id	sid	tid	token	lemma	pos
ap-638	1	1	ap04-bittnar1.vp	ap04-bittnar1.vp	PROPN
ap-638	1	2	1	1	NUM
ap-638	1	3	introduction	introduction	NOUN
ap-638	1	4	concrete	concrete	NOUN
ap-638	1	5	,	,	PUNCT
ap-638	1	6	as	as	ADP
ap-638	1	7	a	a	DET
ap-638	1	8	convenient	convenient	ADJ
ap-638	1	9	building	building	NOUN
ap-638	1	10	material	material	NOUN
ap-638	1	11	,	,	PUNCT
ap-638	1	12	inherently	inherently	ADV
ap-638	1	13	involves	involve	VERB
ap-638	1	14	uncertainty	uncertainty	NOUN
ap-638	1	15	about	about	ADP
ap-638	1	16	its	its	PRON
ap-638	1	17	composition	composition	NOUN
ap-638	1	18	,	,	PUNCT
ap-638	1	19	which	which	PRON
ap-638	1	20	is	be	AUX
ap-638	1	21	difficult	difficult	ADJ
ap-638	1	22	to	to	PART
ap-638	1	23	eliminate	eliminate	VERB
ap-638	1	24	completely	completely	ADV
ap-638	1	25	.	.	PUNCT
ap-638	2	1	however	however	ADV
ap-638	2	2	,	,	PUNCT
ap-638	2	3	this	this	DET
ap-638	2	4	uncertainty	uncertainty	NOUN
ap-638	2	5	can	can	AUX
ap-638	2	6	be	be	AUX
ap-638	2	7	assessed	assess	VERB
ap-638	2	8	by	by	ADP
ap-638	2	9	statistical	statistical	ADJ
ap-638	2	10	,	,	PUNCT
ap-638	2	11	fuzzy	fuzzy	ADJ
ap-638	2	12	,	,	PUNCT
ap-638	2	13	or	or	CCONJ
ap-638	2	14	other	other	ADJ
ap-638	2	15	suitable	suitable	ADJ
ap-638	2	16	tools	tool	NOUN
ap-638	2	17	.	.	PUNCT
ap-638	3	1	in	in	ADP
ap-638	3	2	the	the	DET
ap-638	3	3	case	case	NOUN
ap-638	3	4	of	of	ADP
ap-638	3	5	concrete	concrete	ADJ
ap-638	3	6	structures	structure	NOUN
ap-638	3	7	,	,	PUNCT
ap-638	3	8	such	such	ADJ
ap-638	3	9	as	as	ADP
ap-638	3	10	frames	frame	NOUN
ap-638	3	11	made	make	VERB
ap-638	3	12	of	of	ADP
ap-638	3	13	reinforced	reinforce	VERB
ap-638	3	14	concrete	concrete	NOUN
ap-638	3	15	,	,	PUNCT
ap-638	3	16	it	it	PRON
ap-638	3	17	is	be	AUX
ap-638	3	18	costly	costly	ADJ
ap-638	3	19	to	to	PART
ap-638	3	20	obtain	obtain	VERB
ap-638	3	21	a	a	DET
ap-638	3	22	sufficient	sufficient	ADJ
ap-638	3	23	experimental	experimental	ADJ
ap-638	3	24	data	datum	NOUN
ap-638	3	25	set	set	VERB
ap-638	3	26	which	which	PRON
ap-638	3	27	would	would	AUX
ap-638	3	28	yield	yield	VERB
ap-638	3	29	the	the	DET
ap-638	3	30	desired	desire	VERB
ap-638	3	31	statistical	statistical	ADJ
ap-638	3	32	characteristics	characteristic	NOUN
ap-638	3	33	of	of	ADP
ap-638	3	34	the	the	DET
ap-638	3	35	material	material	NOUN
ap-638	3	36	parameters	parameter	NOUN
ap-638	3	37	.	.	PUNCT
ap-638	4	1	instead	instead	ADV
ap-638	4	2	,	,	PUNCT
ap-638	4	3	the	the	DET
ap-638	4	4	knowledge	knowledge	NOUN
ap-638	4	5	gained	gain	VERB
ap-638	4	6	by	by	ADP
ap-638	4	7	practicing	practice	VERB
ap-638	4	8	engineers	engineer	NOUN
ap-638	4	9	can	can	AUX
ap-638	4	10	be	be	AUX
ap-638	4	11	included	include	VERB
ap-638	4	12	as	as	ADP
ap-638	4	13	fuzzy	fuzzy	ADJ
ap-638	4	14	numbers	number	NOUN
ap-638	4	15	in	in	ADP
ap-638	4	16	the	the	DET
ap-638	4	17	material	material	NOUN
ap-638	4	18	modeling	modeling	NOUN
ap-638	4	19	.	.	PUNCT
ap-638	5	1	for	for	ADP
ap-638	5	2	design	design	NOUN
ap-638	5	3	purposes	purpose	NOUN
ap-638	5	4	,	,	PUNCT
ap-638	5	5	traditionally	traditionally	ADV
ap-638	5	6	,	,	PUNCT
ap-638	5	7	we	we	PRON
ap-638	5	8	may	may	AUX
ap-638	5	9	wish	wish	VERB
ap-638	5	10	to	to	PART
ap-638	5	11	conduct	conduct	VERB
ap-638	5	12	a	a	DET
ap-638	5	13	statistical	statistical	ADJ
ap-638	5	14	analysis	analysis	NOUN
ap-638	5	15	,	,	PUNCT
ap-638	5	16	using	use	VERB
ap-638	5	17	the	the	DET
ap-638	5	18	statistical	statistical	ADJ
ap-638	5	19	characteristics	characteristic	NOUN
ap-638	5	20	of	of	ADP
ap-638	5	21	several	several	ADJ
ap-638	5	22	measured	measured	ADJ
ap-638	5	23	events	event	NOUN
ap-638	5	24	.	.	PUNCT
ap-638	6	1	in	in	ADP
ap-638	6	2	the	the	DET
ap-638	6	3	case	case	NOUN
ap-638	6	4	of	of	ADP
ap-638	6	5	an	an	DET
ap-638	6	6	earthquake	earthquake	NOUN
ap-638	6	7	,	,	PUNCT
ap-638	6	8	however	however	ADV
ap-638	6	9	,	,	PUNCT
ap-638	6	10	the	the	DET
ap-638	6	11	measured	measured	ADJ
ap-638	6	12	data	datum	NOUN
ap-638	6	13	for	for	ADP
ap-638	6	14	each	each	DET
ap-638	6	15	site	site	NOUN
ap-638	6	16	of	of	ADP
ap-638	6	17	interest	interest	NOUN
ap-638	6	18	is	be	AUX
ap-638	6	19	not	not	PART
ap-638	6	20	particularly	particularly	ADV
ap-638	6	21	dense	dense	ADJ
ap-638	6	22	,	,	PUNCT
ap-638	6	23	leaving	leave	VERB
ap-638	6	24	the	the	DET
ap-638	6	25	statistical	statistical	ADJ
ap-638	6	26	characteristics	characteristic	NOUN
ap-638	6	27	with	with	ADP
ap-638	6	28	little	little	ADJ
ap-638	6	29	relevance	relevance	NOUN
ap-638	6	30	.	.	PUNCT
ap-638	7	1	on	on	ADP
ap-638	7	2	the	the	DET
ap-638	7	3	other	other	ADJ
ap-638	7	4	hand	hand	NOUN
ap-638	7	5	,	,	PUNCT
ap-638	7	6	the	the	DET
ap-638	7	7	expected	expect	VERB
ap-638	7	8	seismic	seismic	ADJ
ap-638	7	9	load	load	NOUN
ap-638	7	10	at	at	ADP
ap-638	7	11	a	a	DET
ap-638	7	12	site	site	NOUN
ap-638	7	13	can	can	AUX
ap-638	7	14	alternatively	alternatively	ADV
ap-638	7	15	be	be	AUX
ap-638	7	16	expressed	express	VERB
ap-638	7	17	by	by	ADP
ap-638	7	18	fuzzy	fuzzy	ADJ
ap-638	7	19	sets	set	NOUN
ap-638	7	20	[	[	X
ap-638	7	21	1	1	NUM
ap-638	7	22	]	]	PUNCT
ap-638	7	23	,	,	PUNCT
ap-638	7	24	which	which	PRON
ap-638	7	25	take	take	VERB
ap-638	7	26	into	into	ADP
ap-638	7	27	account	account	NOUN
ap-638	7	28	the	the	DET
ap-638	7	29	scarcity	scarcity	NOUN
ap-638	7	30	of	of	ADP
ap-638	7	31	seismic	seismic	ADJ
ap-638	7	32	stations	station	NOUN
ap-638	7	33	and	and	CCONJ
ap-638	7	34	information	information	NOUN
ap-638	7	35	about	about	ADP
ap-638	7	36	local	local	ADJ
ap-638	7	37	sub	sub	ADJ
ap-638	7	38	-	-	ADJ
ap-638	7	39	soil	soil	ADJ
ap-638	7	40	composition	composition	NOUN
ap-638	7	41	.	.	PUNCT
ap-638	8	1	in	in	ADP
ap-638	8	2	this	this	DET
ap-638	8	3	paper	paper	NOUN
ap-638	8	4	,	,	PUNCT
ap-638	8	5	an	an	DET
ap-638	8	6	approach	approach	NOUN
ap-638	8	7	to	to	ADP
ap-638	8	8	dynamic	dynamic	ADJ
ap-638	8	9	analysis	analysis	NOUN
ap-638	8	10	based	base	VERB
ap-638	8	11	on	on	ADP
ap-638	8	12	fuzzy	fuzzy	ADJ
ap-638	8	13	set	set	NOUN
ap-638	8	14	theory	theory	NOUN
ap-638	8	15	is	be	AUX
ap-638	8	16	presented	present	VERB
ap-638	8	17	as	as	ADP
ap-638	8	18	a	a	DET
ap-638	8	19	germane	germane	NOUN
ap-638	8	20	alternative	alternative	NOUN
ap-638	8	21	to	to	ADP
ap-638	8	22	classical	classical	ADJ
ap-638	8	23	stochastic	stochastic	ADJ
ap-638	8	24	dynamic	dynamic	ADJ
ap-638	8	25	analysis	analysis	NOUN
ap-638	8	26	.	.	PUNCT
ap-638	9	1	the	the	DET
ap-638	9	2	material	material	ADJ
ap-638	9	3	parameters	parameter	NOUN
ap-638	9	4	of	of	ADP
ap-638	9	5	reinforced	reinforce	VERB
ap-638	9	6	concrete	concrete	NOUN
ap-638	9	7	are	be	AUX
ap-638	9	8	considered	consider	VERB
ap-638	9	9	to	to	PART
ap-638	9	10	be	be	AUX
ap-638	9	11	fuzzy	fuzzy	ADJ
ap-638	9	12	quantities	quantity	NOUN
ap-638	9	13	with	with	ADP
ap-638	9	14	a	a	DET
ap-638	9	15	given	give	VERB
ap-638	9	16	distribution	distribution	NOUN
ap-638	9	17	,	,	PUNCT
ap-638	9	18	i.e.	i.e.	X
ap-638	9	19	,	,	PUNCT
ap-638	9	20	fuzzy	fuzzy	ADJ
ap-638	9	21	numbers	number	NOUN
ap-638	9	22	with	with	ADP
ap-638	9	23	a	a	DET
ap-638	9	24	desired	desire	VERB
ap-638	9	25	shape	shape	NOUN
ap-638	9	26	of	of	ADP
ap-638	9	27	the	the	DET
ap-638	9	28	membership	membership	NOUN
ap-638	9	29	function	function	NOUN
ap-638	9	30	[	[	X
ap-638	9	31	2	2	NUM
ap-638	9	32	]	]	PUNCT
ap-638	9	33	.	.	PUNCT
ap-638	10	1	the	the	DET
ap-638	10	2	dynamic	dynamic	ADJ
ap-638	10	3	analysis	analysis	NOUN
ap-638	10	4	is	be	AUX
ap-638	10	5	,	,	PUNCT
ap-638	10	6	then	then	ADV
ap-638	10	7	,	,	PUNCT
ap-638	10	8	performed	perform	VERB
ap-638	10	9	with	with	ADP
ap-638	10	10	the	the	DET
ap-638	10	11	help	help	NOUN
ap-638	10	12	of	of	ADP
ap-638	10	13	fuzzy	fuzzy	ADJ
ap-638	10	14	arithmetic	arithmetic	NOUN
ap-638	10	15	on	on	ADP
ap-638	10	16	either	either	PRON
ap-638	10	17	�	�	NOUN
ap-638	10	18	-cuts	-cut	NOUN
ap-638	10	19	or	or	CCONJ
ap-638	10	20	computation	computation	NOUN
ap-638	10	21	-	-	PUNCT
ap-638	10	22	efficient	efficient	ADJ
ap-638	10	23	(	(	PUNCT
ap-638	10	24	l	l	NOUN
ap-638	10	25	,	,	PUNCT
ap-638	10	26	r	r	NOUN
ap-638	10	27	)	)	PUNCT
ap-638	10	28	numbers	number	NOUN
ap-638	10	29	[	[	X
ap-638	10	30	3	3	NUM
ap-638	10	31	]	]	PUNCT
ap-638	10	32	.	.	PUNCT
ap-638	11	1	the	the	DET
ap-638	11	2	result	result	NOUN
ap-638	11	3	of	of	ADP
