0,64	NUM
ijassa-1111	176	13	finance	finance	NOUN
ijassa-1111	176	14	,	,	PUNCT
ijassa-1111	176	15	𝑓	𝑓	DET
ijassa-1111	176	16	1,99	1,99	PROPN
ijassa-1111	176	17	5,61	5,61	NUM
ijassa-1111	176	18	3,38	3,38	NUM
ijassa-1111	176	19	18,32	18,32	NUM
ijassa-1111	176	20	10,24	10,24	NUM
ijassa-1111	176	21	8,49	8,49	NUM
ijassa-1111	176	22	1,57	1,57	NUM
ijassa-1111	176	23	1,00	1,00	NUM
ijassa-1111	176	24	table	table	NOUN
ijassa-1111	176	25	5.4	5.4	NUM
ijassa-1111	176	26	.	.	PUNCT
ijassa-1111	176	27	multiplicative	multiplicative	ADJ
ijassa-1111	176	28	matrix	matrix	NOUN
ijassa-1111	176	29	𝑊	𝑊	NOUN
ijassa-1111	176	30	formed	form	VERB
ijassa-1111	176	31	from	from	ADP
ijassa-1111	176	32	normalized	normalize	VERB
ijassa-1111	176	33	weights	weight	NOUN
ijassa-1111	176	34	of	of	ADP
ijassa-1111	176	35	the	the	DET
ijassa-1111	176	36	priority	priority	NOUN
ijassa-1111	176	37	vector	vector	NOUN
ijassa-1111	176	38	𝑤	𝑤	ADP
ijassa-1111	176	39	factor	factor	NOUN
ijassa-1111	176	40	(	(	PUNCT
ijassa-1111	176	41	criteria	criterion	NOUN
ijassa-1111	176	42	)	)	PUNCT
ijassa-1111	176	43	𝑓	𝑓	PRON
ijassa-1111	176	44	𝑓	𝑓	PRON
ijassa-1111	176	45	𝑓	𝑓	PRON
ijassa-1111	176	46	𝑓	𝑓	PRON
ijassa-1111	176	47	𝑓	𝑓	PRON
ijassa-1111	176	48	𝑓	𝑓	PRON
ijassa-1111	176	49	𝑓	𝑓	DET
ijassa-1111	176	50	𝑓	𝑓	DET
ijassa-1111	176	51	size	size	NOUN
ijassa-1111	176	52	,	,	PUNCT
ijassa-1111	176	53	𝑓	𝑓	DET
ijassa-1111	176	54	1,00	1,00	NUM
ijassa-1111	176	55	2,54	2,54	NUM
ijassa-1111	176	56	1,62	1,62	NUM
ijassa-1111	176	57	8,37	8,37	NUM
ijassa-1111	177	1	4,63	4,63	NOUN
ijassa-1111	177	2	3,70	3,70	NUM
ijassa-1111	177	3	0,82	0,82	NOUN
ijassa-1111	177	4	0,52	0,52	NUM
ijassa-1111	178	1	transport	transport	NOUN
ijassa-1111	178	2	,	,	PUNCT
ijassa-1111	178	3	𝑓	𝑓	PRON
ijassa-1111	178	4	0,39	0,39	ADV
ijassa-1111	178	5	1,00	1,00	NUM
ijassa-1111	178	6	0,64	0,64	NUM
ijassa-1111	179	1	3,30	3,30	NUM
ijassa-1111	180	1	1,83	1,83	NUM
ijassa-1111	181	1	1,46	1,46	NUM
ijassa-1111	181	2	0,32	0,32	PUNCT
ijassa-1111	182	1	0,21	0,21	NUM
ijassa-1111	182	2	environment	environment	NOUN
ijassa-1111	182	3	,	,	PUNCT
ijassa-1111	182	4	𝑓	𝑓	PRON
ijassa-1111	182	5	0,62	0,62	NUM
ijassa-1111	182	6	1,57	1,57	NUM
ijassa-1111	182	7	1,00	1,00	NUM
ijassa-1111	182	8	5,17	5,17	NUM
ijassa-1111	182	9	2,86	2,86	NUM
ijassa-1111	182	10	2,29	2,29	NUM
ijassa-1111	182	11	0,51	0,51	PUNCT
ijassa-1111	182	12	0,32	0,32	PUNCT
ijassa-1111	183	1	age	age	NOUN
ijassa-1111	183	2	,	,	PUNCT
ijassa-1111	183	3	𝑓	𝑓	DET
ijassa-1111	183	4	0,12	0,12	NOUN
ijassa-1111	183	5	0,30	0,30	NUM
ijassa-1111	183	6	0,19	0,19	PUNCT
ijassa-1111	184	1	1,00	1,00	PUNCT
ijassa-1111	184	2	0,55	0,55	PRON
ijassa-1111	184	3	0,44	0,44	PUNCT
ijassa-1111	185	1	0,10	0,10	NOUN
ijassa-1111	185	2	0,06	0,06	PROPN
ijassa-1111	185	3	yard	yard	PROPN
ijassa-1111	185	4	,	,	PUNCT
ijassa-1111	185	5	𝑓	𝑓	PRON
ijassa-1111	185	6	0,22	0,22	NOUN
ijassa-1111	185	7	0,55	0,55	X
ijassa-1111	186	1	0,35	0,35	PUNCT
ijassa-1111	186	2	1,81	1,81	NUM
ijassa-1111	186	3	1,00	1,00	X
ijassa-1111	186	4	0,80	0,80	NUM
ijassa-1111	186	5	0,18	0,18	SYM
ijassa-1111	186	6	0,11	0,11	NOUN
ijassa-1111	187	1	facilities	facility	NOUN
ijassa-1111	187	2	,	,	PUNCT
ijassa-1111	187	3	𝑓	𝑓	DET
ijassa-1111	187	4	0,27	0,27	NUM
ijassa-1111	187	5	0,69	0,69	PUNCT
ijassa-1111	187	6	0,44	0,44	NUM
ijassa-1111	188	1	2,26	2,26	NUM
ijassa-1111	188	2	1,25	1,25	NUM
ijassa-1111	188	3	1,00	1,00	X
ijassa-1111	188	4	0,22	0,22	X
ijassa-1111	189	1	0,14	0,14	ADP
ijassa-1111	189	2	state	state	PROPN
ijassa-1111	189	3	,	,	PUNCT
ijassa-1111	189	4	𝑓	𝑓	PRON
ijassa-1111	189	5	1,22	1,22	NUM
ijassa-1111	189	6	3,10	3,10	NUM
ijassa-1111	189	7	1,98	1,98	NUM
ijassa-1111	189	8	10,21	10,21	NUM
ijassa-1111	189	9	5,65	5,65	NUM
ijassa-1111	189	10	4,52	4,52	NUM
ijassa-1111	189	11	1,00	1,00	NUM
ijassa-1111	189	12	0,64	0,64	NUM
ijassa-1111	189	13	finance	finance	NOUN
ijassa-1111	189	14	,	,	PUNCT
ijassa-1111	189	15	𝑓	𝑓	PRON
ijassa-1111	189	16	1,91	1,91	NUM
ijassa-1111	189	17	4,86	4,86	NUM
ijassa-1111	189	18	3,10	3,10	NUM
ijassa-1111	189	19	16,02	16,02	NUM
ijassa-1111	189	20	8,86	8,86	NUM
ijassa-1111	189	21	7,08	7,08	NUM
ijassa-1111	189	22	1,57	1,57	NUM
ijassa-1111	189	23	1,00	1,00	NUM
ijassa-1111	189	24	we	we	PRON
ijassa-1111	189	25	find	find	VERB
ijassa-1111	189	26	the	the	DET
ijassa-1111	189	27	values	value	NOUN
ijassa-1111	189	28	of	of	ADP
ijassa-1111	189	29	the	the	DET
ijassa-1111	189	30	norm	norm	NOUN
ijassa-1111	189	31	of	of	ADP
ijassa-1111	189	32	the	the	DET
ijassa-1111	189	33	difference	difference	NOUN
ijassa-1111	189	34	between	between	ADP
ijassa-1111	189	35	the	the	DET
ijassa-1111	189	36	original	original	ADJ
ijassa-1111	189	37	matrices	matrix	NOUN
ijassa-1111	189	38	and	and	CCONJ
ijassa-1111	189	39	the	the	DET
ijassa-1111	189	40	multiplicative	multiplicative	ADJ
ijassa-1111	189	41	matrices	matrix	NOUN
ijassa-1111	189	42	of	of	ADP
ijassa-1111	189	43	relations	relation	NOUN
ijassa-1111	189	44	formed	form	VERB
ijassa-1111	189	45	from	from	ADP
ijassa-1111	189	46	the	the	DET
ijassa-1111	189	47	values	value	NOUN
ijassa-1111	189	48	of	of	ADP
ijassa-1111	189	49	the	the	DET
ijassa-1111	189	50	priority	priority	NOUN
ijassa-1111	189	51	vector	vector	NOUN
ijassa-1111	189	52	(	(	PUNCT
ijassa-1111	189	53	the	the	DET
ijassa-1111	189	54	importance	importance	NOUN
ijassa-1111	189	55	of	of	ADP
ijassa-1111	189	56	objects	object	NOUN
ijassa-1111	189	57	):	):	PUNCT
ijassa-1111	189	58	𝑑	𝑑	PROPN
ijassa-1111	189	59	=	=	NOUN