ap-638	11	4	such	such	DET
ap-638	11	5	an	an	DET
ap-638	11	6	analysis	analysis	NOUN
ap-638	11	7	is	be	AUX
ap-638	11	8	in	in	ADP
ap-638	11	9	the	the	DET
ap-638	11	10	form	form	NOUN
ap-638	11	11	of	of	ADP
ap-638	11	12	fuzzy	fuzzy	ADJ
ap-638	11	13	numbers	number	NOUN
ap-638	11	14	,	,	PUNCT
ap-638	11	15	which	which	PRON
ap-638	11	16	is	be	AUX
ap-638	11	17	less	less	ADV
ap-638	11	18	expensive	expensive	ADJ
ap-638	11	19	than	than	ADP
ap-638	11	20	the	the	DET
ap-638	11	21	stochastic	stochastic	ADJ
ap-638	11	22	approach	approach	NOUN
ap-638	11	23	in	in	ADP
ap-638	11	24	terms	term	NOUN
ap-638	11	25	of	of	ADP
ap-638	11	26	computation	computation	NOUN
ap-638	11	27	time	time	NOUN
ap-638	11	28	,	,	PUNCT
ap-638	11	29	but	but	CCONJ
ap-638	11	30	still	still	ADV
ap-638	11	31	provides	provide	VERB
ap-638	11	32	an	an	DET
ap-638	11	33	idea	idea	NOUN
ap-638	11	34	of	of	ADP
ap-638	11	35	the	the	DET
ap-638	11	36	distribution	distribution	NOUN
ap-638	11	37	of	of	ADP
ap-638	11	38	the	the	DET
ap-638	11	39	sought	seek	VERB
ap-638	11	40	quantity	quantity	NOUN
ap-638	11	41	.	.	PUNCT
ap-638	12	1	in	in	ADP
ap-638	12	2	order	order	NOUN
ap-638	12	3	to	to	PART
ap-638	12	4	further	far	ADV
ap-638	12	5	improve	improve	VERB
ap-638	12	6	the	the	DET
ap-638	12	7	computational	computational	ADJ
ap-638	12	8	efficiency	efficiency	NOUN
ap-638	12	9	,	,	PUNCT
ap-638	12	10	inspired	inspire	VERB
ap-638	12	11	by	by	ADP
ap-638	12	12	[	[	X
ap-638	12	13	4	4	NUM
ap-638	12	14	]	]	PUNCT
ap-638	12	15	,	,	PUNCT
ap-638	12	16	the	the	DET
ap-638	12	17	concept	concept	NOUN
ap-638	12	18	of	of	ADP
ap-638	12	19	a	a	DET
ap-638	12	20	surface	surface	NOUN
ap-638	12	21	response	response	NOUN
ap-638	12	22	function	function	NOUN
ap-638	12	23	is	be	AUX
ap-638	12	24	utilized	utilize	VERB
ap-638	12	25	,	,	PUNCT
ap-638	12	26	[	[	X
ap-638	12	27	5	5	NUM
ap-638	12	28	,	,	PUNCT
ap-638	12	29	6	6	NUM
ap-638	12	30	]	]	PUNCT
ap-638	12	31	.	.	PUNCT
ap-638	13	1	this	this	DET
ap-638	13	2	approach	approach	NOUN
ap-638	13	3	is	be	AUX
ap-638	13	4	demonstrated	demonstrate	VERB
ap-638	13	5	in	in	ADP
ap-638	13	6	an	an	DET
ap-638	13	7	illustrative	illustrative	ADJ
ap-638	13	8	example	example	NOUN
ap-638	13	9	of	of	ADP
ap-638	13	10	a	a	DET
ap-638	13	11	2d	2d	NUM
ap-638	13	12	frame	frame	NOUN
ap-638	13	13	,	,	PUNCT
ap-638	13	14	where	where	SCONJ
ap-638	13	15	the	the	DET
ap-638	13	16	effect	effect	NOUN
ap-638	13	17	of	of	ADP
ap-638	13	18	uncertain	uncertain	ADJ
ap-638	13	19	material	material	NOUN
ap-638	13	20	parameters	parameter	NOUN
ap-638	13	21	transpires	transpire	VERB
ap-638	13	22	in	in	ADP
ap-638	13	23	the	the	DET
ap-638	13	24	corresponding	corresponding	ADJ
ap-638	13	25	distributions	distribution	NOUN
ap-638	13	26	of	of	ADP
ap-638	13	27	the	the	DET
ap-638	13	28	natural	natural	ADJ
ap-638	13	29	modal	modal	ADJ
ap-638	13	30	shapes	shape	NOUN
ap-638	13	31	and	and	CCONJ
ap-638	13	32	natural	natural	ADJ
ap-638	13	33	frequencies	frequency	NOUN
ap-638	13	34	of	of	ADP
ap-638	13	35	the	the	DET
ap-638	13	36	analyzed	analyze	VERB
ap-638	13	37	two	two	NUM
ap-638	13	38	-	-	PUNCT
ap-638	13	39	dimensional	dimensional	ADJ
ap-638	13	40	frame	frame	NOUN
ap-638	13	41	.	.	PUNCT
ap-638	14	1	a	a	DET
ap-638	14	2	methodology	methodology	NOUN
ap-638	14	3	for	for	ADP
ap-638	14	4	a	a	DET
ap-638	14	5	possible	possible	ADJ
ap-638	14	6	application	application	NOUN
ap-638	14	7	to	to	ADP
ap-638	14	8	seismic	seismic	ADJ
ap-638	14	9	design	design	NOUN
ap-638	14	10	is	be	AUX
ap-638	14	11	also	also	ADV
ap-638	14	12	explained	explain	VERB
ap-638	14	13	.	.	PUNCT
ap-638	15	1	it	it	PRON
ap-638	15	2	is	be	AUX
ap-638	15	3	believed	believe	VERB
ap-638	15	4	that	that	SCONJ
ap-638	15	5	this	this	DET
ap-638	15	6	approach	approach	NOUN
ap-638	15	7	enables	enable	VERB
ap-638	15	8	practicing	practice	VERB
ap-638	15	9	engineers	engineer	NOUN
ap-638	15	10	and	and	CCONJ
ap-638	15	11	other	other	ADJ
ap-638	15	12	people	people	NOUN
ap-638	15	13	with	with	ADP
ap-638	15	14	knowledge	knowledge	NOUN
ap-638	15	15	to	to	PART
ap-638	15	16	contribute	contribute	VERB
ap-638	15	17	actively	actively	ADV
ap-638	15	18	to	to	ADP
ap-638	15	19	analyses	analysis	NOUN
ap-638	15	20	of	of	ADP
ap-638	15	21	seismic	seismic	ADJ
ap-638	15	22	-	-	PUNCT
ap-638	15	23	sensitive	sensitive	ADJ
ap-638	15	24	structures	structure	NOUN
ap-638	15	25	.	.	PUNCT
ap-638	16	1	2	2	NUM
ap-638	16	2	dynamic	dynamic	ADJ
ap-638	16	3	finite	finite	NOUN
ap-638	16	4	element	element	NOUN
ap-638	16	5	analysis	analysis	NOUN
ap-638	16	6	the	the	DET
ap-638	16	7	finite	finite	PROPN
ap-638	16	8	element	element	NOUN
ap-638	16	9	method	method	NOUN
ap-638	16	10	applied	apply	VERB
ap-638	16	11	to	to	ADP
ap-638	16	12	dynamical	dynamical	ADJ
ap-638	16	13	problems	problem	NOUN
ap-638	16	14	of	of	ADP
ap-638	16	15	structures	structure	NOUN
ap-638	16	16	results	result	VERB
ap-638	16	17	in	in	ADP
ap-638	16	18	the	the	DET
ap-638	16	19	form	form	NOUN
ap-638	16	20	m	m	NOUN
ap-638	16	21	c	c	NOUN
ap-638	16	22	k	k	PROPN
ap-638	16	23	d	d	PROPN
ap-638	16	24	d	d	PROPN
ap-638	16	25	d	d	PROPN
ap-638	16	26	d	d	SYM
ap-638	16	27	2	2	NUM
ap-638	16	28	2	2	NUM
ap-638	16	29	r	r	NOUN
ap-638	16	30	r	r	NOUN
ap-638	16	31	r	r	NOUN
ap-638	16	32	f	f	X
ap-638	16	33	(	(	PUNCT
ap-638	16	34	)	)	PUNCT
ap-638	16	35	(	(	PUNCT
ap-638	16	36	)	)	PUNCT
ap-638	16	37	(	(	PUNCT
ap-638	16	38	)	)	PUNCT
ap-638	16	39	(	(	PUNCT
ap-638	16	40	)	)	PUNCT
ap-638	16	41	t	t	NOUN
ap-638	16	42	t	t	PROPN
ap-638	16	43	t	t	PROPN
ap-638	16	44	t	t	PROPN
ap-638	16	45	t	t	PROPN
ap-638	16	46	t	t	PROPN
ap-638	16	47	�	�	PROPN
ap-638	16	48	�	�	PROPN
ap-638	16	49	�	�	PROPN
ap-638	16	50	,	,	PUNCT
ap-638	16	51	(	(	PUNCT
ap-638	16	52	1	1	X
ap-638	16	53	)	)	PUNCT
ap-638	16	54	where	where	SCONJ
ap-638	16	55	m	m	PROPN
ap-638	16	56	denotes	denote	VERB
ap-638	16	57	the	the	DET
ap-638	16	58	mass	mass	NOUN
ap-638	16	59	matrix	matrix	NOUN
ap-638	16	60	,	,	PUNCT
ap-638	16	61	c	c	PROPN
ap-638	16	62	stands	stand	VERB
ap-638	16	63	for	for	ADP
ap-638	16	64	the	the	DET
ap-638	16	65	damping	damp	VERB
ap-638	16	66	matrix	matrix	NOUN
ap-638	16	67	,	,	PUNCT
ap-638	16	68	k	k	PROPN
ap-638	16	69	denotes	denote	VERB
ap-638	16	70	the	the	DET
ap-638	16	71	stiffness	stiffness	ADJ
ap-638	16	72	matrix	matrix	NOUN
ap-638	16	73	,	,	PUNCT
ap-638	16	74	f(t	f(t	PROPN
ap-638	16	75	)	)	PUNCT
ap-638	16	76	expresses	express	VERB
ap-638	16	77	the	the	DET
ap-638	16	78	load	load	NOUN
ap-638	16	79	vector	vector	NOUN
ap-638	16	80	and	and	CCONJ
ap-638	16	81	r(t	r(t	NOUN
ap-638	16	82	)	)	PUNCT
ap-638	16	83	is	be	AUX
ap-638	16	84	the	the	DET
ap-638	16	85	vector	vector	NOUN
ap-638	16	86	of	of	ADP
ap-638	16	87	the	the	DET
ap-638	16	88	nodal	nodal	NOUN
ap-638	16	89	displacements	displacement	NOUN
ap-638	16	90	which	which	PRON
ap-638	16	91	are	be	AUX
ap-638	16	92	computed	compute	VERB
ap-638	16	93	,	,	PUNCT
ap-638	16	94	t	t	PROPN
ap-638	16	95	stands	stand	VERB
ap-638	16	96	for	for	ADP
ap-638	16	97	time	time	NOUN
ap-638	16	98	.	.	PUNCT
ap-638	17	1	eq	eq	ADJ
ap-638	17	2	.	.	PUNCT
ap-638	18	1	(	(	PUNCT
ap-638	18	2	1	1	X
ap-638	18	3	)	)	PUNCT
ap-638	18	4	represents	represent	VERB
ap-638	18	5	a	a	DET
ap-638	18	6	semidiscrete	semidiscrete	ADJ
ap-638	18	7	problem	problem	NOUN
ap-638	18	8	where	where	SCONJ
ap-638	18	9	the	the	DET
ap-638	18	10	spatial	spatial	ADJ
ap-638	18	11	coordinates	coordinate	NOUN
ap-638	18	12	are	be	AUX
ap-638	18	13	discretized	discretize	VERB
ap-638	18	14	while	while	SCONJ
ap-638	18	15	the	the	DET
ap-638	18	16	time	time	NOUN
ap-638	18	17	is	be	AUX
ap-638	18	18	still	still	ADV
ap-638	18	19	assumed	assume	VERB
ap-638	18	20	to	to	PART
ap-638	18	21	be	be	AUX
ap-638	18	22	continuous	continuous	ADJ
ap-638	18	23	[	[	X
ap-638	18	24	7	7	NUM
ap-638	18	25	]	]	PUNCT
ap-638	18	26	.	.	PUNCT
ap-638	19	1	the	the	DET
ap-638	19	2	analysis	analysis	NOUN
ap-638	19	3	of	of	ADP
ap-638	19	4	the	the	DET
ap-638	19	5	natural	natural	ADJ
ap-638	19	6	frequencies	frequency	NOUN
ap-638	19	7	(	(	PUNCT
ap-638	19	8	eigenvalues	eigenvalue	NOUN
ap-638	19	9	)	)	PUNCT
ap-638	19	10	and	and	CCONJ
ap-638	19	11	natural	natural	ADJ
ap-638	19	12	mode	mode	NOUN
ap-638	19	13	shapes	shape	NOUN
ap-638	19	14	(	(	PUNCT
ap-638	19	15	eigenvectors	eigenvector	NOUN
ap-638	19	16	)	)	PUNCT
ap-638	19	17	of	of	ADP
ap-638	19	18	an	an	DET
ap-638	19	19	undamped	undamped	ADJ
ap-638	19	20	structure	structure	NOUN
ap-638	19	21	is	be	AUX
ap-638	19	22	based	base	VERB
ap-638	19	23	on	on	ADP
ap-638	19	24	the	the	DET
ap-638	19	25	simplified	simplified	ADJ
ap-638	19	26	relation	relation	NOUN
ap-638	19	27	eq	eq	ADJ
ap-638	19	28	.	.	PUNCT
ap-638	20	1	(	(	PUNCT
ap-638	20	2	1	1	NUM
ap-638	20	3	)	)	PUNCT
ap-638	20	4	,	,	PUNCT
ap-638	20	5	which	which	PRON
ap-638	20	6	has	have	VERB
ap-638	20	7	the	the	DET
ap-638	20	8	form	form	NOUN
ap-638	20	9	(	(	PUNCT
ap-638	20	10	)	)	PUNCT
ap-638	20	11	k	k	PROPN
ap-638	20	12	m	m	PROPN
ap-638	20	13	0	0	NUM
ap-638	20	14	�	�	PROPN
ap-638	20	15	�	�	PROPN
ap-638	20	16	�	�	PROPN
ap-638	20	17	0	0	NUM
ap-638	20	18	2	2	NUM
ap-638	20	19	v	v	NOUN
ap-638	20	20	.	.	PUNCT
ap-638	21	1	(	(	PUNCT
ap-638	21	2	2	2	X
ap-638	21	3	)	)	PUNCT
ap-638	21	4	the	the	DET
ap-638	21	5	nonzero	nonzero	PROPN
ap-638	21	6	vector	vector	PROPN
ap-638	21	7	v	v	PROPN
ap-638	21	8	is	be	AUX
ap-638	21	9	the	the	DET
ap-638	21	10	eigenvector	eigenvector	NOUN
ap-638	21	11	containing	contain	VERB
ap-638	21	12	the	the	DET
ap-638	21	13	natural	natural	ADJ
ap-638	21	14	mode	mode	NOUN
ap-638	21	15	shapes	shape	NOUN
ap-638	21	16	and	and	CCONJ
ap-638	21	17	�	�	PROPN
ap-638	21	18	0	0	NUM
ap-638	21	19	stands	stand	VERB
ap-638	21	20	for	for	ADP
ap-638	21	21	the	the	DET
ap-638	21	22	natural	natural	ADJ
ap-638	21	23	frequency	frequency	NOUN
ap-638	21	24	.	.	PUNCT
ap-638	22	1	eq	eq	ADP
ap-638	22	2	.	.	PUNCT
ap-638	23	1	(	(	PUNCT
ap-638	23	2	2	2	X
ap-638	23	3	)	)	PUNCT
ap-638	23	4	represents	represent	VERB
ap-638	23	5	a	a	DET
ap-638	23	6	generalized	generalized	ADJ
ap-638	23	7	problem	problem	NOUN
ap-638	23	8	of	of	ADP
ap-638	23	9	eigenvalues	eigenvalue	NOUN
ap-638	23	10	.	.	PUNCT
ap-638	24	1	the	the	DET
ap-638	24	2	most	most	ADV
ap-638	24	3	common	common	ADJ
ap-638	24	4	method	method	NOUN
ap-638	24	5	for	for	ADP
ap-638	24	6	solving	solving	NOUN
ap-638	24	7	of	of	ADP
ap-638	24	8	such	such	ADJ
ap-638	24	9	problems	problem	NOUN
ap-638	24	10	is	be	AUX
ap-638	24	11	subspace	subspace	NOUN
ap-638	24	12	iteration	iteration	NOUN
ap-638	24	13	[	[	X
ap-638	24	14	8	8	NUM
ap-638	24	15	]	]	PUNCT
ap-638	24	16	.	.	PUNCT
ap-638	25	1	3	3	NUM
ap-638	25	2	fuzzification	fuzzification	NOUN
ap-638	25	3	of	of	ADP
ap-638	25	4	dynamic	dynamic	ADJ
ap-638	25	5	finite	finite	NOUN
ap-638	25	6	element	element	NOUN
ap-638	25	7	analysis	analysis	NOUN
ap-638	25	8	the	the	DET
ap-638	25	9	uncertainty	uncertainty	NOUN
ap-638	25	10	,	,	PUNCT
ap-638	25	11	that	that	PRON
ap-638	25	12	is	be	AUX
ap-638	25	13	present	present	ADJ
ap-638	25	14	in	in	ADP
ap-638	25	15	the	the	DET
ap-638	25	16	input	input	NOUN
ap-638	25	17	parameters	parameter	NOUN
ap-638	25	18	can	can	AUX
ap-638	25	19	be	be	AUX
ap-638	25	20	tackled	tackle	VERB
ap-638	25	21	with	with	ADP
ap-638	25	22	the	the	DET
ap-638	25	23	help	help	NOUN
ap-638	25	24	of	of	ADP
ap-638	25	25	fuzzy	fuzzy	ADJ
ap-638	25	26	set	set	NOUN
ap-638	25	27	theory	theory	NOUN
ap-638	25	28	[	[	X
ap-638	25	29	1	1	NUM
ap-638	25	30	]	]	PUNCT
ap-638	25	31	.	.	PUNCT
ap-638	26	1	in	in	ADP
ap-638	26	2	this	this	DET
ap-638	26	3	theory	theory	NOUN
ap-638	26	4	,	,	PUNCT
ap-638	26	5	uncertain	uncertain	ADJ
ap-638	26	6	quantities	quantity	NOUN
ap-638	26	7	are	be	AUX
ap-638	26	8	defined	define	VERB
ap-638	26	9	in	in	ADP
ap-638	26	10	terms	term	NOUN
ap-638	26	11	of	of	ADP
ap-638	26	12	fuzzy	fuzzy	ADJ
ap-638	26	13	sets	set	NOUN
ap-638	26	14	.	.	PUNCT
ap-638	27	1	unlike	unlike	ADP
ap-638	27	2	in	in	ADP
ap-638	27	3	the	the	DET
ap-638	27	4	classical	classical	ADJ
ap-638	27	5	set	set	NOUN
ap-638	27	6	theory	theory	NOUN
ap-638	27	7	,	,	PUNCT
ap-638	27	8	here	here	ADV
ap-638	27	9	membership	membership	NOUN
ap-638	27	10	of	of	ADP
ap-638	27	11	an	an	DET
ap-638	27	12	element	element	NOUN
ap-638	27	13	in	in	ADP
ap-638	27	14	a	a	DET
ap-638	27	15	fuzzy	fuzzy	ADJ
ap-638	27	16	set	set	NOUN
ap-638	27	17	also	also	ADV
ap-638	27	18	assumes	assume	VERB
ap-638	27	19	values	value	NOUN
ap-638	27	20	between	between	ADP
ap-638	27	21	0	0	NUM
ap-638	27	22	and	and	CCONJ
ap-638	27	23	1	1	NUM
ap-638	27	24	,	,	PUNCT
ap-638	27	25	where	where	SCONJ
ap-638	27	26	0	0	NUM
ap-638	27	27	means	mean	VERB
ap-638	27	28	“	"	PUNCT
ap-638	27	29	does	do	AUX
ap-638	27	30	not	not	PART
ap-638	27	31	belong	belong	VERB
ap-638	27	32	”	"	PUNCT
ap-638	27	33	and	and	CCONJ
ap-638	27	34	1	1	NUM
ap-638	27	35	means	mean	VERB
ap-638	27	36	“	"	PUNCT
ap-638	27	37	definitely	definitely	ADV
ap-638	27	38	belongs	belong	VERB
ap-638	27	39	”	"	PUNCT
ap-638	27	40	to	to	ADP
ap-638	27	41	a	a	DET
ap-638	27	42	fuzzy	fuzzy	ADJ
ap-638	27	43	set	set	NOUN
ap-638	27	44	.	.	PUNCT
ap-638	28	1	usually	usually	ADV
ap-638	28	2	,	,	PUNCT
ap-638	28	3	fuzzy	fuzzy	ADJ
ap-638	28	4	sets	set	NOUN
ap-638	28	5	represent	represent	VERB
ap-638	28	6	a	a	DET
ap-638	28	7	vague	vague	ADJ
ap-638	28	8	verbal	verbal	ADJ
ap-638	28	9	evaluation	evaluation	NOUN
ap-638	28	10	.	.	PUNCT
ap-638	29	1	in	in	ADP
ap-638	29	2	cases	case	NOUN
ap-638	29	3	when	when	SCONJ
ap-638	29	4	a	a	DET
ap-638	29	5	fuzzy	fuzzy	ADJ
ap-638	29	6	set	set	NOUN
ap-638	29	7	represents	represent	VERB
ap-638	29	8	a	a	DET
ap-638	29	9	numeral	numeral	ADJ
ap-638	29	10	,	,	PUNCT
ap-638	29	11	it	it	PRON
ap-638	29	12	is	be	AUX
ap-638	29	13	called	call	VERB
ap-638	29	14	a	a	DET
ap-638	29	15	fuzzy	fuzzy	ADJ
ap-638	29	16	number	number	NOUN
ap-638	29	17	.	.	PUNCT
ap-638	30	1	3.1	3.1	NUM
ap-638	30	2	fuzzy	fuzzy	ADJ
ap-638	30	3	numbers	number	NOUN
ap-638	30	4	the	the	DET
ap-638	30	5	notion	notion	NOUN
ap-638	30	6	of	of	ADP
ap-638	30	7	a	a	DET
ap-638	30	8	fuzzy	fuzzy	ADJ
ap-638	30	9	number	number	NOUN
ap-638	30	10	arises	arise	VERB
ap-638	30	11	from	from	ADP
ap-638	30	12	experience	experience	NOUN
ap-638	30	13	of	of	ADP
ap-638	30	14	everyday	everyday	ADJ
ap-638	30	15	life	life	NOUN
ap-638	30	16	where	where	SCONJ
ap-638	30	17	many	many	ADJ
ap-638	30	18	phenomena	phenomenon	NOUN
ap-638	30	19	which	which	PRON
ap-638	30	20	can	can	AUX
ap-638	30	21	be	be	AUX
ap-638	30	22	quantified	quantify	VERB
ap-638	30	23	are	be	AUX
ap-638	30	24	not	not	PART
ap-638	30	25	characterized	characterize	VERB
ap-638	30	26	in	in	ADP
ap-638	30	27	terms	term	NOUN
ap-638	30	28	of	of	ADP
ap-638	30	29	absolutely	absolutely	ADV
ap-638	30	30	precise	precise	ADJ
ap-638	30	31	numbers	number	NOUN
ap-638	30	32	.	.	PUNCT
ap-638	31	1	©	©	PROPN
ap-638	31	2	czech	czech	PROPN
ap-638	31	3	technical	technical	PROPN
ap-638	31	4	university	university	PROPN
ap-638	31	5	publishing	publishing	NOUN
ap-638	31	6	house	house	NOUN
ap-638	31	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-638	31	8	117	117	NUM
ap-638	31	9	acta	acta	PROPN
ap-638	31	10	polytechnica	polytechnica	PROPN
ap-638	31	11	vol	vol	NOUN
ap-638	31	12	.	.	PROPN
ap-638	32	1	44	44	NUM
ap-638	32	2	no	no	NOUN
ap-638	32	3	.	.	PUNCT
ap-638	33	1	5–6/2004	5–6/2004	NUM
ap-638	33	2	fuzzy	fuzzy	ADJ
ap-638	33	3	dynamic	dynamic	ADJ
ap-638	33	4	analysis	analysis	NOUN
ap-638	33	5	of	of	ADP
ap-638	33	6	a	a	DET
ap-638	33	7	2d	2d	NUM
ap-638	33	8	frame	frame	NOUN
ap-638	33	9	p.	p.	NOUN
ap-638	33	10	štemberk	štemberk	NOUN
ap-638	33	11	,	,	PUNCT
ap-638	33	12	j.	j.	PROPN
ap-638	33	13	kruis	kruis	PROPN
ap-638	33	14	this	this	DET
ap-638	33	15	paper	paper	NOUN
ap-638	33	16	deals	deal	NOUN
ap-638	33	17	with	with	ADP
ap-638	33	18	the	the	DET
ap-638	33	19	dynamic	dynamic	ADJ
ap-638	33	20	analysis	analysis	NOUN
ap-638	33	21	of	of	ADP
ap-638	33	22	a	a	DET
ap-638	33	23	2d	2d	NUM
ap-638	33	24	concrete	concrete	ADJ
ap-638	33	25	frame	frame	NOUN
ap-638	33	26	with	with	ADP
ap-638	33	27	uncertainties	uncertainty	NOUN
ap-638	33	28	which	which	PRON
ap-638	33	29	are	be	AUX
ap-638	33	30	an	an	DET
ap-638	33	31	integral	integral	ADJ
ap-638	33	32	part	part	NOUN
ap-638	33	33	of	of	ADP
ap-638	33	34	any	any	DET
ap-638	33	35	real	real	ADJ
ap-638	33	36	structure	structure	NOUN
ap-638	33	37	.	.	PUNCT
ap-638	34	1	the	the	DET
ap-638	34	2	uncertainties	uncertainty	NOUN
ap-638	34	3	can	can	AUX
ap-638	34	4	be	be	AUX
ap-638	34	5	modeled	model	VERB
ap-638	34	6	by	by	ADP