ijassa-1111	189	60	‖𝑉	‖𝑉	NOUN
ijassa-1111	190	1	−	−	PROPN
ijassa-1111	190	2	w	w	PROPN
ijassa-1111	190	3	‖	‖	PROPN
ijassa-1111	190	4	=	=	SYM
ijassa-1111	190	5	√200,66	√200,66	PROPN
ijassa-1111	190	6	≈	≈	PROPN
ijassa-1111	190	7	14,2	14,2	NUM
ijassa-1111	190	8	;	;	PUNCT
ijassa-1111	190	9	𝑑	𝑑	PROPN
ijassa-1111	190	10	=	=	NOUN
ijassa-1111	190	11	‖𝑉	‖𝑉	NOUN
ijassa-1111	190	12	−	−	PROPN
ijassa-1111	190	13	𝑊	𝑊	PROPN
ijassa-1111	190	14	‖	‖	PROPN
ijassa-1111	190	15	=	=	SYM
ijassa-1111	190	16	√139,61	√139,61	PROPN
ijassa-1111	190	17	≈	≈	PROPN
ijassa-1111	190	18	11,8	11,8	PROPN
ijassa-1111	190	19	.	.	PUNCT
ijassa-1111	191	1	let	let	VERB
ijassa-1111	191	2	us	we	PRON
ijassa-1111	191	3	determine	determine	VERB
ijassa-1111	191	4	the	the	DET
ijassa-1111	191	5	accuracy	accuracy	NOUN
ijassa-1111	191	6	of	of	ADP
ijassa-1111	191	7	the	the	DET
ijassa-1111	191	8	solution	solution	NOUN
ijassa-1111	191	9	𝑑	𝑑	X
ijassa-1111	191	10	by	by	ADP
ijassa-1111	191	11	the	the	DET
ijassa-1111	191	12	method	method	NOUN
ijassa-1111	191	13	of	of	ADP
ijassa-1111	191	14	t.	t.	PROPN
ijassa-1111	191	15	saaty	saaty	NOUN
ijassa-1111	191	16	concerning	concern	VERB
ijassa-1111	191	17	the	the	DET
ijassa-1111	191	18	optimal	optimal	ADJ
ijassa-1111	191	19	𝑑	𝑑	PROPN
ijassa-1111	191	20	obtained	obtain	VERB
ijassa-1111	191	21	in	in	ADP
ijassa-1111	191	22	the	the	DET
ijassa-1111	191	23	framework	framework	NOUN
ijassa-1111	191	24	of	of	ADP
ijassa-1111	191	25	the	the	DET
ijassa-1111	191	26	optimization	optimization	NOUN
ijassa-1111	191	27	problem	problem	NOUN
ijassa-1111	191	28	by	by	ADP
ijassa-1111	191	29	the	the	DET
ijassa-1111	191	30	criterion	criterion	NOUN
ijassa-1111	191	31	(	(	PUNCT
ijassa-1111	191	32	4.11	4.11	NUM
ijassa-1111	191	33	)	)	PUNCT
ijassa-1111	191	34	.	.	PUNCT
ijassa-1111	192	1	using	use	VERB
ijassa-1111	192	2	the	the	DET
ijassa-1111	192	3	ε	ε	NOUN
ijassa-1111	192	4	-	-	PUNCT
ijassa-1111	192	5	approximation	approximation	NOUN
ijassa-1111	192	6	formula	formula	NOUN
ijassa-1111	192	7	,	,	PUNCT
ijassa-1111	192	8	we	we	PRON
ijassa-1111	192	9	find	find	VERB
ijassa-1111	192	10	that	that	SCONJ
ijassa-1111	192	11	:	:	PUNCT
ijassa-1111	192	12	𝜀	𝜀	PROPN
ijassa-1111	192	13	=	=	SYM
ijassa-1111	192	14	|𝑑	|𝑑	PROPN
ijassa-1111	192	15	−	−	NOUN
ijassa-1111	193	1	𝑑	𝑑	NOUN
ijassa-1111	193	2	|	|	ADV
ijassa-1111	193	3	𝑑	𝑑	PROPN
ijassa-1111	193	4	×	×	NOUN
ijassa-1111	193	5	100	100	NUM
ijassa-1111	193	6	%	%	NOUN
ijassa-1111	193	7	=	=	SYM
ijassa-1111	193	8	14,2	14,2	NUM
ijassa-1111	193	9	−	−	NUM
ijassa-1111	193	10	11,8	11,8	NUM
ijassa-1111	194	1	11,8	11,8	NUM
ijassa-1111	194	2	×	×	NOUN
ijassa-1111	194	3	100	100	NUM
ijassa-1111	194	4	%	%	NOUN
ijassa-1111	195	1	≈	≈	PROPN
ijassa-1111	195	2	20,3	20,3	NUM
ijassa-1111	195	3	%	%	NOUN
ijassa-1111	195	4	.	.	PUNCT
ijassa-1111	196	1	comparison	comparison	NOUN
ijassa-1111	196	2	of	of	ADP
ijassa-1111	196	3	methods	method	NOUN
ijassa-1111	196	4	for	for	ADP
ijassa-1111	196	5	the	the	DET
ijassa-1111	196	6	accuracy	accuracy	NOUN
ijassa-1111	196	7	of	of	ADP
ijassa-1111	196	8	obtaining	obtain	VERB
ijassa-1111	196	9	the	the	DET
ijassa-1111	196	10	weights	weight	NOUN
ijassa-1111	196	11	of	of	ADP
ijassa-1111	196	12	objects	object	NOUN
ijassa-1111	196	13	for	for	ADP
ijassa-1111	196	14	the	the	DET
ijassa-1111	196	15	original	original	ADJ
ijassa-1111	196	16	perturbed	perturb	VERB
ijassa-1111	196	17	matrix	matrix	NOUN
ijassa-1111	196	18	of	of	ADP
ijassa-1111	196	19	the	the	DET
ijassa-1111	196	20	8th	8th	ADJ
ijassa-1111	196	21	order	order	NOUN
ijassa-1111	196	22	is	be	AUX
ijassa-1111	196	23	shown	show	VERB
ijassa-1111	196	24	in	in	ADP
ijassa-1111	196	25	fig	fig	NOUN
ijassa-1111	196	26	.	.	PUNCT
ijassa-1111	197	1	5.1	5.1	NUM
ijassa-1111	197	2	.	.	PUNCT
ijassa-1111	197	3	fig	fig	PROPN
ijassa-1111	197	4	5.1	5.1	NUM
ijassa-1111	197	5	.	.	PUNCT
ijassa-1111	198	1	comparison	comparison	NOUN
ijassa-1111	198	2	of	of	ADP
ijassa-1111	198	3	methods	method	NOUN
ijassa-1111	198	4	based	base	VERB
ijassa-1111	198	5	on	on	ADP
ijassa-1111	198	6	the	the	DET
ijassa-1111	198	7	accuracy	accuracy	NOUN
ijassa-1111	198	8	of	of	ADP
ijassa-1111	198	9	obtaining	obtain	VERB
ijassa-1111	198	10	object	object	NOUN
ijassa-1111	198	11	weights	weight	NOUN
ijassa-1111	198	12	it	it	PRON
ijassa-1111	198	13	follows	follow	VERB
ijassa-1111	198	14	that	that	SCONJ
ijassa-1111	198	15	the	the	DET
ijassa-1111	198	16	error	error	NOUN
ijassa-1111	198	17	estimate	estimate	NOUN
ijassa-1111	198	18	is	be	AUX
ijassa-1111	198	19	20,3	20,3	NUM
ijassa-1111	198	20	%	%	NOUN
ijassa-1111	198	21	and	and	CCONJ
ijassa-1111	198	22	the	the	DET
ijassa-1111	198	23	ahp	ahp	NOUN
ijassa-1111	198	24	solution	solution	NOUN
ijassa-1111	198	25	that	that	PRON
ijassa-1111	198	26	differs	differ	VERB
ijassa-1111	198	27	from	from	ADP
ijassa-1111	198	28	the	the	DET
ijassa-1111	198	29	optimal	optimal	ADJ
ijassa-1111	198	30	one	one	NUM
ijassa-1111	198	31	by	by	ADP
ijassa-1111	198	32	this	this	DET
ijassa-1111	198	33	value	value	NOUN
ijassa-1111	198	34	can	can	AUX
ijassa-1111	198	35	not	not	PART
ijassa-1111	198	36	be	be	AUX
ijassa-1111	198	37	considered	consider	VERB
ijassa-1111	198	38	satisfactory	satisfactory	ADJ
ijassa-1111	198	39	.	.	PUNCT
ijassa-1111	199	1	thus	thus	ADV
ijassa-1111	199	2	,	,	PUNCT
ijassa-1111	199	3	t.	t.	PROPN
ijassa-1111	199	4	saaty	saaty	NOUN
ijassa-1111	199	5	's	's	PART
ijassa-1111	199	6	method	method	NOUN
ijassa-1111	199	7	of	of	ADP