ap-638	34	7	a	a	DET
ap-638	34	8	stochastic	stochastic	NOUN
ap-638	34	9	or	or	CCONJ
ap-638	34	10	a	a	DET
ap-638	34	11	fuzzy	fuzzy	ADJ
ap-638	34	12	approach	approach	NOUN
ap-638	34	13	.	.	PUNCT
ap-638	35	1	the	the	DET
ap-638	35	2	fuzzy	fuzzy	ADJ
ap-638	35	3	approach	approach	NOUN
ap-638	35	4	is	be	AUX
ap-638	35	5	used	use	VERB
ap-638	35	6	and	and	CCONJ
ap-638	35	7	the	the	DET
ap-638	35	8	influence	influence	NOUN
ap-638	35	9	of	of	ADP
ap-638	35	10	uncertain	uncertain	ADJ
ap-638	35	11	input	input	NOUN
ap-638	35	12	data	datum	NOUN
ap-638	35	13	(	(	PUNCT
ap-638	35	14	modulus	modulus	NOUN
ap-638	35	15	of	of	ADP
ap-638	35	16	elasticity	elasticity	NOUN
ap-638	35	17	and	and	CCONJ
ap-638	35	18	density	density	NOUN
ap-638	35	19	)	)	PUNCT
ap-638	35	20	on	on	ADP
ap-638	35	21	output	output	NOUN
ap-638	35	22	data	datum	NOUN
ap-638	35	23	is	be	AUX
ap-638	35	24	studied	study	VERB
ap-638	35	25	.	.	PUNCT
ap-638	36	1	fuzzy	fuzzy	ADJ
ap-638	36	2	numbers	number	NOUN
ap-638	36	3	are	be	AUX
ap-638	36	4	represented	represent	VERB
ap-638	36	5	by	by	ADP
ap-638	36	6	�	�	NOUN
ap-638	36	7	-cuts	-cut	NOUN
ap-638	36	8	.	.	PUNCT
ap-638	37	1	in	in	ADP
ap-638	37	2	order	order	NOUN
ap-638	37	3	to	to	PART
ap-638	37	4	reduce	reduce	VERB
ap-638	37	5	the	the	DET
ap-638	37	6	volume	volume	NOUN
ap-638	37	7	of	of	ADP
ap-638	37	8	computation	computation	NOUN
ap-638	37	9	in	in	ADP
ap-638	37	10	the	the	DET
ap-638	37	11	fuzzy	fuzzy	ADJ
ap-638	37	12	approach	approach	NOUN
ap-638	37	13	,	,	PUNCT
ap-638	37	14	the	the	DET
ap-638	37	15	response	response	NOUN
ap-638	37	16	surface	surface	NOUN
ap-638	37	17	function	function	NOUN
ap-638	37	18	concept	concept	NOUN
ap-638	37	19	is	be	AUX
ap-638	37	20	applied	apply	VERB
ap-638	37	21	.	.	PUNCT
ap-638	38	1	in	in	ADP
ap-638	38	2	this	this	DET
ap-638	38	3	way	way	NOUN
ap-638	38	4	the	the	DET
ap-638	38	5	natural	natural	ADJ
ap-638	38	6	frequencies	frequency	NOUN
ap-638	38	7	and	and	CCONJ
ap-638	38	8	mode	mode	NOUN
ap-638	38	9	shapes	shape	NOUN
ap-638	38	10	described	describe	VERB
ap-638	38	11	by	by	ADP
ap-638	38	12	fuzzy	fuzzy	ADJ
ap-638	38	13	numbers	number	NOUN
ap-638	38	14	are	be	AUX
ap-638	38	15	obtained	obtain	VERB
ap-638	38	16	.	.	PUNCT
ap-638	39	1	the	the	DET
ap-638	39	2	results	result	NOUN
ap-638	39	3	of	of	ADP
ap-638	39	4	fuzzy	fuzzy	ADJ
ap-638	39	5	dynamic	dynamic	ADJ
ap-638	39	6	analysis	analysis	NOUN
ap-638	39	7	can	can	AUX
ap-638	39	8	be	be	AUX
ap-638	39	9	used	use	VERB
ap-638	39	10	,	,	PUNCT
ap-638	39	11	e.g.	e.g.	ADV
ap-638	39	12	,	,	PUNCT
ap-638	39	13	in	in	ADP
ap-638	39	14	seismic	seismic	ADJ
ap-638	39	15	design	design	NOUN
ap-638	39	16	of	of	ADP
ap-638	39	17	structures	structure	NOUN
ap-638	39	18	based	base	VERB
ap-638	39	19	on	on	ADP
ap-638	39	20	the	the	DET
ap-638	39	21	response	response	NOUN
ap-638	39	22	spectrum	spectrum	NOUN
ap-638	39	23	.	.	PUNCT
ap-638	40	1	keywords	keyword	NOUN
ap-638	40	2	:	:	PUNCT
ap-638	40	3	fuzzy	fuzzy	ADJ
ap-638	40	4	numbers	number	NOUN
ap-638	40	5	,	,	PUNCT
ap-638	40	6	natural	natural	ADJ
ap-638	40	7	frequency	frequency	NOUN
ap-638	40	8	,	,	PUNCT
ap-638	40	9	mode	mode	NOUN
ap-638	40	10	shape	shape	NOUN
ap-638	40	11	,	,	PUNCT
ap-638	40	12	response	response	NOUN
ap-638	40	13	surface	surface	NOUN
ap-638	40	14	function	function	NOUN
ap-638	40	15	.	.	PUNCT
ap-638	41	1	fuzzy	fuzzy	ADJ
ap-638	41	2	numbers	number	NOUN
ap-638	41	3	are	be	AUX
ap-638	41	4	fuzzy	fuzzy	ADJ
ap-638	41	5	sets	set	NOUN
ap-638	41	6	which	which	PRON
ap-638	41	7	are	be	AUX
ap-638	41	8	defined	define	VERB
ap-638	41	9	on	on	ADP
ap-638	41	10	the	the	DET
ap-638	41	11	set	set	NOUN
ap-638	41	12	of	of	ADP
ap-638	41	13	real	real	ADJ
ap-638	41	14	numbers	number	NOUN
ap-638	41	15	.	.	PUNCT
ap-638	42	1	their	their	PRON
ap-638	42	2	membership	membership	NOUN
ap-638	42	3	function	function	NOUN
ap-638	42	4	assigns	assign	VERB
ap-638	42	5	the	the	DET
ap-638	42	6	degree	degree	NOUN
ap-638	42	7	of	of	ADP
ap-638	42	8	1	1	NUM
ap-638	42	9	to	to	ADP
ap-638	42	10	the	the	DET
ap-638	42	11	central	central	ADJ
ap-638	42	12	,	,	PUNCT
ap-638	42	13	also	also	ADV
ap-638	42	14	called	call	VERB
ap-638	42	15	nominal	nominal	ADJ
ap-638	42	16	,	,	PUNCT
ap-638	42	17	modal	modal	NOUN
ap-638	42	18	or	or	CCONJ
ap-638	42	19	mean	mean	VERB
ap-638	42	20	,	,	PUNCT
ap-638	42	21	value	value	NOUN
ap-638	42	22	and	and	CCONJ
ap-638	42	23	lower	low	ADJ
ap-638	42	24	degrees	degree	NOUN
ap-638	42	25	to	to	ADP
ap-638	42	26	other	other	ADJ
ap-638	42	27	numbers	number	NOUN
ap-638	42	28	which	which	PRON
ap-638	42	29	reflect	reflect	VERB
ap-638	42	30	their	their	PRON
ap-638	42	31	proximity	proximity	NOUN
ap-638	42	32	to	to	ADP
ap-638	42	33	the	the	DET
ap-638	42	34	central	central	ADJ
ap-638	42	35	value	value	NOUN
ap-638	42	36	according	accord	VERB
ap-638	42	37	to	to	ADP
ap-638	42	38	the	the	DET
ap-638	42	39	used	use	VERB
ap-638	42	40	membership	membership	NOUN
ap-638	42	41	function	function	NOUN
ap-638	42	42	.	.	PUNCT
ap-638	43	1	the	the	DET
ap-638	43	2	membership	membership	NOUN
ap-638	43	3	function	function	NOUN
ap-638	43	4	should	should	AUX
ap-638	43	5	thus	thus	ADV
ap-638	43	6	decrease	decrease	VERB
ap-638	43	7	from	from	ADP
ap-638	43	8	1	1	NUM
ap-638	43	9	to	to	ADP
ap-638	43	10	0	0	NUM
ap-638	43	11	on	on	ADP
ap-638	43	12	both	both	DET
ap-638	43	13	sides	side	NOUN
ap-638	43	14	of	of	ADP
ap-638	43	15	the	the	DET
ap-638	43	16	central	central	ADJ
ap-638	43	17	value	value	NOUN
ap-638	43	18	.	.	PUNCT
ap-638	44	1	such	such	ADJ
ap-638	44	2	fuzzy	fuzzy	ADJ
ap-638	44	3	sets	set	NOUN
ap-638	44	4	are	be	AUX
ap-638	44	5	called	call	VERB
ap-638	44	6	fuzzy	fuzzy	ADJ
ap-638	44	7	numbers	number	NOUN
ap-638	44	8	.	.	PUNCT
ap-638	45	1	an	an	DET
ap-638	45	2	example	example	NOUN
ap-638	45	3	of	of	ADP
ap-638	45	4	a	a	DET
ap-638	45	5	fuzzy	fuzzy	ADJ
ap-638	45	6	number	number	NOUN
ap-638	45	7	is	be	AUX
ap-638	45	8	shown	show	VERB
ap-638	45	9	in	in	ADP
ap-638	45	10	fig	fig	NOUN
ap-638	45	11	.	.	PUNCT
ap-638	46	1	1	1	NUM
ap-638	46	2	,	,	PUNCT
ap-638	46	3	where	where	SCONJ
ap-638	46	4	�	�	PROPN
ap-638	46	5	represents	represent	VERB
ap-638	46	6	the	the	DET
ap-638	46	7	membership	membership	NOUN
ap-638	46	8	function	function	NOUN
ap-638	46	9	and	and	CCONJ
ap-638	46	10	a1	a1	NOUN
ap-638	46	11	and	and	CCONJ
ap-638	46	12	a2	a2	PROPN
ap-638	46	13	stand	stand	VERB
ap-638	46	14	for	for	ADP
ap-638	46	15	two	two	NUM
ap-638	46	16	real	real	ADJ
ap-638	46	17	numbers	number	NOUN
ap-638	46	18	on	on	ADP
ap-638	46	19	the	the	DET
ap-638	46	20	real	real	ADJ
ap-638	46	21	axis	axis	NOUN
ap-638	46	22	.	.	PUNCT
ap-638	47	1	the	the	DET
ap-638	47	2	intervals	interval	NOUN
ap-638	47	3	defined	define	VERB
ap-638	47	4	for	for	ADP
ap-638	47	5	a	a	DET
ap-638	47	6	specific	specific	ADJ
ap-638	47	7	value	value	NOUN
ap-638	47	8	of	of	ADP
ap-638	47	9	the	the	DET
ap-638	47	10	membership	membership	NOUN
ap-638	47	11	function	function	NOUN
ap-638	47	12	,	,	PUNCT
ap-638	47	13	e.g.	e.g.	ADV
ap-638	47	14	�	�	PROPN
ap-638	47	15	�	�	PROPN
ap-638	47	16	0.7	0.7	NUM
ap-638	47	17	,	,	PUNCT
ap-638	47	18	represent	represent	VERB
ap-638	47	19	the	the	DET
ap-638	47	20	so	so	ADV
ap-638	47	21	-	-	PUNCT
ap-638	47	22	called	call	VERB
ap-638	47	23	�	�	NOUN
ap-638	47	24	-cuts	-cut	NOUN
ap-638	47	25	.	.	PUNCT
ap-638	48	1	a	a	DET
ap-638	48	2	fuzzy	fuzzy	ADJ
ap-638	48	3	number	number	NOUN
ap-638	48	4	can	can	AUX
ap-638	48	5	be	be	AUX
ap-638	48	6	equally	equally	ADV
ap-638	48	7	expressed	express	VERB
ap-638	48	8	by	by	ADP
ap-638	48	9	either	either	CCONJ
ap-638	48	10	a	a	DET
ap-638	48	11	nominal	nominal	ADJ
ap-638	48	12	value	value	NOUN
ap-638	48	13	and	and	CCONJ
ap-638	48	14	a	a	DET
ap-638	48	15	membership	membership	NOUN
ap-638	48	16	function	function	NOUN
ap-638	48	17	on	on	ADP
ap-638	48	18	each	each	DET
ap-638	48	19	side	side	NOUN
ap-638	48	20	of	of	ADP
ap-638	48	21	the	the	DET
ap-638	48	22	nominal	nominal	ADJ
ap-638	48	23	value	value	NOUN
ap-638	48	24	or	or	CCONJ
ap-638	48	25	by	by	ADP
ap-638	48	26	a	a	DET
ap-638	48	27	set	set	NOUN
ap-638	48	28	of	of	ADP
ap-638	48	29	�	�	NOUN
ap-638	48	30	-cuts	-cut	NOUN
ap-638	48	31	.	.	PUNCT
ap-638	48	32	3.2	3.2	NUM
ap-638	48	33	fuzzy	fuzzy	ADJ
ap-638	48	34	arithmetic	arithmetic	ADJ