ijassa-1111	199	8	finding	find	VERB
ijassa-1111	199	9	priorities	priority	NOUN
ijassa-1111	199	10	for	for	ADP
ijassa-1111	199	11	the	the	DET
ijassa-1111	199	12	importance	importance	NOUN
ijassa-1111	199	13	of	of	ADP
ijassa-1111	199	14	criteria	criterion	NOUN
ijassa-1111	199	15	and	and	CCONJ
ijassa-1111	199	16	objects	object	NOUN
ijassa-1111	199	17	based	base	VERB
ijassa-1111	199	18	on	on	ADP
ijassa-1111	199	19	the	the	DET
ijassa-1111	199	20	eigenvector	eigenvector	NOUN
ijassa-1111	199	21	of	of	ADP
ijassa-1111	199	22	the	the	DET
ijassa-1111	199	23	matrix	matrix	NOUN
ijassa-1111	199	24	of	of	ADP
ijassa-1111	199	25	pairwise	pairwise	NOUN
ijassa-1111	199	26	comparisons	comparison	NOUN
ijassa-1111	199	27	should	should	AUX
ijassa-1111	199	28	be	be	AUX
ijassa-1111	199	29	attributed	attribute	VERB
ijassa-1111	199	30	to	to	PART
ijassa-1111	199	31	approximate	approximate	ADJ
ijassa-1111	199	32	,	,	PUNCT
ijassa-1111	199	33	and	and	CCONJ
ijassa-1111	199	34	not	not	PART
ijassa-1111	199	35	to	to	PART
ijassa-1111	199	36	exact	exact	VERB
ijassa-1111	199	37	,	,	PUNCT
ijassa-1111	199	38	as	as	SCONJ
ijassa-1111	199	39	the	the	DET
ijassa-1111	199	40	author	author	NOUN
ijassa-1111	199	41	of	of	ADP
ijassa-1111	199	42	ahp	ahp	PROPN
ijassa-1111	199	43	declares	declare	VERB
ijassa-1111	199	44	.	.	PUNCT
ijassa-1111	200	1	7	7	X
ijassa-1111	200	2	.	.	X
ijassa-1111	200	3	conclusion	conclusion	NOUN
ijassa-1111	200	4	the	the	DET
ijassa-1111	200	5	paper	paper	NOUN
ijassa-1111	200	6	explores	explore	VERB
ijassa-1111	200	7	the	the	DET
ijassa-1111	200	8	problem	problem	NOUN
ijassa-1111	200	9	of	of	ADP
ijassa-1111	200	10	forming	form	VERB
ijassa-1111	200	11	quantitative	quantitative	ADJ
ijassa-1111	200	12	weights	weight	NOUN
ijassa-1111	200	13	of	of	ADP
ijassa-1111	200	14	objects	object	NOUN
ijassa-1111	200	15	based	base	VERB
ijassa-1111	200	16	on	on	ADP
ijassa-1111	200	17	the	the	DET
ijassa-1111	200	18	matrix	matrix	NOUN
ijassa-1111	200	19	of	of	ADP
ijassa-1111	200	20	pairwise	pairwise	NOUN
ijassa-1111	200	21	comparisons	comparison	NOUN
ijassa-1111	200	22	in	in	ADP
ijassa-1111	200	23	the	the	DET
ijassa-1111	200	24	relationship	relationship	NOUN
ijassa-1111	200	25	scale	scale	NOUN
ijassa-1111	200	26	.	.	PUNCT
ijassa-1111	201	1	since	since	SCONJ
ijassa-1111	201	2	in	in	ADP
ijassa-1111	201	3	the	the	DET
ijassa-1111	201	4	hierarchy	hierarchy	NOUN
ijassa-1111	201	5	analysis	analysis	NOUN
ijassa-1111	201	6	process	process	NOUN
ijassa-1111	201	7	of	of	ADP
ijassa-1111	201	8	t.	t.	PROPN
ijassa-1111	201	9	saaty	saaty	PROPN
ijassa-1111	201	10	,	,	PUNCT
ijassa-1111	201	11	the	the	DET
ijassa-1111	201	12	method	method	NOUN
ijassa-1111	201	13	of	of	ADP
ijassa-1111	201	14	determining	determine	VERB
ijassa-1111	201	15	the	the	DET
ijassa-1111	201	16	weight	weight	NOUN
ijassa-1111	201	17	vector	vector	NOUN
ijassa-1111	201	18	is	be	AUX
ijassa-1111	201	19	carried	carry	VERB
ijassa-1111	201	20	out	out	ADP
ijassa-1111	201	21	using	use	VERB
ijassa-1111	201	22	polynomials	polynomial	NOUN
ijassa-1111	201	23	,	,	PUNCT
ijassa-1111	201	24	the	the	DET
ijassa-1111	201	25	problem	problem	NOUN
ijassa-1111	201	26	of	of	ADP
ijassa-1111	201	27	finding	find	VERB
ijassa-1111	201	28	the	the	DET
ijassa-1111	201	29	roots	root	NOUN
ijassa-1111	201	30	of	of	ADP
ijassa-1111	201	31	polynomials	polynomial	NOUN
ijassa-1111	201	32	of	of	ADP
ijassa-1111	201	33	degree	degree	NOUN
ijassa-1111	201	34	𝑛	𝑛	DET
ijassa-1111	201	35	≥	≥	NUM
ijassa-1111	201	36	5	5	NUM
ijassa-1111	201	37	is	be	AUX
ijassa-1111	201	38	unsolvable	unsolvable	ADJ
ijassa-1111	201	39	in	in	ADP
ijassa-1111	201	40	radicals	radical	NOUN
ijassa-1111	201	41	.	.	PUNCT
ijassa-1111	202	1	therefore	therefore	ADV
ijassa-1111	202	2	,	,	PUNCT
ijassa-1111	202	3	in	in	ADP
ijassa-1111	202	4	t.	t.	PROPN
ijassa-1111	202	5	saaty	saaty	NOUN
ijassa-1111	202	6	's	's	PART
ijassa-1111	202	7	method	method	NOUN
ijassa-1111	202	8	,	,	PUNCT
ijassa-1111	202	9	for	for	ADP
ijassa-1111	202	10	the	the	DET
ijassa-1111	202	11	number	number	NOUN
ijassa-1111	202	12	of	of	ADP
ijassa-1111	202	13	objects	object	NOUN
ijassa-1111	202	14	at	at	ADP
ijassa-1111	202	15	least	least	ADJ
ijassa-1111	202	16	five	five	NUM
ijassa-1111	202	17	,	,	PUNCT
ijassa-1111	202	18	the	the	DET
ijassa-1111	202	19	procedure	procedure	NOUN
ijassa-1111	202	20	for	for	ADP
ijassa-1111	202	21	finding	find	VERB
ijassa-1111	202	22	the	the	DET
ijassa-1111	202	23	eigenvalues	eigenvalue	NOUN
ijassa-1111	202	24	of	of	ADP
ijassa-1111	202	25	the	the	DET
ijassa-1111	202	26	matrix	matrix	NOUN
ijassa-1111	202	27	of	of	ADP
ijassa-1111	202	28	degrees	degree	NOUN
ijassa-1111	202	29	of	of	ADP
ijassa-1111	202	30	the	the	DET
ijassa-1111	202	31	superiority	superiority	NOUN
ijassa-1111	202	32	of	of	ADP
ijassa-1111	202	33	the	the	DET
ijassa-1111	202	34	importance	importance	NOUN
ijassa-1111	202	35	of	of	ADP
ijassa-1111	202	36	criteria	criterion	NOUN
ijassa-1111	202	37	11,8	11,8	NUM
ijassa-1111	202	38	14,2	14,2	NUM
ijassa-1111	202	39	10,0	10,0	NUM
ijassa-1111	202	40	11,0	11,0	NUM
ijassa-1111	202	41	12,0	12,0	NUM
ijassa-1111	203	1	13,0	13,0	NUM
ijassa-1111	203	2	14,0	14,0	NUM
ijassa-1111	203	3	15,0	15,0	NUM
ijassa-1111	203	4	the	the	DET
ijassa-1111	203	5	approximation	approximation	NOUN
ijassa-1111	203	6	matrix	matrix	NOUN
ijassa-1111	203	7	method	method	VERB
ijassa-1111	203	8	the	the	DET
ijassa-1111	203	9	analytical	analytical	ADJ
ijassa-1111	203	10	hierarchy	hierarchy	NOUN
ijassa-1111	203	11	process	process	NOUN
ijassa-1111	203	12	the	the	DET
ijassa-1111	203	13	distance	distance	NOUN
ijassa-1111	203	14	of	of	ADP
ijassa-1111	203	15	multiplicative	multiplicative	ADJ
ijassa-1111	203	16	matrices	matrix	NOUN
ijassa-1111	203	17	to	to	ADP
ijassa-1111	203	18	the	the	DET
ijassa-1111	203	19	original	original	ADJ
ijassa-1111	203	20	matrix	matrix	NOUN
ijassa-1111	203	21	of	of	ADP
ijassa-1111	203	22	judgments	judgment	NOUN
ijassa-1111	203	23	the	the	DET
ijassa-1111	203	24	approximation	approximation	NOUN
ijassa-1111	203	25	matrix	matrix	NOUN
ijassa-1111	203	26	method	method	NOUN
ijassa-1111	203	27	and	and	CCONJ
ijassa-1111	203	28	its	its	PRON
ijassa-1111	203	29	comparison	comparison	NOUN
ijassa-1111	203	30	…	…	PUNCT
ijassa-1111	203	31	113	113	NUM
ijassa-1111	203	32	copyright	copyright	NOUN
ijassa-1111	203	33	©	©	PROPN
ijassa-1111	203	34	2024	2024	NUM
ijassa-1111	203	35	assa	assa	PROPN
ijassa-1111	203	36	adv	adv	PROPN
ijassa-1111	203	37	.	.	PUNCT
ijassa-1111	204	1	in	in	ADP
ijassa-1111	204	2	systems	system	NOUN
ijassa-1111	204	3	science	science	NOUN
ijassa-1111	204	4	and	and	CCONJ
ijassa-1111	204	5	appl	appl	NOUN
ijassa-1111	204	6	.	.	PUNCT
ijassa-1111	205	1	(	(	PUNCT
ijassa-1111	205	2	2024	2024	NUM
ijassa-1111	205	3	)	)	PUNCT
ijassa-1111	205	4	or	or	CCONJ
ijassa-1111	205	5	preferences	preference	NOUN
ijassa-1111	205	6	of	of	ADP
ijassa-1111	205	7	alternatives	alternative	NOUN
ijassa-1111	205	8	is	be	AUX
ijassa-1111	205	9	carried	carry	VERB
ijassa-1111	205	10	out	out	ADP
ijassa-1111	205	11	using	use	VERB
ijassa-1111	205	12	numerical	numerical	ADJ
ijassa-1111	205	13	methods	method	NOUN
ijassa-1111	205	14	for	for	ADP
ijassa-1111	205	15	finding	find	VERB
ijassa-1111	205	16	the	the	DET
ijassa-1111	205	17	roots	root	NOUN
ijassa-1111	205	18	of	of	ADP
ijassa-1111	205	19	a	a	DET
ijassa-1111	205	20	polynomial	polynomial	NOUN
ijassa-1111	205	21	implemented	implement	VERB
ijassa-1111	205	22	in	in	ADP
ijassa-1111	205	23	the	the	DET
ijassa-1111	205	24	package	package	NOUN
ijassa-1111	205	25	expert	expert	NOUN
ijassa-1111	205	26	choice	choice	NOUN
ijassa-1111	206	1	[	[	X
ijassa-1111	206	2	17	17	NUM
ijassa-1111	206	3	]	]	PUNCT
ijassa-1111	206	4	.	.	PUNCT
ijassa-1111	207	1	on	on	ADP
ijassa-1111	207	2	the	the	DET
ijassa-1111	207	3	other	other	ADJ
ijassa-1111	207	4	hand	hand	NOUN
ijassa-1111	207	5	,	,	PUNCT
ijassa-1111	207	6	and	and	CCONJ
ijassa-1111	207	7	because	because	SCONJ
ijassa-1111	207	8	of	of	ADP
ijassa-1111	207	9	the	the	DET
ijassa-1111	207	10	inverse	inverse	NOUN
ijassa-1111	207	11	symmetry	symmetry	NOUN
ijassa-1111	207	12	of	of	ADP
ijassa-1111	207	13	the	the	DET
ijassa-1111	207	14	elements	element	NOUN
ijassa-1111	207	15	of	of	ADP
ijassa-1111	207	16	the	the	DET
ijassa-1111	207	17	matrix	matrix	NOUN
ijassa-1111	207	18	of	of	ADP
ijassa-1111	207	19	judgments	judgment	NOUN
ijassa-1111	207	20	𝑉	𝑉	PROPN
ijassa-1111	207	21	=	=	PUNCT
ijassa-1111	207	22	[	[	X
ijassa-1111	207	23	𝑣	𝑣	X
ijassa-1111	207	24	]	]	PUNCT
ijassa-1111	207	25	,	,	PUNCT
ijassa-1111	207	26	𝑖	𝑖	PROPN
ijassa-1111	207	27	,	,	PUNCT
ijassa-1111	207	28	𝑗	𝑗	NOUN
ijassa-1111	207	29	=	=	SYM
ijassa-1111	207	30	1	1	NUM
ijassa-1111	207	31	,	,	PUNCT
ijassa-1111	207	32	𝑛	𝑛	PROPN
ijassa-1111	207	33	,	,	PUNCT
ijassa-1111	207	34	obtained	obtain	VERB
ijassa-1111	207	35	by	by	ADP
ijassa-1111	207	36	sequential	sequential	ADJ
ijassa-1111	207	37	comparison	comparison	NOUN
ijassa-1111	207	38	of	of	ADP
ijassa-1111	207	39	all	all	DET
ijassa-1111	207	40	pairs	pair	NOUN
ijassa-1111	207	41	of	of	ADP
ijassa-1111	207	42	objects	object	NOUN
ijassa-1111	207	43	,	,	PUNCT
ijassa-1111	207	44	the	the	DET
ijassa-1111	207	45	expert	expert	NOUN
ijassa-1111	207	46	has	have	VERB
ijassa-1111	207	47	to	to	PART
ijassa-1111	207	48	answer	answer	VERB
ijassa-1111	207	49	(	(	PUNCT
ijassa-1111	207	50	)	)	PUNCT
ijassa-1111	207	51	questions	question	NOUN
ijassa-1111	207	52	about	about	ADP
ijassa-1111	207	53	the	the	DET
ijassa-1111	207	54	values	value	NOUN
ijassa-1111	207	55	𝑣	𝑣	X
ijassa-1111	207	56	.	.	PUNCT
ijassa-1111	208	1	in	in	ADP
ijassa-1111	208	2	this	this	DET
ijassa-1111	208	3	regard	regard	NOUN
ijassa-1111	208	4	,	,	PUNCT
ijassa-1111	208	5	the	the	DET
ijassa-1111	208	6	t.	t.	PROPN
ijassa-1111	208	7	saaty	saaty	NOUN
ijassa-1111	208	8	's	's	PART
ijassa-1111	208	9	method	method	NOUN
ijassa-1111	208	10	is	be	AUX
ijassa-1111	208	11	justified	justify	VERB
ijassa-1111	208	12	only	only	ADV
ijassa-1111	208	13	for	for	ADP
ijassa-1111	208	14	a	a	DET
ijassa-1111	208	15	small	small	ADJ
ijassa-1111	208	16	number	number	NOUN
ijassa-1111	208	17	of	of	ADP
ijassa-1111	208	18	criteria	criterion	NOUN
ijassa-1111	208	19	and	and	CCONJ
ijassa-1111	208	20	objects	object	NOUN
ijassa-1111	208	21	.	.	PUNCT
ijassa-1111	209	1	in	in	ADP
ijassa-1111	209	2	this	this	DET
ijassa-1111	209	3	article	article	NOUN
ijassa-1111	209	4	,	,	PUNCT
ijassa-1111	209	5	using	use	VERB
ijassa-1111	209	6	a	a	DET
ijassa-1111	209	7	concrete	concrete	ADJ
ijassa-1111	209	8	example	example	NOUN
ijassa-1111	209	9	,	,	PUNCT
ijassa-1111	209	10	it	it	PRON
ijassa-1111	209	11	is	be	AUX
ijassa-1111	209	12	shown	show	VERB
ijassa-1111	209	13	that	that	SCONJ
ijassa-1111	209	14	the	the	DET
ijassa-1111	209	15	analytical	analytical	ADJ
ijassa-1111	209	16	hierarchy	hierarchy	NOUN
ijassa-1111	209	17	method	method	NOUN
ijassa-1111	209	18	is	be	AUX
ijassa-1111	209	19	approximate	approximate	ADJ