ap-638	48	35	a	a	DET
ap-638	48	36	fuzzy	fuzzy	ADJ
ap-638	48	37	arithmetic	arithmetic	ADJ
ap-638	48	38	operation	operation	NOUN
ap-638	48	39	depends	depend	VERB
ap-638	48	40	on	on	ADP
ap-638	48	41	the	the	DET
ap-638	48	42	definition	definition	NOUN
ap-638	48	43	of	of	ADP
ap-638	48	44	a	a	DET
ap-638	48	45	fuzzy	fuzzy	ADJ
ap-638	48	46	number	number	NOUN
ap-638	48	47	.	.	PUNCT
ap-638	49	1	in	in	ADP
ap-638	49	2	the	the	DET
ap-638	49	3	cases	case	NOUN
ap-638	49	4	when	when	SCONJ
ap-638	49	5	fuzzy	fuzzy	ADJ
ap-638	49	6	numbers	number	NOUN
ap-638	49	7	are	be	AUX
ap-638	49	8	defined	define	VERB
ap-638	49	9	by	by	ADP
ap-638	49	10	a	a	DET
ap-638	49	11	set	set	NOUN
ap-638	49	12	of	of	ADP
ap-638	49	13	�	�	NOUN
ap-638	49	14	-cuts	-cut	NOUN
ap-638	49	15	,	,	PUNCT
ap-638	49	16	the	the	DET
ap-638	49	17	problem	problem	NOUN
ap-638	49	18	of	of	ADP
ap-638	49	19	fuzzy	fuzzy	ADJ
ap-638	49	20	arithmetic	arithmetic	NOUN
ap-638	49	21	is	be	AUX
ap-638	49	22	reduced	reduce	VERB
ap-638	49	23	to	to	ADP
ap-638	49	24	the	the	DET
ap-638	49	25	well	well	ADV
ap-638	49	26	-	-	PUNCT
ap-638	49	27	known	know	VERB
ap-638	49	28	arithmetic	arithmetic	ADJ
ap-638	49	29	operations	operation	NOUN
ap-638	49	30	on	on	ADP
ap-638	49	31	intervals	interval	NOUN
ap-638	49	32	,	,	PUNCT
ap-638	49	33	which	which	PRON
ap-638	49	34	are	be	AUX
ap-638	49	35	applied	apply	VERB
ap-638	49	36	to	to	ADP
ap-638	49	37	each	each	DET
ap-638	49	38	�	�	NOUN
ap-638	49	39	-cut	-cut	VERB
ap-638	49	40	.	.	PUNCT
ap-638	50	1	implicitly	implicitly	ADV
ap-638	50	2	,	,	PUNCT
ap-638	50	3	this	this	PRON
ap-638	50	4	means	mean	VERB
ap-638	50	5	a	a	DET
ap-638	50	6	sequence	sequence	NOUN
ap-638	50	7	of	of	ADP
ap-638	50	8	binary	binary	ADJ
ap-638	50	9	combinations	combination	NOUN
ap-638	50	10	on	on	ADP
ap-638	50	11	each	each	DET
ap-638	50	12	�	�	NOUN
ap-638	50	13	-cut	-cut	PUNCT
ap-638	50	14	in	in	ADP
ap-638	50	15	order	order	NOUN
ap-638	50	16	to	to	PART
ap-638	50	17	obtain	obtain	VERB
ap-638	50	18	the	the	DET
ap-638	50	19	minimum	minimum	NOUN
ap-638	50	20	and	and	CCONJ
ap-638	50	21	the	the	DET
ap-638	50	22	maximum	maximum	ADJ
ap-638	50	23	value	value	NOUN
ap-638	50	24	for	for	ADP
ap-638	50	25	each	each	DET
ap-638	50	26	�	�	NOUN
ap-638	50	27	-cut	-cut	VERB
ap-638	50	28	.	.	PUNCT
ap-638	51	1	the	the	DET
ap-638	51	2	finite	finite	PROPN
ap-638	51	3	element	element	NOUN
ap-638	51	4	method	method	NOUN
ap-638	51	5	converts	convert	VERB
ap-638	51	6	a	a	DET
ap-638	51	7	problem	problem	NOUN
ap-638	51	8	into	into	ADP
ap-638	51	9	a	a	DET
ap-638	51	10	system	system	NOUN
ap-638	51	11	of	of	ADP
ap-638	51	12	linear	linear	PROPN
ap-638	51	13	equations	equation	NOUN
ap-638	51	14	,	,	PUNCT
ap-638	51	15	in	in	ADP
ap-638	51	16	this	this	DET
ap-638	51	17	case	case	NOUN
ap-638	51	18	a	a	DET
ap-638	51	19	system	system	NOUN
ap-638	51	20	of	of	ADP
ap-638	51	21	fuzzy	fuzzy	ADJ
ap-638	51	22	linear	linear	ADJ
ap-638	51	23	equations	equation	NOUN
ap-638	51	24	,	,	PUNCT
ap-638	51	25	which	which	PRON
ap-638	51	26	comprises	comprise	VERB
ap-638	51	27	an	an	DET
ap-638	51	28	extensive	extensive	ADJ
ap-638	51	29	number	number	NOUN
ap-638	51	30	of	of	ADP
ap-638	51	31	arithmetic	arithmetic	ADJ
ap-638	51	32	operations	operation	NOUN
ap-638	51	33	.	.	PUNCT
ap-638	52	1	this	this	DET
ap-638	52	2	fact	fact	NOUN
ap-638	52	3	makes	make	VERB
ap-638	52	4	the	the	DET
ap-638	52	5	formulation	formulation	NOUN
ap-638	52	6	in	in	ADP
ap-638	52	7	the	the	DET
ap-638	52	8	above	above	ADJ
ap-638	52	9	terms	term	NOUN
ap-638	52	10	merely	merely	ADV
ap-638	52	11	unsolvable	unsolvable	ADJ
ap-638	52	12	due	due	ADP
ap-638	52	13	to	to	ADP
ap-638	52	14	the	the	DET
ap-638	52	15	number	number	NOUN
ap-638	52	16	of	of	ADP
ap-638	52	17	all	all	DET
ap-638	52	18	necessary	necessary	ADJ
ap-638	52	19	binary	binary	ADJ
ap-638	52	20	operations	operation	NOUN
ap-638	52	21	.	.	PUNCT
ap-638	53	1	to	to	PART
ap-638	53	2	eliminate	eliminate	VERB
ap-638	53	3	the	the	DET
ap-638	53	4	drawback	drawback	NOUN
ap-638	53	5	of	of	ADP
ap-638	53	6	the	the	DET
ap-638	53	7	�	�	PROPN
ap-638	53	8	-cut	-cut	ADJ
ap-638	53	9	formulation	formulation	NOUN
ap-638	53	10	,	,	PUNCT
ap-638	53	11	new	new	ADJ
ap-638	53	12	techniques	technique	NOUN
ap-638	53	13	for	for	ADP
ap-638	53	14	solving	solve	VERB
ap-638	53	15	fuzzy	fuzzy	ADJ
ap-638	53	16	linear	linear	ADJ
ap-638	53	17	equation	equation	NOUN
ap-638	53	18	systems	system	NOUN
ap-638	53	19	have	have	AUX
ap-638	53	20	been	be	AUX
ap-638	53	21	developed	develop	VERB
ap-638	53	22	,	,	PUNCT
ap-638	53	23	e.g.	e.g.	ADV
ap-638	54	1	[	[	X
ap-638	54	2	9	9	NUM
ap-638	54	3	]	]	PUNCT
ap-638	54	4	.	.	PUNCT
ap-638	55	1	however	however	ADV
ap-638	55	2	,	,	PUNCT
ap-638	55	3	these	these	DET
ap-638	55	4	techniques	technique	NOUN
ap-638	55	5	are	be	AUX
ap-638	55	6	not	not	PART
ap-638	55	7	easily	easily	ADV
ap-638	55	8	applicable	applicable	ADJ
ap-638	55	9	to	to	ADP
ap-638	55	10	robust	robust	ADJ
ap-638	55	11	problems	problem	NOUN
ap-638	55	12	,	,	PUNCT
ap-638	55	13	such	such	ADJ
ap-638	55	14	as	as	ADP
ap-638	55	15	fuzzy	fuzzy	ADJ
ap-638	55	16	dynamic	dynamic	ADJ
ap-638	55	17	finite	finite	NOUN
ap-638	55	18	element	element	NOUN
ap-638	55	19	analysis	analysis	NOUN
ap-638	55	20	.	.	PUNCT
ap-638	56	1	therefore	therefore	ADV
ap-638	56	2	,	,	PUNCT
ap-638	56	3	another	another	DET
ap-638	56	4	technique	technique	NOUN
ap-638	56	5	for	for	ADP
ap-638	56	6	reducing	reduce	VERB
ap-638	56	7	the	the	DET
ap-638	56	8	large	large	ADJ
ap-638	56	9	number	number	NOUN
ap-638	56	10	of	of	ADP
ap-638	56	11	binary	binary	ADJ
ap-638	56	12	combinations	combination	NOUN
ap-638	56	13	has	have	AUX
ap-638	56	14	been	be	AUX
ap-638	56	15	exploited.this	exploited.this	PRON
ap-638	56	16	technique	technique	NOUN
ap-638	56	17	was	be	AUX
ap-638	56	18	originally	originally	ADV
ap-638	56	19	developed	develop	VERB
ap-638	56	20	for	for	ADP
ap-638	56	21	other	other	ADJ
ap-638	56	22	problems	problem	NOUN
ap-638	56	23	,	,	PUNCT
ap-638	56	24	such	such	ADJ
ap-638	56	25	as	as	ADP
ap-638	56	26	statistical	statistical	ADJ
ap-638	56	27	analysis	analysis	NOUN
ap-638	56	28	.	.	PUNCT
ap-638	57	1	3.3	3.3	NUM
ap-638	57	2	surface	surface	NOUN
ap-638	57	3	response	response	NOUN
ap-638	57	4	function	function	VERB
ap-638	57	5	fuzzy	fuzzy	ADJ
ap-638	57	6	analyses	analysis	NOUN
ap-638	57	7	,	,	PUNCT
ap-638	57	8	as	as	ADV
ap-638	57	9	well	well	ADV
ap-638	57	10	as	as	ADP
ap-638	57	11	stochastic	stochastic	ADJ
ap-638	57	12	analyses	analysis	NOUN
ap-638	57	13	,	,	PUNCT
ap-638	57	14	suffer	suffer	VERB
ap-638	57	15	from	from	ADP
ap-638	57	16	non	non	ADJ
ap-638	57	17	-	-	NOUN
ap-638	57	18	occurrence	occurrence	NOUN
ap-638	57	19	of	of	ADP
ap-638	57	20	analytical	analytical	ADJ
ap-638	57	21	solutions	solution	NOUN
ap-638	57	22	in	in	ADP
ap-638	57	23	the	the	DET
ap-638	57	24	case	case	NOUN
ap-638	57	25	of	of	ADP
ap-638	57	26	non	non	ADJ
ap-638	57	27	-	-	ADJ
ap-638	57	28	deterministic	deterministic	ADJ
ap-638	57	29	input	input	NOUN
ap-638	57	30	data	datum	NOUN
ap-638	57	31	.	.	PUNCT
ap-638	58	1	this	this	DET
ap-638	58	2	situation	situation	NOUN
ap-638	58	3	can	can	AUX
ap-638	58	4	be	be	AUX
ap-638	58	5	remedied	remedie	VERB
ap-638	58	6	by	by	ADP
ap-638	58	7	the	the	DET
ap-638	58	8	following	following	NOUN
ap-638	58	9	.	.	PUNCT
ap-638	59	1	let	let	VERB
ap-638	59	2	~	~	PUNCT
ap-638	59	3	~x	~x	PUNCT
ap-638	59	4	x	x	X
ap-638	59	5	�	�	PROPN
ap-638	59	6	denote	denote	VERB
ap-638	59	7	the	the	DET
ap-638	59	8	vector	vector	NOUN
ap-638	59	9	of	of	ADP
ap-638	59	10	input	input	NOUN
ap-638	59	11	data	datum	NOUN
ap-638	59	12	from	from	ADP
ap-638	59	13	the	the	DET
ap-638	59	14	space	space	NOUN
ap-638	59	15	of	of	ADP
ap-638	59	16	input	input	NOUN
ap-638	59	17	data	datum	NOUN
ap-638	59	18	~x	~x	PUNCT
ap-638	59	19	and	and	CCONJ
ap-638	59	20	~	~	PUNCT
ap-638	59	21	~y	~y	NUM
ap-638	59	22	y	y	PROPN
ap-638	59	23	�	�	PROPN
ap-638	59	24	denote	denote	VERB
ap-638	59	25	the	the	DET
ap-638	59	26	vector	vector	NOUN
ap-638	59	27	of	of	ADP
ap-638	59	28	output	output	NOUN
ap-638	59	29	data	datum	NOUN
ap-638	59	30	from	from	ADP
ap-638	59	31	the	the	DET
ap-638	59	32	space	space	NOUN
ap-638	59	33	of	of	ADP
ap-638	59	34	output	output	NOUN