ijassa-1111	209	20	and	and	CCONJ
ijassa-1111	209	21	at	at	ADP
ijassa-1111	209	22	the	the	DET
ijassa-1111	209	23	same	same	ADJ
ijassa-1111	209	24	time	time	NOUN
ijassa-1111	209	25	,	,	PUNCT
ijassa-1111	209	26	its	its	PRON
ijassa-1111	209	27	error	error	NOUN
ijassa-1111	209	28	is	be	AUX
ijassa-1111	209	29	estimated	estimate	VERB
ijassa-1111	209	30	relative	relative	ADJ
ijassa-1111	209	31	to	to	ADP
ijassa-1111	209	32	the	the	DET
ijassa-1111	209	33	optimal	optimal	ADJ
ijassa-1111	209	34	solution	solution	NOUN
ijassa-1111	209	35	obtained	obtain	VERB
ijassa-1111	209	36	by	by	ADP
ijassa-1111	209	37	the	the	DET
ijassa-1111	209	38	method	method	NOUN
ijassa-1111	209	39	of	of	ADP
ijassa-1111	209	40	the	the	DET
ijassa-1111	209	41	approximation	approximation	NOUN
ijassa-1111	209	42	matrix	matrix	NOUN
ijassa-1111	209	43	for	for	ADP
ijassa-1111	209	44	the	the	DET
ijassa-1111	209	45	formation	formation	NOUN
ijassa-1111	209	46	of	of	ADP
ijassa-1111	209	47	object	object	NOUN
ijassa-1111	209	48	weights	weight	NOUN
ijassa-1111	209	49	in	in	ADP
ijassa-1111	209	50	multi	multi	ADJ
ijassa-1111	209	51	-	-	ADJ
ijassa-1111	209	52	criteria	criterion	NOUN
ijassa-1111	209	53	problems	problem	NOUN
ijassa-1111	209	54	.	.	PUNCT
ijassa-1111	210	1	since	since	SCONJ
ijassa-1111	210	2	the	the	DET
ijassa-1111	210	3	presented	present	VERB
ijassa-1111	210	4	method	method	NOUN
ijassa-1111	210	5	is	be	AUX
ijassa-1111	210	6	mathematically	mathematically	ADV
ijassa-1111	210	7	justified	justify	VERB
ijassa-1111	210	8	,	,	PUNCT
ijassa-1111	210	9	and	and	CCONJ
ijassa-1111	210	10	also	also	ADV
ijassa-1111	210	11	because	because	SCONJ
ijassa-1111	210	12	of	of	ADP
ijassa-1111	210	13	the	the	DET
ijassa-1111	210	14	computational	computational	ADJ
ijassa-1111	210	15	simplicity	simplicity	NOUN
ijassa-1111	210	16	of	of	ADP
ijassa-1111	210	17	forming	form	VERB
ijassa-1111	210	18	object	object	NOUN
ijassa-1111	210	19	weights	weight	NOUN
ijassa-1111	210	20	,	,	PUNCT
ijassa-1111	210	21	it	it	PRON
ijassa-1111	210	22	can	can	AUX
ijassa-1111	210	23	be	be	AUX
ijassa-1111	210	24	recommended	recommend	VERB
ijassa-1111	210	25	instead	instead	ADV
ijassa-1111	210	26	of	of	ADP
ijassa-1111	210	27	the	the	DET
ijassa-1111	210	28	method	method	NOUN
ijassa-1111	210	29	t.	t.	NOUN
ijassa-1111	210	30	saaty	saaty	NOUN
ijassa-1111	210	31	in	in	ADP
ijassa-1111	210	32	solving	solve	VERB
ijassa-1111	210	33	applied	apply	VERB
ijassa-1111	210	34	problems	problem	NOUN
ijassa-1111	210	35	.	.	PUNCT
ijassa-1111	211	1	references	reference	NOUN
ijassa-1111	211	2	1	1	NUM
ijassa-1111	211	3	.	.	PUNCT
ijassa-1111	211	4	figueira	figueira	PROPN
ijassa-1111	211	5	,	,	PUNCT
ijassa-1111	211	6	j.	j.	PROPN
ijassa-1111	211	7	,	,	PUNCT
ijassa-1111	211	8	greco	greco	PROPN
ijassa-1111	211	9	,	,	PUNCT
ijassa-1111	211	10	s.	s.	PROPN
ijassa-1111	211	11	,	,	PUNCT
ijassa-1111	211	12	&	&	CCONJ
ijassa-1111	211	13	ehrgott	ehrgott	PROPN
ijassa-1111	211	14	,	,	PUNCT
ijassa-1111	211	15	m.	m.	NOUN
ijassa-1111	211	16	(	(	PUNCT
ijassa-1111	211	17	2005	2005	NUM
ijassa-1111	211	18	)	)	PUNCT
ijassa-1111	211	19	.	.	PUNCT
ijassa-1111	212	1	multiple	multiple	ADJ
ijassa-1111	212	2	criteria	criterion	NOUN
ijassa-1111	212	3	decision	decision	NOUN
ijassa-1111	212	4	analysis	analysis	NOUN
ijassa-1111	212	5	:	:	PUNCT
ijassa-1111	212	6	state	state	NOUN
ijassa-1111	212	7	of	of	ADP
ijassa-1111	212	8	the	the	DET
ijassa-1111	212	9	art	art	NOUN
ijassa-1111	212	10	surveys	survey	NOUN
ijassa-1111	212	11	multiple	multiple	ADJ
ijassa-1111	212	12	criteria	criterion	NOUN
ijassa-1111	212	13	decision	decision	NOUN
ijassa-1111	212	14	analysis	analysis	NOUN
ijassa-1111	212	15	:	:	PUNCT
ijassa-1111	212	16	state	state	NOUN
ijassa-1111	212	17	of	of	ADP
ijassa-1111	212	18	the	the	DET
ijassa-1111	212	19	art	art	NOUN
ijassa-1111	212	20	surveys	survey	NOUN
ijassa-1111	212	21	.	.	PUNCT
ijassa-1111	213	1	berlin	berlin	PROPN
ijassa-1111	213	2	,	,	PUNCT
ijassa-1111	213	3	germany	germany	PROPN
ijassa-1111	213	4	:	:	PUNCT
ijassa-1111	213	5	springer	springer	NOUN
ijassa-1111	213	6	.	.	PUNCT
ijassa-1111	214	1	2	2	X
ijassa-1111	214	2	.	.	X
ijassa-1111	214	3	noghin	noghin	PROPN
ijassa-1111	214	4	,	,	PUNCT
ijassa-1111	214	5	v.	v.	PROPN
ijassa-1111	214	6	d.	d.	PROPN
ijassa-1111	214	7	(	(	PUNCT
ijassa-1111	214	8	2018	2018	NUM
ijassa-1111	214	9	)	)	PUNCT
ijassa-1111	214	10	.	.	PUNCT
ijassa-1111	215	1	reduction	reduction	NOUN
ijassa-1111	215	2	of	of	ADP
ijassa-1111	215	3	the	the	DET
ijassa-1111	215	4	pareto	pareto	NOUN
ijassa-1111	215	5	set	set	NOUN
ijassa-1111	215	6	:	:	PUNCT
ijassa-1111	215	7	an	an	DET
ijassa-1111	215	8	axiomatic	axiomatic	ADJ
ijassa-1111	215	9	approach	approach	NOUN
ijassa-1111	215	10	.	.	PUNCT
ijassa-1111	216	1	berlin	berlin	PROPN
ijassa-1111	216	2	,	,	PUNCT
ijassa-1111	216	3	germany	germany	PROPN
ijassa-1111	216	4	:	:	PUNCT
ijassa-1111	216	5	springer	springer	NOUN
ijassa-1111	216	6	.	.	PUNCT
ijassa-1111	217	1	3	3	X
ijassa-1111	217	2	.	.	X
ijassa-1111	217	3	korneenko	korneenko	NOUN
ijassa-1111	217	4	,	,	PUNCT
ijassa-1111	217	5	v.	v.	ADP
ijassa-1111	218	1	p.	p.	NOUN
ijassa-1111	218	2	(	(	PUNCT
ijassa-1111	218	3	2019	2019	NUM
ijassa-1111	218	4	)	)	PUNCT
ijassa-1111	218	5	.	.	PUNCT
ijassa-1111	219	1	optimizatsionniy	optimizatsionniy	PROPN
ijassa-1111	219	2	metod	metod	PROPN
ijassa-1111	219	3	vybora	vybora	PROPN
ijassa-1111	219	4	rezuliruyushego	rezuliruyushego	PROPN