ap-638	59	35	data	datum	NOUN
ap-638	59	36	~y	~y	NUM
ap-638	59	37	.	.	PUNCT
ap-638	60	1	both	both	PRON
ap-638	60	2	,	,	PUNCT
ap-638	60	3	stochastic	stochastic	ADJ
ap-638	60	4	and	and	CCONJ
ap-638	60	5	fuzzy	fuzzy	ADJ
ap-638	60	6	analyses	analysis	NOUN
ap-638	60	7	require	require	VERB
ap-638	60	8	knowledge	knowledge	NOUN
ap-638	60	9	of	of	ADP
ap-638	60	10	the	the	DET
ap-638	60	11	response	response	NOUN
ap-638	60	12	,	,	PUNCT
ap-638	60	13	which	which	PRON
ap-638	60	14	can	can	AUX
ap-638	60	15	be	be	AUX
ap-638	60	16	written	write	VERB
ap-638	60	17	in	in	ADP
ap-638	60	18	the	the	DET
ap-638	60	19	form	form	NOUN
ap-638	60	20	~	~	PUNCT
ap-638	60	21	(	(	PUNCT
ap-638	60	22	~)y	~)y	PUNCT
ap-638	60	23	x	x	SYM
ap-638	60	24	�	�	PROPN
ap-638	60	25	f	f	PROPN
ap-638	60	26	,	,	PUNCT
ap-638	60	27	(	(	PUNCT
ap-638	60	28	3	3	X
ap-638	60	29	)	)	PUNCT
ap-638	60	30	where	where	SCONJ
ap-638	60	31	f	f	PROPN
ap-638	60	32	denotes	denote	VERB
ap-638	60	33	the	the	DET
ap-638	60	34	response	response	NOUN
ap-638	60	35	of	of	ADP
ap-638	60	36	a	a	DET
ap-638	60	37	system	system	NOUN
ap-638	60	38	(	(	PUNCT
ap-638	60	39	structure	structure	NOUN
ap-638	60	40	)	)	PUNCT
ap-638	60	41	to	to	ADP
ap-638	60	42	the	the	DET
ap-638	60	43	input	input	NOUN
ap-638	60	44	data	datum	NOUN
ap-638	60	45	collected	collect	VERB
ap-638	60	46	in	in	ADP
ap-638	60	47	vector	vector	NOUN
ap-638	60	48	~x	~x	PUNCT
ap-638	60	49	.	.	PUNCT
ap-638	61	1	this	this	PRON
ap-638	61	2	represents	represent	VERB
ap-638	61	3	a	a	DET
ap-638	61	4	mapping	mapping	NOUN
ap-638	61	5	from	from	ADP
ap-638	61	6	the	the	DET
ap-638	61	7	space	space	NOUN
ap-638	61	8	~x	~x	PUNCT
ap-638	61	9	to	to	ADP
ap-638	61	10	the	the	DET
ap-638	61	11	space	space	NOUN
ap-638	61	12	~y	~y	NUM
ap-638	61	13	.	.	PUNCT
ap-638	62	1	the	the	DET
ap-638	62	2	non	non	NOUN
ap-638	62	3	-	-	NOUN
ap-638	62	4	occurrence	occurrence	NOUN
ap-638	62	5	of	of	ADP
ap-638	62	6	an	an	DET
ap-638	62	7	analytical	analytical	ADJ
ap-638	62	8	solution	solution	NOUN
ap-638	62	9	requires	require	VERB
ap-638	62	10	the	the	DET
ap-638	62	11	application	application	NOUN
ap-638	62	12	of	of	ADP
ap-638	62	13	a	a	DET
ap-638	62	14	suitable	suitable	ADJ
ap-638	62	15	numerical	numerical	ADJ
ap-638	62	16	method	method	NOUN
ap-638	62	17	which	which	PRON
ap-638	62	18	discretizes	discretize	VERB
ap-638	62	19	the	the	DET
ap-638	62	20	problem	problem	NOUN
ap-638	62	21	and	and	CCONJ
ap-638	62	22	solves	solve	VERB
ap-638	62	23	it	it	PRON
ap-638	62	24	numerically	numerically	ADV
ap-638	62	25	.	.	PUNCT
ap-638	63	1	the	the	DET
ap-638	63	2	space	space	NOUN
ap-638	63	3	~x	~x	PUNCT
ap-638	63	4	is	be	AUX
ap-638	63	5	discretized	discretize	VERB
ap-638	63	6	by	by	ADP
ap-638	63	7	an	an	DET
ap-638	63	8	n	n	ADV
ap-638	63	9	-	-	PUNCT
ap-638	63	10	dimensional	dimensional	ADJ
ap-638	63	11	space	space	NOUN
ap-638	63	12	,	,	PUNCT
ap-638	63	13	x	x	PRON
ap-638	63	14	,	,	PUNCT
ap-638	63	15	and	and	CCONJ
ap-638	63	16	similarly	similarly	ADV
ap-638	63	17	the	the	DET
ap-638	63	18	space	space	NOUN
ap-638	63	19	~y	~y	NUM
ap-638	63	20	by	by	ADP
ap-638	63	21	an	an	DET
ap-638	63	22	m	m	ADJ
ap-638	63	23	-	-	ADJ
ap-638	63	24	dimensional	dimensional	ADJ
ap-638	63	25	space	space	NOUN
ap-638	63	26	,	,	PUNCT
ap-638	63	27	y.	y.	NOUN
ap-638	63	28	a	a	DET
ap-638	63	29	stochastic	stochastic	ADJ
ap-638	63	30	analysis	analysis	NOUN
ap-638	63	31	based	base	VERB
ap-638	63	32	on	on	ADP
ap-638	63	33	simulation	simulation	NOUN
ap-638	63	34	methods	method	NOUN
ap-638	63	35	generates	generate	VERB
ap-638	63	36	thousands	thousand	NOUN
ap-638	63	37	or	or	CCONJ
ap-638	63	38	millions	million	NOUN
ap-638	63	39	of	of	ADP
ap-638	63	40	samples	sample	NOUN
ap-638	63	41	of	of	ADP
ap-638	63	42	input	input	NOUN
ap-638	63	43	data	datum	NOUN
ap-638	63	44	(	(	PUNCT
ap-638	63	45	the	the	DET
ap-638	63	46	vectors	vector	NOUN
ap-638	63	47	x	x	PRON
ap-638	63	48	)	)	PUNCT
ap-638	63	49	and	and	CCONJ
ap-638	63	50	then	then	ADV
ap-638	63	51	deterministic	deterministic	ADJ
ap-638	63	52	computation	computation	NOUN
ap-638	63	53	follows	follow	VERB
ap-638	63	54	.	.	PUNCT
ap-638	64	1	fuzzy	fuzzy	ADJ
ap-638	64	2	analysis	analysis	NOUN
ap-638	64	3	based	base	VERB
ap-638	64	4	on	on	ADP
ap-638	64	5	�	�	NOUN
ap-638	64	6	-cuts	-cut	NOUN
ap-638	64	7	requires	require	VERB
ap-638	64	8	computation	computation	NOUN
ap-638	64	9	of	of	ADP
ap-638	64	10	all	all	DET
ap-638	64	11	combinations	combination	NOUN
ap-638	64	12	of	of	ADP
ap-638	64	13	input	input	NOUN
ap-638	64	14	data	datum	NOUN
ap-638	64	15	,	,	PUNCT
ap-638	64	16	which	which	PRON
ap-638	64	17	also	also	ADV
ap-638	64	18	leads	lead	VERB
ap-638	64	19	to	to	ADP
ap-638	64	20	thousands	thousand	NOUN
ap-638	64	21	or	or	CCONJ
ap-638	64	22	millions	million	NOUN
ap-638	64	23	of	of	ADP
ap-638	64	24	samples	sample	NOUN
ap-638	64	25	.	.	PUNCT
ap-638	65	1	both	both	DET
ap-638	65	2	approaches	approach	NOUN
ap-638	65	3	yield	yield	VERB
ap-638	65	4	the	the	DET
ap-638	65	5	response	response	NOUN
ap-638	65	6	of	of	ADP
ap-638	65	7	a	a	DET
ap-638	65	8	system	system	NOUN
ap-638	65	9	based	base	VERB
ap-638	65	10	on	on	ADP
ap-638	65	11	a	a	DET
ap-638	65	12	huge	huge	ADJ
ap-638	65	13	amount	amount	NOUN
ap-638	65	14	of	of	ADP
ap-638	65	15	output	output	NOUN
ap-638	65	16	data	datum	NOUN
ap-638	65	17	(	(	PUNCT
ap-638	65	18	thousands	thousand	NOUN
ap-638	65	19	or	or	CCONJ
ap-638	65	20	millions	million	NOUN
ap-638	65	21	of	of	ADP
ap-638	65	22	vectors	vector	NOUN
ap-638	65	23	y	y	NOUN
ap-638	65	24	)	)	PUNCT
ap-638	65	25	obtained	obtain	VERB
ap-638	65	26	from	from	ADP
ap-638	65	27	many	many	ADJ
ap-638	65	28	executions	execution	NOUN
ap-638	65	29	of	of	ADP
ap-638	65	30	standard	standard	ADJ
ap-638	65	31	(	(	PUNCT
ap-638	65	32	deterministic	deterministic	ADJ
ap-638	65	33	or	or	CCONJ
ap-638	65	34	crisp	crisp	ADJ
ap-638	65	35	)	)	PUNCT
ap-638	65	36	solutions	solution	NOUN
ap-638	65	37	.	.	PUNCT
ap-638	66	1	in	in	ADP
ap-638	66	2	order	order	NOUN
ap-638	66	3	to	to	PART
ap-638	66	4	reduce	reduce	VERB
ap-638	66	5	the	the	DET
ap-638	66	6	necessary	necessary	ADJ
ap-638	66	7	number	number	NOUN
ap-638	66	8	of	of	ADP
ap-638	66	9	computation	computation	NOUN
ap-638	66	10	runs	run	NOUN
ap-638	66	11	,	,	PUNCT
ap-638	66	12	the	the	DET
ap-638	66	13	concept	concept	NOUN
ap-638	66	14	of	of	ADP
ap-638	66	15	a	a	DET
ap-638	66	16	response	response	NOUN
ap-638	66	17	surface	surface	NOUN
ap-638	66	18	function	function	NOUN
ap-638	66	19	has	have	AUX
ap-638	66	20	been	be	AUX
ap-638	66	21	used	use	VERB
ap-638	66	22	many	many	ADJ
ap-638	66	23	times	time	NOUN
ap-638	66	24	.	.	PUNCT
ap-638	67	1	the	the	DET
ap-638	67	2	basic	basic	ADJ
ap-638	67	3	idea	idea	NOUN
ap-638	67	4	of	of	ADP
ap-638	67	5	the	the	DET
ap-638	67	6	response	response	NOUN
ap-638	67	7	function	function	NOUN
ap-638	67	8	is	be	AUX
ap-638	67	9	to	to	PART
ap-638	67	10	approximate	approximate	VERB
ap-638	67	11	operator	operator	NOUN
ap-638	67	12	f	f	PROPN
ap-638	67	13	by	by	ADP
ap-638	67	14	a	a	DET
ap-638	67	15	suitable	suitable	ADJ
ap-638	67	16	function	function	NOUN
ap-638	67	17	which	which	PRON
ap-638	67	18	should	should	AUX
ap-638	67	19	be	be	AUX
ap-638	67	20	as	as	ADV
ap-638	67	21	simple	simple	ADJ
ap-638	67	22	as	as	ADP
ap-638	67	23	possible	possible	ADJ
ap-638	67	24	.	.	PUNCT
ap-638	68	1	the	the	DET
ap-638	68	2	function	function	NOUN
ap-638	68	3	for	for	ADP
ap-638	68	4	the	the	DET
ap-638	68	5	k	k	NOUN
ap-638	68	6	-	-	PUNCT
ap-638	68	7	th	th	VERB
ap-638	68	8	output	output	NOUN
ap-638	68	9	parameter	parameter	NOUN
ap-638	68	10	can	can	AUX
ap-638	68	11	be	be	AUX
ap-638	68	12	written	write	VERB
ap-638	68	13	in	in	ADP
ap-638	68	14	the	the	DET
ap-638	68	15	form	form	NOUN
ap-638	69	1	f	f	NOUN
ap-638	69	2	x	x	X
ap-638	69	3	a	a	DET
ap-638	69	4	b	b	X
ap-638	69	5	x	x	SYM
ap-638	69	6	c	c	NOUN
ap-638	69	7	x	x	SYM
ap-638	69	8	xk	xk	PROPN
ap-638	70	1	k	k	PROPN
ap-638	71	1	i	i	PRON
ap-638	71	2	k	k	INTJ
ap-638	72	1	i	i	PRON
ap-638	72	2	ij	ij	INTJ
ap-638	72	3	k	k	NOUN
ap-638	73	1	i	i	PRON
ap-638	73	2	j	j	PROPN
ap-638	74	1	j	j	PROPN
ap-638	74	2	n	n	CCONJ
ap-638	74	3	i	i	PRON
ap-638	74	4	n	n	VERB
ap-638	74	5	i	i	PRON
ap-638	74	6	n	n	PROPN
ap-638	74	7	(	(	PUNCT
ap-638	74	8	)	)	PUNCT
ap-638	74	9	(	(	PUNCT