ijassa-1111	219	5	ranzhirovaniya	ranzhirovaniya	PROPN
ijassa-1111	219	6	obiektov	obiektov	PROPN
ijassa-1111	219	7	,	,	PUNCT
ijassa-1111	219	8	predstablennyh	predstablennyh	PROPN
ijassa-1111	219	9	v	v	NUM
ijassa-1111	219	10	rangovoy	rangovoy	NOUN
ijassa-1111	219	11	shkale	shkale	PROPN
ijassa-1111	219	12	izmereniya	izmereniya	NOUN
ijassa-1111	220	1	[	[	X
ijassa-1111	220	2	optimization	optimization	NOUN
ijassa-1111	220	3	method	method	NOUN
ijassa-1111	220	4	for	for	ADP
ijassa-1111	220	5	selecting	select	VERB
ijassa-1111	220	6	the	the	DET
ijassa-1111	220	7	resulting	result	VERB
ijassa-1111	220	8	ranking	ranking	NOUN
ijassa-1111	220	9	of	of	ADP
ijassa-1111	220	10	objects	object	NOUN
ijassa-1111	220	11	represented	represent	VERB
ijassa-1111	220	12	in	in	ADP
ijassa-1111	220	13	the	the	DET
ijassa-1111	220	14	rank	rank	NOUN
ijassa-1111	220	15	scale	scale	NOUN
ijassa-1111	220	16	of	of	ADP
ijassa-1111	220	17	measurement	measurement	NOUN
ijassa-1111	220	18	]	]	X
ijassa-1111	220	19	,	,	PUNCT
ijassa-1111	220	20	large	large	ADJ
ijassa-1111	220	21	-	-	PUNCT
ijassa-1111	220	22	scale	scale	NOUN
ijassa-1111	220	23	systems	system	NOUN
ijassa-1111	220	24	control	control	NOUN
ijassa-1111	220	25	,	,	PUNCT
ijassa-1111	220	26	82	82	NUM
ijassa-1111	220	27	,	,	PUNCT
ijassa-1111	220	28	44–60	44–60	NOUN
ijassa-1111	220	29	,	,	PUNCT
ijassa-1111	220	30	[	[	X
ijassa-1111	220	31	in	in	ADP
ijassa-1111	220	32	russian	russian	PROPN
ijassa-1111	220	33	]	]	X
ijassa-1111	220	34	,	,	PUNCT
ijassa-1111	220	35	doi	doi	NOUN
ijassa-1111	220	36	:	:	PUNCT
ijassa-1111	220	37	10.25728	10.25728	NUM
ijassa-1111	220	38	/	/	SYM
ijassa-1111	220	39	ubs.2019.82.3	ubs.2019.82.3	NOUN
ijassa-1111	220	40	4	4	NUM
ijassa-1111	220	41	.	.	X
ijassa-1111	220	42	sigford	sigford	NOUN
ijassa-1111	220	43	,	,	PUNCT
ijassa-1111	220	44	s.	s.	PROPN
ijassa-1111	220	45	v.	v.	PROPN
ijassa-1111	220	46	,	,	PUNCT
ijassa-1111	220	47	&	&	CCONJ
ijassa-1111	220	48	parvin	parvin	PROPN
ijassa-1111	220	49	,	,	PUNCT
ijassa-1111	220	50	r.	r.	PROPN
ijassa-1111	220	51	h.	h.	PROPN
ijassa-1111	220	52	(	(	PUNCT
ijassa-1111	220	53	1995	1995	NUM
ijassa-1111	220	54	)	)	PUNCT
ijassa-1111	220	55	.	.	PUNCT
ijassa-1111	221	1	project	project	NOUN
ijassa-1111	221	2	pattern	pattern	NOUN
ijassa-1111	221	3	a	a	DET
ijassa-1111	221	4	methodology	methodology	NOUN
ijassa-1111	221	5	for	for	ADP
ijassa-1111	221	6	delernining	delernine	VERB
ijassa-1111	221	7	relevance	relevance	NOUN
ijassa-1111	221	8	in	in	ADP
ijassa-1111	221	9	complex	complex	ADJ
ijassa-1111	221	10	decision	decision	NOUN
ijassa-1111	221	11	-	-	PUNCT
ijassa-1111	221	12	making	making	NOUN
ijassa-1111	221	13	,	,	PUNCT
ijassa-1111	221	14	ieee	ieee	NOUN
ijassa-1111	221	15	trans	tran	NOUN
ijassa-1111	221	16	.	.	PROPN
ijassa-1111	221	17	,	,	PUNCT
ijassa-1111	221	18	12(1	12(1	NUM
ijassa-1111	221	19	)	)	PUNCT
ijassa-1111	221	20	,	,	PUNCT
ijassa-1111	221	21	9–13	9–13	NOUN
ijassa-1111	221	22	.	.	PUNCT
ijassa-1111	222	1	5	5	NUM
ijassa-1111	222	2	.	.	X
ijassa-1111	222	3	saaty	saaty	NOUN
ijassa-1111	222	4	,	,	PUNCT
ijassa-1111	222	5	t.	t.	PROPN
ijassa-1111	222	6	l.	l.	PROPN
ijassa-1111	222	7	,	,	PUNCT
ijassa-1111	222	8	&	&	CCONJ
ijassa-1111	222	9	vargas	vargas	PROPN
ijassa-1111	222	10	,	,	PUNCT
ijassa-1111	222	11	l.	l.	PROPN
ijassa-1111	222	12	g.	g.	PROPN
ijassa-1111	222	13	(	(	PUNCT
ijassa-1111	222	14	1984	1984	NUM
ijassa-1111	222	15	)	)	PUNCT
ijassa-1111	222	16	.	.	PUNCT
ijassa-1111	223	1	comparison	comparison	NOUN
ijassa-1111	223	2	of	of	ADP
ijassa-1111	223	3	eigenvalue	eigenvalue	PROPN
ijassa-1111	223	4	,	,	PUNCT
ijassa-1111	223	5	logarithmic	logarithmic	ADJ
ijassa-1111	223	6	least	least	ADJ
ijassa-1111	223	7	squares	square	NOUN
ijassa-1111	223	8	and	and	CCONJ
ijassa-1111	223	9	least	least	ADJ
ijassa-1111	223	10	squares	square	NOUN
ijassa-1111	223	11	method	method	NOUN
ijassa-1111	223	12	in	in	ADP
ijassa-1111	223	13	estimating	estimate	VERB
ijassa-1111	223	14	ratios	ratio	NOUN
ijassa-1111	223	15	,	,	PUNCT
ijassa-1111	223	16	mathematical	mathematical	ADJ
ijassa-1111	223	17	modeling	modeling	NOUN
ijassa-1111	223	18	,	,	PUNCT
ijassa-1111	223	19	5	5	NUM
ijassa-1111	223	20	,	,	PUNCT
ijassa-1111	223	21	309–324	309–324	NUM
ijassa-1111	223	22	.	.	NOUN
ijassa-1111	223	23	6	6	NUM
ijassa-1111	223	24	.	.	X
ijassa-1111	223	25	saaty	saaty	NOUN
ijassa-1111	223	26	,	,	PUNCT
ijassa-1111	223	27	t.	t.	PROPN
ijassa-1111	223	28	l.	l.	PROPN
ijassa-1111	223	29	(	(	PUNCT
ijassa-1111	223	30	1986	1986	NUM
ijassa-1111	223	31	)	)	PUNCT
ijassa-1111	223	32	.	.	PUNCT
ijassa-1111	224	1	axiomatic	axiomatic	ADJ
ijassa-1111	224	2	foundation	foundation	NOUN
ijassa-1111	224	3	of	of	ADP
ijassa-1111	224	4	the	the	DET
ijassa-1111	224	5	analytic	analytic	ADJ
ijassa-1111	224	6	hierarchy	hierarchy	NOUN
ijassa-1111	224	7	process	process	NOUN
ijassa-1111	224	8	,	,	PUNCT
ijassa-1111	224	9	management	management	NOUN
ijassa-1111	224	10	science	science	NOUN
ijassa-1111	224	11	,	,	PUNCT
ijassa-1111	224	12	32(7	32(7	NOUN
ijassa-1111	224	13	)	)	PUNCT
ijassa-1111	224	14	,	,	PUNCT
ijassa-1111	224	15	841–855	841–855	NUM
ijassa-1111	224	16	.	.	PUNCT
ijassa-1111	225	1	7	7	NUM
ijassa-1111	225	2	.	.	X
ijassa-1111	225	3	saaty	saaty	NOUN
ijassa-1111	225	4	,	,	PUNCT
ijassa-1111	225	5	t.	t.	PROPN
ijassa-1111	225	6	l.	l.	PROPN
ijassa-1111	225	7	(	(	PUNCT
ijassa-1111	225	8	1990	1990	NUM
ijassa-1111	225	9	)	)	PUNCT
ijassa-1111	225	10	.	.	PUNCT
ijassa-1111	226	1	the	the	DET
ijassa-1111	226	2	analytic	analytic	ADJ
ijassa-1111	226	3	hierarchy	hierarchy	NOUN
ijassa-1111	226	4	process	process	NOUN
ijassa-1111	226	5	:	:	PUNCT
ijassa-1111	226	6	planning	planning	NOUN
ijassa-1111	226	7	,	,	PUNCT
ijassa-1111	226	8	priority	priority	NOUN
ijassa-1111	226	9	setting	setting	NOUN
ijassa-1111	226	10	,	,	PUNCT
ijassa-1111	226	11	resource	resource	NOUN
ijassa-1111	226	12	allocation	allocation	NOUN
ijassa-1111	226	13	.	.	PUNCT
ijassa-1111	227	1	pittsburgh	pittsburgh	PROPN
ijassa-1111	227	2	,	,	PUNCT
ijassa-1111	227	3	pa	pa	PROPN
ijassa-1111	227	4	:	:	PUNCT
ijassa-1111	227	5	rws	rws	VERB
ijassa-1111	227	6	.	.	PUNCT
ijassa-1111	228	1	8	8	X
ijassa-1111	228	2	.	.	X
ijassa-1111	228	3	saaty	saaty	NOUN
ijassa-1111	228	4	,	,	PUNCT
ijassa-1111	228	5	t.	t.	PROPN
ijassa-1111	228	6	(	(	PUNCT
ijassa-1111	228	7	2008	2008	NUM
ijassa-1111	228	8	)	)	PUNCT
ijassa-1111	228	9	.	.	PUNCT
ijassa-1111	229	1	prinyatie	prinyatie	PROPN
ijassa-1111	229	2	resheniy	resheniy	NOUN
ijassa-1111	229	3	pri	pri	NOUN
ijassa-1111	229	4	zavisimostyah	zavisimostyah	NOUN
ijassa-1111	229	5	i	i	PROPN
ijassa-1111	229	6	obratnyh	obratnyh	PROPN
ijassa-1111	229	7	svyazyah	svyazyah	NOUN
ijassa-1111	229	8	:	:	PUNCT
ijassa-1111	229	9	analiticheskiye	analiticheskiye	VERB
ijassa-1111	229	10	seti	seti	NOUN
ijassa-1111	230	1	[	[	X
ijassa-1111	230	2	decision	decision	NOUN
ijassa-1111	230	3	-	-	PUNCT
ijassa-1111	230	4	making	making	NOUN
ijassa-1111	230	5	under	under	ADP
ijassa-1111	230	6	dependencies	dependency	NOUN
ijassa-1111	230	7	and	and	CCONJ
ijassa-1111	230	8	feedback	feedback	NOUN
ijassa-1111	230	9	:	:	PUNCT
ijassa-1111	230	10	analytical	analytical	ADJ
ijassa-1111	230	11	networks	network	NOUN
ijassa-1111	230	12	]	]	PUNCT
ijassa-1111	230	13	.	.	PUNCT
ijassa-1111	231	1	moscow	moscow	PROPN
ijassa-1111	231	2	,	,	PUNCT
ijassa-1111	231	3	lki	lki	PROPN
ijassa-1111	231	4	,	,	PUNCT
ijassa-1111	231	5	360	360	NUM
ijassa-1111	231	6	p.	p.	NOUN
ijassa-1111	232	1	[	[	X
ijassa-1111	232	2	in	in	ADP
ijassa-1111	232	3	russian	russian	PROPN
ijassa-1111	232	4	]	]	PUNCT
ijassa-1111	232	5	.	.	PUNCT
ijassa-1111	232	6	9	9	X
ijassa-1111	232	7	.	.	X
ijassa-1111	232	8	horn	horn	PROPN
ijassa-1111	232	9	,	,	PUNCT
ijassa-1111	232	10	r.	r.	PROPN
ijassa-1111	232	11	a.	a.	PROPN
ijassa-1111	232	12	,	,	PUNCT
ijassa-1111	232	13	&	&	CCONJ
ijassa-1111	232	14	johnson	johnson	PROPN
ijassa-1111	232	15	,	,	PUNCT
ijassa-1111	232	16	c.	c.	PROPN
ijassa-1111	232	17	r.	r.	PROPN
ijassa-1111	232	18	(	(	PUNCT
ijassa-1111	232	19	2013	2013	NUM
ijassa-1111	232	20	)	)	PUNCT
ijassa-1111	232	21	.	.	PUNCT
ijassa-1111	233	1	matrix	matrix	NOUN
ijassa-1111	233	2	analysis	analysis	NOUN
ijassa-1111	233	3	.	.	PUNCT
ijassa-1111	234	1	cambridge	cambridge	PROPN
ijassa-1111	234	2	,	,	PUNCT
ijassa-1111	234	3	uk	uk	PROPN
ijassa-1111	234	4	:	:	PUNCT
ijassa-1111	234	5	cambridge	cambridge	PROPN
ijassa-1111	234	6	university	university	PROPN
ijassa-1111	234	7	press	press	NOUN
ijassa-1111	234	8	.	.	PUNCT
ijassa-1111	235	1	10	10	NUM
ijassa-1111	235	2	.	.	PUNCT
ijassa-1111	236	1	noghin	noghin	PROPN
ijassa-1111	236	2	,	,	PUNCT
ijassa-1111	236	3	v.	v.	PROPN
ijassa-1111	236	4	d.	d.	PROPN
ijassa-1111	236	5	(	(	PUNCT
ijassa-1111	236	6	2004	2004	NUM
ijassa-1111	236	7	)	)	PUNCT
ijassa-1111	236	8	.	.	PUNCT
ijassa-1111	237	1	a	a	DET
ijassa-1111	237	2	simplified	simplified	ADJ
ijassa-1111	237	3	variant	variant	NOUN
ijassa-1111	237	4	of	of	ADP
ijassa-1111	237	5	the	the	DET
ijassa-1111	237	6	analytic	analytic	ADJ
ijassa-1111	237	7	hierarchy	hierarchy	NOUN
ijassa-1111	237	8	processes	process	NOUN
ijassa-1111	237	9	based	base	VERB
ijassa-1111	237	10	on	on	ADP
ijassa-1111	237	11	a	a	DET
ijassa-1111	237	12	nonlinear	nonlinear	ADJ
ijassa-1111	237	13	scalarizing	scalarize	VERB
ijassa-1111	237	14	function	function	NOUN
ijassa-1111	237	15	,	,	PUNCT
ijassa-1111	237	16	computational	computational	ADJ
ijassa-1111	237	17	mathematics	mathematic	NOUN
ijassa-1111	237	18	and	and	CCONJ
ijassa-1111	237	19	mathematical	mathematical	ADJ
ijassa-1111	237	20	physics	physics	NOUN
ijassa-1111	237	21	,	,	PUNCT
ijassa-1111	237	22	44(7	44(7	NOUN
ijassa-1111	237	23	)	)	PUNCT
ijassa-1111	237	24	,	,	PUNCT
ijassa-1111	237	25	1194–1202	1194–1202	NUM
ijassa-1111	237	26	.	.	PUNCT
ijassa-1111	238	1	11	11	NUM
ijassa-1111	238	2	.	.	X
ijassa-1111	239	1	zahedi	zahedi	PROPN
ijassa-1111	239	2	,	,	PUNCT
ijassa-1111	239	3	f.	f.	PROPN
ijassa-1111	239	4	(	(	PUNCT
ijassa-1111	239	5	1986	1986	NUM
ijassa-1111	239	6	)	)	PUNCT
ijassa-1111	239	7	.	.	PUNCT
ijassa-1111	240	1	the	the	DET
ijassa-1111	240	2	analytic	analytic	ADJ
ijassa-1111	240	3	hierarchy	hierarchy	NOUN
ijassa-1111	240	4	process	process	NOUN
ijassa-1111	240	5	–	–	PUNCT
ijassa-1111	240	6	a	a	DET
ijassa-1111	240	7	survey	survey	NOUN
ijassa-1111	240	8	of	of	ADP
ijassa-1111	240	9	the	the	DET
ijassa-1111	240	10	method	method	NOUN
ijassa-1111	240	11	and	and	CCONJ
ijassa-1111	240	12	its	its	PRON
ijassa-1111	240	13	applications	application	NOUN
ijassa-1111	240	14	,	,	PUNCT
ijassa-1111	240	15	interfaces	interface	NOUN
ijassa-1111	240	16	,	,	PUNCT
ijassa-1111	240	17	16	16	NUM
ijassa-1111	240	18	,	,	PUNCT
ijassa-1111	240	19	96–108	96–108	NUM
ijassa-1111	240	20	.	.	NOUN
ijassa-1111	240	21	12	12	NUM
ijassa-1111	240	22	.	.	PUNCT
ijassa-1111	240	23	takeda	takeda	PROPN
ijassa-1111	240	24	,	,	PUNCT
ijassa-1111	240	25	e.	e.	PROPN
ijassa-1111	240	26	(	(	PUNCT
ijassa-1111	240	27	1990	1990	NUM