ap-638	74	10	)	)	PUNCT
ap-638	74	11	(	(	PUNCT
ap-638	74	12	)	)	PUNCT
ap-638	74	13	(	(	PUNCT
ap-638	74	14	)	)	PUNCT
ap-638	74	15	(	(	PUNCT
ap-638	74	16	)	)	PUNCT
ap-638	74	17	�	�	PROPN
ap-638	74	18	�	�	PROPN
ap-638	74	19	�	�	PROPN
ap-638	74	20	�	�	PROPN
ap-638	74	21	�	�	PROPN
ap-638	74	22	�	�	PROPN
ap-638	74	23	�	�	PROPN
ap-638	74	24	�	�	PROPN
ap-638	74	25	�	�	PROPN
ap-638	74	26	111	111	NUM
ap-638	74	27	,	,	PUNCT
ap-638	74	28	(	(	PUNCT
ap-638	74	29	4	4	X
ap-638	74	30	)	)	PUNCT
ap-638	74	31	where	where	SCONJ
ap-638	74	32	the	the	DET
ap-638	74	33	superscript	superscript	PROPN
ap-638	74	34	identifies	identify	VERB
ap-638	74	35	an	an	DET
ap-638	74	36	output	output	NOUN
ap-638	74	37	parameter	parameter	NOUN
ap-638	74	38	and	and	CCONJ
ap-638	74	39	n	n	NOUN
ap-638	74	40	denotes	denote	VERB
ap-638	74	41	the	the	DET
ap-638	74	42	dimension	dimension	NOUN
ap-638	74	43	of	of	ADP
ap-638	74	44	the	the	DET
ap-638	74	45	space	space	NOUN
ap-638	74	46	of	of	ADP
ap-638	74	47	the	the	DET
ap-638	74	48	input	input	NOUN
ap-638	74	49	data	datum	NOUN
ap-638	74	50	,	,	PUNCT
ap-638	74	51	x.	x.	NOUN
ap-638	74	52	the	the	DET
ap-638	74	53	unknown	unknown	ADJ
ap-638	74	54	coefficients	coefficient	NOUN
ap-638	74	55	are	be	AUX
ap-638	74	56	obtained	obtain	VERB
ap-638	74	57	from	from	ADP
ap-638	74	58	the	the	DET
ap-638	74	59	least	least	ADJ
ap-638	74	60	square	square	ADJ
ap-638	74	61	method	method	NOUN
ap-638	74	62	in	in	ADP
ap-638	74	63	the	the	DET
ap-638	74	64	following	following	ADJ
ap-638	74	65	way	way	NOUN
ap-638	74	66	.	.	PUNCT
ap-638	75	1	let	let	VERB
ap-638	75	2	the	the	DET
ap-638	75	3	set	set	NOUN
ap-638	75	4	of	of	ADP
ap-638	75	5	input	input	NOUN
ap-638	75	6	parameters	parameter	NOUN
ap-638	75	7	contain	contain	VERB
ap-638	75	8	s	s	NOUN
ap-638	75	9	samples	sample	NOUN
ap-638	75	10	.	.	PUNCT
ap-638	76	1	each	each	DET
ap-638	76	2	sample	sample	NOUN
ap-638	76	3	is	be	AUX
ap-638	76	4	located	locate	VERB
ap-638	76	5	in	in	ADP
ap-638	76	6	the	the	DET
ap-638	76	7	vector	vector	NOUN
ap-638	76	8	x	x	PUNCT
ap-638	77	1	[	[	X
ap-638	77	2	i	i	X
ap-638	77	3	]	]	X
ap-638	77	4	,	,	PUNCT
ap-638	77	5	where	where	SCONJ
ap-638	77	6	the	the	DET
ap-638	77	7	superscript	superscript	PROPN
ap-638	77	8	identifies	identify	VERB
ap-638	77	9	a	a	DET
ap-638	77	10	sample	sample	NOUN
ap-638	77	11	.	.	PUNCT
ap-638	78	1	the	the	DET
ap-638	78	2	standard	standard	ADJ
ap-638	78	3	computation	computation	NOUN
ap-638	78	4	gives	give	VERB
ap-638	78	5	the	the	DET
ap-638	78	6	output	output	NOUN
ap-638	78	7	data	datum	NOUN
ap-638	78	8	,	,	PUNCT
ap-638	78	9	which	which	PRON
ap-638	78	10	are	be	AUX
ap-638	78	11	collected	collect	VERB
ap-638	78	12	in	in	ADP
ap-638	78	13	the	the	DET
ap-638	78	14	vectors	vector	NOUN
ap-638	79	1	y	y	PROPN
ap-638	80	1	[	[	X
ap-638	80	2	i	i	X
ap-638	80	3	]	]	X
ap-638	80	4	.	.	PUNCT
ap-638	81	1	the	the	DET
ap-638	81	2	coefficients	coefficient	NOUN
ap-638	81	3	of	of	ADP
ap-638	81	4	the	the	DET
ap-638	81	5	response	response	NOUN
ap-638	81	6	function	function	NOUN
ap-638	81	7	minimize	minimize	VERB
ap-638	81	8	the	the	DET
ap-638	81	9	following	follow	VERB
ap-638	81	10	expression	expression	NOUN
ap-638	81	11	�	�	PROPN
ap-638	81	12	�	�	PROPN
ap-638	81	13	f	f	PROPN
ap-638	81	14	a	a	DET
ap-638	81	15	b	b	NOUN
ap-638	82	1	c	c	X
ap-638	82	2	f	f	PROPN
ap-638	82	3	yk	yk	PROPN
ap-638	83	1	k	k	PROPN
ap-638	84	1	i	i	PRON
ap-638	84	2	k	k	INTJ
ap-638	85	1	ij	ij	INTJ
ap-638	86	1	k	k	PROPN
ap-638	86	2	k	k	PROPN
ap-638	87	1	i	i	PRON
ap-638	87	2	k	k	INTJ
ap-638	88	1	i	i	PRON
ap-638	88	2	i	i	PRON
ap-638	88	3	s	s	X
ap-638	88	4	(	(	PUNCT
ap-638	88	5	)	)	PUNCT
ap-638	88	6	(	(	PUNCT
ap-638	88	7	)	)	PUNCT
ap-638	88	8	(	(	PUNCT
ap-638	88	9	)	)	PUNCT
ap-638	88	10	(	(	PUNCT
ap-638	88	11	)	)	PUNCT
ap-638	88	12	(	(	PUNCT
ap-638	88	13	)	)	PUNCT
ap-638	89	1	[	[	PUNCT
ap-638	89	2	]	]	X
ap-638	89	3	[	[	PUNCT
ap-638	89	4	]	]	X
ap-638	89	5	(	(	PUNCT
ap-638	89	6	,	,	PUNCT
ap-638	89	7	,	,	PUNCT
ap-638	89	8	)	)	PUNCT
ap-638	89	9	(	(	PUNCT
ap-638	89	10	)	)	PUNCT
ap-638	89	11	�	�	PROPN
ap-638	89	12	�	�	PROPN
ap-638	89	13	�	�	PROPN
ap-638	89	14	�	�	PROPN
ap-638	89	15	x	x	PROPN
ap-638	89	16	2	2	NUM
ap-638	89	17	1	1	NUM
ap-638	89	18	.	.	PUNCT
ap-638	90	1	(	(	PUNCT
ap-638	90	2	5	5	NUM
ap-638	90	3	)	)	PUNCT
ap-638	90	4	in	in	ADP
ap-638	90	5	many	many	ADJ
ap-638	90	6	cases	case	NOUN
ap-638	90	7	,	,	PUNCT
ap-638	90	8	it	it	PRON
ap-638	90	9	is	be	AUX
ap-638	90	10	not	not	PART
ap-638	90	11	necessary	necessary	ADJ
ap-638	90	12	to	to	PART
ap-638	90	13	use	use	VERB
ap-638	90	14	quadratic	quadratic	ADJ
ap-638	90	15	terms	term	NOUN
ap-638	90	16	.	.	PUNCT
ap-638	91	1	considering	consider	VERB
ap-638	91	2	only	only	ADV
ap-638	91	3	the	the	DET
ap-638	91	4	linear	linear	ADJ
ap-638	91	5	terms	term	NOUN
ap-638	91	6	simplifies	simplify	VERB
ap-638	91	7	further	further	ADJ
ap-638	91	8	computations	computation	NOUN
ap-638	91	9	.	.	PUNCT
ap-638	92	1	4	4	NUM
ap-638	92	2	numerical	numerical	ADJ
ap-638	92	3	example	example	NOUN
ap-638	92	4	as	as	ADP
ap-638	92	5	an	an	DET
ap-638	92	6	example	example	NOUN
ap-638	92	7	,	,	PUNCT
ap-638	92	8	the	the	DET
ap-638	92	9	natural	natural	ADJ
ap-638	92	10	frequency	frequency	NOUN
ap-638	92	11	analysis	analysis	NOUN
ap-638	92	12	of	of	ADP
ap-638	92	13	a	a	DET
ap-638	92	14	two	two	NUM
ap-638	92	15	-	-	PUNCT
ap-638	92	16	dimensional	dimensional	ADJ
ap-638	92	17	frame	frame	NOUN
ap-638	92	18	with	with	ADP
ap-638	92	19	four	four	NUM
ap-638	92	20	floors	floor	NOUN
ap-638	92	21	made	make	VERB
ap-638	92	22	of	of	ADP
ap-638	92	23	reinforced	reinforce	VERB
ap-638	92	24	concrete	concrete	NOUN
ap-638	92	25	is	be	AUX
ap-638	92	26	considered	consider	VERB
ap-638	92	27	.	.	PUNCT
ap-638	93	1	the	the	DET
ap-638	93	2	overall	overall	ADJ
ap-638	93	3	height	height	NOUN
ap-638	93	4	of	of	ADP
ap-638	93	5	the	the	DET
ap-638	93	6	frame	frame	NOUN
ap-638	93	7	is	be	AUX
ap-638	93	8	16	16	NUM
ap-638	93	9	meters	meter	NOUN
ap-638	93	10	and	and	CCONJ
ap-638	93	11	the	the	DET
ap-638	93	12	width	width	NOUN
ap-638	93	13	is	be	AUX
ap-638	93	14	5	5	NUM
ap-638	93	15	+	+	SYM
ap-638	93	16	5	5	NUM
ap-638	93	17	meters	meter	NOUN
ap-638	93	18	.	.	PUNCT
ap-638	94	1	the	the	DET
ap-638	94	2	dimensions	dimension	NOUN
ap-638	94	3	of	of	ADP
ap-638	94	4	the	the	DET
ap-638	94	5	beams	beam	NOUN
ap-638	94	6	and	and	CCONJ
ap-638	94	7	columns	column	NOUN
ap-638	94	8	are	be	AUX
ap-638	94	9	identical	identical	ADJ
ap-638	94	10	(	(	PUNCT
ap-638	94	11	0.5×0.5	0.5×0.5	NUM
ap-638	94	12	m	m	NOUN
ap-638	94	13	)	)	PUNCT
ap-638	94	14	.	.	PUNCT
ap-638	95	1	it	it	PRON
ap-638	95	2	is	be	AUX
ap-638	95	3	assumed	assume	VERB
ap-638	95	4	that	that	SCONJ
ap-638	95	5	the	the	DET
ap-638	95	6	building	building	NOUN
ap-638	95	7	was	be	AUX
ap-638	95	8	erected	erect	VERB
ap-638	95	9	in	in	ADP
ap-638	95	10	four	four	NUM
ap-638	95	11	consecutive	consecutive	ADJ
ap-638	95	12	lifts	lift	NOUN
ap-638	95	13	.	.	PUNCT
ap-638	96	1	each	each	DET
ap-638	96	2	lift	lift	NOUN
ap-638	96	3	consists	consist	VERB
ap-638	96	4	of	of	ADP
ap-638	96	5	placing	place	VERB
ap-638	96	6	concrete	concrete	NOUN
ap-638	96	7	in	in	ADP
ap-638	96	8	three	three	NUM
ap-638	96	9	columns	column	NOUN
ap-638	96	10	and	and	CCONJ
ap-638	96	11	in	in	ADP
ap-638	96	12	the	the	DET
ap-638	96	13	beam	beam	NOUN
ap-638	96	14	which	which	PRON
ap-638	96	15	connects	connect	VERB
ap-638	96	16	the	the	DET
ap-638	96	17	upper	upper	ADJ
ap-638	96	18	ends	end	NOUN
ap-638	96	19	of	of	ADP
ap-638	96	20	the	the	DET
ap-638	96	21	columns	column	NOUN
ap-638	96	22	.	.	PUNCT
ap-638	97	1	118	118	NUM
ap-638	97	2	©	©	PROPN
ap-638	97	3	czech	czech	PROPN
ap-638	97	4	technical	technical	PROPN
ap-638	97	5	university	university	PROPN
ap-638	97	6	publishing	publishing	NOUN
ap-638	97	7	house	house	NOUN
ap-638	97	8	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-638	97	9	acta	acta	PROPN
ap-638	97	10	polytechnica	polytechnica	PROPN
ap-638	97	11	vol	vol	NOUN
ap-638	97	12	.	.	PROPN
ap-638	98	1	44	44	NUM
ap-638	98	2	no	no	NOUN
ap-638	98	3	.	.	PUNCT
ap-638	99	1	5–6/2004	5–6/2004	NUM
ap-638	99	2	.	.	PUNCT
ap-638	99	3	.	.	PUNCT
ap-638	99	4	.	.	PUNCT
ap-638	100	1	fig	fig	NOUN
ap-638	100	2	.	.	PUNCT