ijassa-1111	240	28	)	)	PUNCT
ijassa-1111	240	29	.	.	PUNCT
ijassa-1111	241	1	the	the	DET
ijassa-1111	241	2	analytic	analytic	ADJ
ijassa-1111	241	3	hierarchy	hierarchy	NOUN
ijassa-1111	241	4	process	process	NOUN
ijassa-1111	241	5	:	:	PUNCT
ijassa-1111	241	6	an	an	DET
ijassa-1111	241	7	overview	overview	NOUN
ijassa-1111	241	8	,	,	PUNCT
ijassa-1111	241	9	systems	system	NOUN
ijassa-1111	241	10	,	,	PUNCT
ijassa-1111	241	11	control	control	NOUN
ijassa-1111	241	12	and	and	CCONJ
ijassa-1111	241	13	information	information	NOUN
ijassa-1111	241	14	,	,	PUNCT
ijassa-1111	241	15	34	34	NUM
ijassa-1111	241	16	,	,	PUNCT
ijassa-1111	241	17	669–675	669–675	NUM
ijassa-1111	241	18	.	.	PUNCT
ijassa-1111	242	1	13	13	NUM
ijassa-1111	242	2	.	.	PUNCT
ijassa-1111	242	3	forman	forman	NOUN
ijassa-1111	242	4	,	,	PUNCT
ijassa-1111	242	5	t.	t.	PROPN
ijassa-1111	242	6	y.	y.	PROPN
ijassa-1111	242	7	,	,	PUNCT
ijassa-1111	242	8	&	&	CCONJ
ijassa-1111	242	9	gass	gass	PROPN
ijassa-1111	242	10	,	,	PUNCT
ijassa-1111	242	11	s.	s.	PROPN
ijassa-1111	242	12	i.	i.	PROPN
ijassa-1111	242	13	(	(	PUNCT
ijassa-1111	242	14	2001	2001	NUM
ijassa-1111	242	15	)	)	PUNCT
ijassa-1111	242	16	.	.	PUNCT
ijassa-1111	243	1	the	the	DET
ijassa-1111	243	2	analytic	analytic	ADJ
ijassa-1111	243	3	hierarchy	hierarchy	NOUN
ijassa-1111	243	4	process	process	NOUN
ijassa-1111	243	5	–	–	PUNCT
ijassa-1111	243	6	an	an	DET
ijassa-1111	243	7	exposition	exposition	NOUN
ijassa-1111	243	8	,	,	PUNCT
ijassa-1111	243	9	operations	operation	NOUN
ijassa-1111	243	10	research	research	NOUN
ijassa-1111	243	11	,	,	PUNCT
ijassa-1111	243	12	21	21	NUM
ijassa-1111	243	13	,	,	PUNCT
ijassa-1111	243	14	469–486	469–486	NUM
ijassa-1111	243	15	.	.	PUNCT
ijassa-1111	243	16	14	14	NUM
ijassa-1111	243	17	.	.	PUNCT
ijassa-1111	244	1	bodin	bodin	PROPN
ijassa-1111	244	2	,	,	PUNCT
ijassa-1111	244	3	l.	l.	PROPN
ijassa-1111	244	4	,	,	PUNCT
ijassa-1111	244	5	&	&	CCONJ
ijassa-1111	244	6	gass	gass	PROPN
ijassa-1111	244	7	,	,	PUNCT
ijassa-1111	244	8	s.	s.	PROPN
ijassa-1111	244	9	i.	i.	PROPN
ijassa-1111	244	10	(	(	PUNCT
ijassa-1111	244	11	2003	2003	NUM
ijassa-1111	244	12	)	)	PUNCT
ijassa-1111	244	13	.	.	PUNCT
ijassa-1111	245	1	on	on	ADP
ijassa-1111	245	2	teaching	teach	VERB
ijassa-1111	245	3	the	the	DET
ijassa-1111	245	4	analytic	analytic	ADJ
ijassa-1111	245	5	hierarchy	hierarchy	NOUN
ijassa-1111	245	6	process	process	NOUN
ijassa-1111	245	7	,	,	PUNCT
ijassa-1111	245	8	computer	computer	NOUN
ijassa-1111	245	9	and	and	CCONJ
ijassa-1111	245	10	operations	operation	NOUN
ijassa-1111	245	11	research	research	NOUN
ijassa-1111	245	12	,	,	PUNCT
ijassa-1111	245	13	30	30	NUM
ijassa-1111	245	14	,	,	PUNCT
ijassa-1111	245	15	487–1497	487–1497	NUM
ijassa-1111	245	16	.	.	NOUN
ijassa-1111	245	17	15	15	NUM
ijassa-1111	245	18	.	.	PUNCT
ijassa-1111	245	19	vaidia	vaidia	PROPN
ijassa-1111	245	20	,	,	PUNCT
ijassa-1111	245	21	j.	j.	PROPN
ijassa-1111	245	22	s.	s.	PROPN
ijassa-1111	245	23	,	,	PUNCT
ijassa-1111	245	24	&	&	CCONJ
ijassa-1111	245	25	kumar	kumar	PROPN
ijassa-1111	245	26	,	,	PUNCT
ijassa-1111	245	27	s.	s.	PROPN
ijassa-1111	245	28	(	(	PUNCT
ijassa-1111	245	29	2006	2006	NUM
ijassa-1111	245	30	)	)	PUNCT
ijassa-1111	245	31	.	.	PUNCT
ijassa-1111	246	1	analytic	analytic	ADJ
ijassa-1111	246	2	hierarchy	hierarchy	NOUN
ijassa-1111	246	3	process	process	NOUN
ijassa-1111	246	4	:	:	PUNCT
ijassa-1111	246	5	an	an	DET
ijassa-1111	246	6	overview	overview	NOUN
ijassa-1111	246	7	of	of	ADP
ijassa-1111	246	8	applications	application	NOUN
ijassa-1111	246	9	,	,	PUNCT
ijassa-1111	246	10	european	european	PROPN
ijassa-1111	246	11	journal	journal	PROPN
ijassa-1111	246	12	of	of	ADP
ijassa-1111	246	13	operational	operational	ADJ
ijassa-1111	246	14	research	research	NOUN
ijassa-1111	246	15	,	,	PUNCT
ijassa-1111	246	16	168	168	NUM
ijassa-1111	246	17	,	,	PUNCT
ijassa-1111	246	18	1–29	1–29	PROPN
ijassa-1111	246	19	.	.	PUNCT
ijassa-1111	247	1	16	16	NUM
ijassa-1111	247	2	.	.	PUNCT
ijassa-1111	248	1	expert	expert	NOUN
ijassa-1111	248	2	choice	choice	NOUN
ijassa-1111	248	3	.	.	PUNCT
ijassa-1111	249	1	(	(	PUNCT
ijassa-1111	249	2	2021	2021	NUM
ijassa-1111	249	3	)	)	PUNCT
ijassa-1111	249	4	.	.	PUNCT
ijassa-1111	250	1	[	[	X
ijassa-1111	250	2	online	online	X
ijassa-1111	250	3	]	]	X
ijassa-1111	250	4	.	.	PUNCT
ijassa-1111	251	1	available	available	ADJ
ijassa-1111	251	2	:	:	PUNCT
ijassa-1111	252	1	www.expertchoice.com	www.expertchoice.com	X
ijassa-1111	252	2	.	.	PROPN
ijassa-1111	253	1	17	17	NUM
ijassa-1111	253	2	.	.	PUNCT
ijassa-1111	254	1	mirkin	mirkin	ADV
ijassa-1111	254	2	,	,	PUNCT
ijassa-1111	254	3	b.	b.	PROPN
ijassa-1111	254	4	g.	g.	PROPN
ijassa-1111	254	5	(	(	PUNCT
ijassa-1111	254	6	1974	1974	NUM
ijassa-1111	254	7	)	)	PUNCT
ijassa-1111	254	8	.	.	PUNCT
ijassa-1111	255	1	problema	problema	PROPN
ijassa-1111	255	2	gruppovovo	gruppovovo	PROPN
ijassa-1111	255	3	vybora	vybora	NOUN
ijassa-1111	256	1	[	[	X
ijassa-1111	256	2	the	the	DET
ijassa-1111	256	3	problem	problem	NOUN
ijassa-1111	256	4	of	of	ADP
ijassa-1111	256	5	group	group	NOUN
ijassa-1111	256	6	selection	selection	NOUN
ijassa-1111	256	7	]	]	PUNCT
ijassa-1111	256	8	.	.	PUNCT
ijassa-1111	257	1	moscow	moscow	PROPN
ijassa-1111	257	2	,	,	PUNCT
ijassa-1111	257	3	ussr	ussr	PROPN
ijassa-1111	257	4	:	:	PUNCT
ijassa-1111	257	5	nauka	nauka	PROPN
ijassa-1111	258	1	[	[	X
ijassa-1111	258	2	in	in	ADP
ijassa-1111	258	3	russian	russian	PROPN
ijassa-1111	258	4	]	]	PUNCT
ijassa-1111	258	5	.	.	PUNCT