ap-638	101	1	1	1	NUM
ap-638	101	2	:	:	PUNCT
ap-638	101	3	a	a	DET
ap-638	101	4	normal	normal	ADJ
ap-638	101	5	fuzzy	fuzzy	ADJ
ap-638	101	6	number	number	NOUN
ap-638	101	7	and	and	CCONJ
ap-638	101	8	its	its	PRON
ap-638	101	9	�	�	NOUN
ap-638	101	10	-cuts	-cut	NOUN
ap-638	101	11	therefore	therefore	ADV
ap-638	101	12	,	,	PUNCT
ap-638	101	13	it	it	PRON
ap-638	101	14	is	be	AUX
ap-638	101	15	further	far	ADV
ap-638	101	16	assumed	assume	VERB
ap-638	101	17	that	that	SCONJ
ap-638	101	18	there	there	PRON
ap-638	101	19	are	be	VERB
ap-638	101	20	only	only	ADV
ap-638	101	21	four	four	NUM
ap-638	101	22	types	type	NOUN
ap-638	101	23	of	of	ADP
ap-638	101	24	concrete	concrete	NOUN
ap-638	101	25	whose	whose	DET
ap-638	101	26	composition	composition	NOUN
ap-638	101	27	can	can	AUX
ap-638	101	28	possibly	possibly	ADV
ap-638	101	29	differ	differ	VERB
ap-638	101	30	.	.	PUNCT
ap-638	102	1	the	the	DET
ap-638	102	2	influencing	influence	VERB
ap-638	102	3	material	material	NOUN
ap-638	102	4	parameters	parameter	NOUN
ap-638	102	5	are	be	AUX
ap-638	102	6	the	the	DET
ap-638	102	7	modulus	modulus	NOUN
ap-638	102	8	of	of	ADP
ap-638	102	9	elasticity	elasticity	NOUN
ap-638	102	10	,	,	PUNCT
ap-638	102	11	e	e	NOUN
ap-638	102	12	and	and	CCONJ
ap-638	102	13	the	the	DET
ap-638	102	14	density	density	NOUN
ap-638	102	15	,	,	PUNCT
ap-638	102	16	�	�	PROPN
ap-638	102	17	.	.	PUNCT
ap-638	103	1	e	e	PROPN
ap-638	103	2	and	and	CCONJ
ap-638	103	3	�	�	PROPN
ap-638	103	4	are	be	AUX
ap-638	103	5	fuzzy	fuzzy	ADJ
ap-638	103	6	input	input	NOUN
ap-638	103	7	parameters	parameter	NOUN
ap-638	103	8	with	with	ADP
ap-638	103	9	nominal	nominal	ADJ
ap-638	103	10	values	value	NOUN
ap-638	103	11	of	of	ADP
ap-638	103	12	30	30	NUM
ap-638	103	13	gpa	gpa	NOUN
ap-638	103	14	and	and	CCONJ
ap-638	103	15	2500	2500	NUM
ap-638	103	16	kg	kg	NOUN
ap-638	103	17	/	/	SYM
ap-638	103	18	m3	m3	PROPN
ap-638	103	19	,	,	PUNCT
ap-638	103	20	respectively	respectively	ADV
ap-638	103	21	,	,	PUNCT
ap-638	103	22	which	which	PRON
ap-638	103	23	can	can	AUX
ap-638	103	24	change	change	VERB
ap-638	103	25	by	by	ADP
ap-638	103	26	�	�	PROPN
ap-638	103	27	10	10	NUM
ap-638	103	28	%	%	NOUN
ap-638	103	29	and	and	CCONJ
ap-638	103	30	with	with	ADP
ap-638	103	31	a	a	DET
ap-638	103	32	linear	linear	ADJ
ap-638	103	33	membership	membership	NOUN
ap-638	103	34	function	function	NOUN
ap-638	103	35	(	(	PUNCT
ap-638	103	36	triangular	triangular	NOUN
ap-638	103	37	fuzzy	fuzzy	ADJ
ap-638	103	38	numbers	number	NOUN
ap-638	103	39	)	)	PUNCT
ap-638	103	40	.	.	PUNCT
ap-638	104	1	©	©	PROPN
ap-638	104	2	czech	czech	PROPN
ap-638	104	3	technical	technical	PROPN
ap-638	104	4	university	university	PROPN
ap-638	104	5	publishing	publishing	NOUN
ap-638	104	6	house	house	NOUN
ap-638	104	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-638	104	8	119	119	NUM
ap-638	104	9	acta	acta	PROPN
ap-638	104	10	polytechnica	polytechnica	PROPN
ap-638	104	11	vol	vol	NOUN
ap-638	104	12	.	.	PROPN
ap-638	105	1	44	44	NUM
ap-638	105	2	no	no	NOUN
ap-638	105	3	.	.	PUNCT
ap-638	106	1	5–6/2004	5–6/2004	NUM
ap-638	106	2	fig	fig	NOUN
ap-638	106	3	.	.	PUNCT
ap-638	107	1	2	2	NUM
ap-638	107	2	:	:	PUNCT
ap-638	107	3	mode	mode	NOUN
ap-638	107	4	shape	shape	NOUN
ap-638	107	5	fig	fig	NOUN
ap-638	107	6	.	.	PUNCT
ap-638	108	1	3	3	NUM
ap-638	108	2	:	:	PUNCT
ap-638	108	3	enlarged	enlarge	VERB
ap-638	108	4	section	section	NOUN
ap-638	108	5	of	of	ADP
ap-638	108	6	mode	mode	NOUN
ap-638	108	7	shape	shape	NOUN
ap-638	108	8	1	1	NUM
ap-638	108	9	fig	fig	NOUN
ap-638	108	10	.	.	PUNCT
ap-638	109	1	4	4	NUM
ap-638	109	2	:	:	PUNCT
ap-638	109	3	mode	mode	NOUN
ap-638	109	4	shape	shape	NOUN
ap-638	109	5	2	2	NUM
ap-638	109	6	fig	fig	NOUN
ap-638	109	7	.	.	PUNCT
ap-638	110	1	5	5	NUM
ap-638	110	2	:	:	PUNCT
ap-638	110	3	mode	mode	NOUN
ap-638	110	4	shape	shape	NOUN
ap-638	110	5	3	3	NUM
ap-638	110	6	fig	fig	NOUN
ap-638	110	7	.	.	PUNCT
ap-638	111	1	6	6	NUM
ap-638	111	2	:	:	PUNCT
ap-638	111	3	mode	mode	NOUN
ap-638	111	4	shape	shape	NOUN
ap-638	111	5	4	4	NUM
ap-638	111	6	fig	fig	NOUN
ap-638	111	7	.	.	PUNCT
ap-638	112	1	7	7	NUM
ap-638	112	2	:	:	PUNCT
ap-638	112	3	mode	mode	NOUN
ap-638	112	4	shape	shape	NOUN
ap-638	112	5	5	5	NUM
ap-638	112	6	for	for	ADP
ap-638	112	7	illustrative	illustrative	ADJ
ap-638	112	8	purposes	purpose	NOUN
ap-638	112	9	,	,	PUNCT
ap-638	112	10	we	we	PRON
ap-638	112	11	need	need	VERB
ap-638	112	12	125	125	NUM
ap-638	112	13	response	response	NOUN
ap-638	112	14	surface	surface	NOUN
ap-638	112	15	functions	function	NOUN
ap-638	112	16	to	to	PART
ap-638	112	17	describe	describe	VERB
ap-638	112	18	the	the	DET
ap-638	112	19	first	first	ADJ
ap-638	112	20	five	five	NUM
ap-638	112	21	natural	natural	ADJ
ap-638	112	22	vibration	vibration	NOUN
ap-638	112	23	modes	mode	NOUN
ap-638	112	24	,	,	PUNCT
ap-638	112	25	i.e.	i.e.	X
ap-638	112	26	a	a	DET
ap-638	112	27	response	response	NOUN
ap-638	112	28	surface	surface	NOUN
ap-638	112	29	function	function	NOUN
ap-638	112	30	to	to	PART
ap-638	112	31	express	express	VERB
ap-638	112	32	each	each	DET
ap-638	112	33	natural	natural	ADJ
ap-638	112	34	frequency	frequency	NOUN
ap-638	112	35	and	and	CCONJ
ap-638	112	36	the	the	DET
ap-638	112	37	horizontal	horizontal	ADJ
ap-638	112	38	and	and	CCONJ
ap-638	112	39	vertical	vertical	ADJ
ap-638	112	40	displacements	displacement	NOUN
ap-638	112	41	in	in	ADP
ap-638	112	42	each	each	DET
ap-638	112	43	joint	joint	NOUN
ap-638	112	44	(	(	PUNCT
ap-638	112	45	three	three	NUM
ap-638	112	46	joints	joint	NOUN
ap-638	112	47	on	on	ADP
ap-638	112	48	each	each	PRON
ap-638	112	49	of	of	ADP
ap-638	112	50	the	the	DET
ap-638	112	51	four	four	NUM
ap-638	112	52	floors	floor	NOUN
ap-638	112	53	)	)	PUNCT
ap-638	112	54	for	for	ADP
ap-638	112	55	each	each	DET
ap-638	112	56	natural	natural	ADJ
ap-638	112	57	mode	mode	NOUN
ap-638	112	58	shape	shape	NOUN
ap-638	112	59	.	.	PUNCT
ap-638	113	1	in	in	ADP
ap-638	113	2	order	order	NOUN
ap-638	113	3	to	to	PART
ap-638	113	4	obtain	obtain	VERB
ap-638	113	5	sufficient	sufficient	ADJ
ap-638	113	6	input	input	NOUN
ap-638	113	7	and	and	CCONJ
ap-638	113	8	output	output	NOUN
ap-638	113	9	data	datum	NOUN
ap-638	113	10	for	for	ADP
ap-638	113	11	calculation	calculation	NOUN
ap-638	113	12	of	of	ADP
ap-638	113	13	the	the	DET
ap-638	113	14	coefficients	coefficient	NOUN
ap-638	113	15	of	of	ADP
ap-638	113	16	the	the	DET
ap-638	113	17	response	response	NOUN
ap-638	113	18	surface	surface	NOUN
ap-638	113	19	functions	function	NOUN
ap-638	113	20	it	it	PRON
ap-638	113	21	was	be	AUX
ap-638	113	22	decided	decide	VERB
ap-638	113	23	to	to	PART
ap-638	113	24	take	take	VERB
ap-638	113	25	three	three	NUM
ap-638	113	26	values	value	NOUN
ap-638	113	27	(	(	PUNCT
ap-638	113	28	minimum	minimum	ADJ
ap-638	113	29	,	,	PUNCT
ap-638	113	30	modal	modal	ADJ
ap-638	113	31	value	value	NOUN
ap-638	113	32	,	,	PUNCT
ap-638	113	33	maximum	maximum	ADJ
ap-638	113	34	)	)	PUNCT
ap-638	113	35	for	for	ADP
ap-638	113	36	each	each	DET
ap-638	113	37	material	material	NOUN
ap-638	113	38	parameter	parameter	NOUN
ap-638	113	39	,	,	PUNCT
ap-638	113	40	e	e	PROPN
ap-638	113	41	and	and	CCONJ
ap-638	113	42	�	�	PROPN
ap-638	113	43	,	,	PUNCT
ap-638	113	44	i.e.	i.e.	X
ap-638	113	45	,	,	PUNCT
ap-638	113	46	(	(	PUNCT
ap-638	113	47	�	�	PROPN
ap-638	113	48	6561	6561	NUM
ap-638	113	49	)	)	PUNCT
ap-638	113	50	independent	independent	ADJ
ap-638	113	51	runs	run	NOUN
ap-638	113	52	of	of	ADP
ap-638	113	53	the	the	DET
ap-638	113	54	dynamic	dynamic	ADJ
ap-638	113	55	finite	finite	NOUN
ap-638	113	56	element	element	NOUN
ap-638	113	57	analysis	analysis	NOUN
ap-638	113	58	.	.	PUNCT
ap-638	114	1	the	the	DET
ap-638	114	2	specific	specific	ADJ
ap-638	114	3	form	form	NOUN
ap-638	114	4	of	of	ADP
ap-638	114	5	eq	eq	PROPN
ap-638	114	6	.	.	PUNCT
ap-638	114	7	(	(	PUNCT
ap-638	114	8	4	4	NUM
ap-638	114	9	)	)	PUNCT
ap-638	114	10	in	in	ADP
ap-638	114	11	this	this	DET
ap-638	114	12	example	example	NOUN
ap-638	114	13	was	be	AUX
ap-638	114	14	f	f	PROPN
ap-638	114	15	x	x	SYM
ap-638	114	16	b	b	PROPN
ap-638	114	17	e	e	X
ap-638	114	18	b	b	PROPN
ap-638	114	19	e	e	X
ap-638	114	20	b	b	PROPN
ap-638	114	21	e	e	X
ap-638	114	22	b	b	PROPN
ap-638	114	23	e	e	PROPN
ap-638	114	24	b	b	PROPN
ap-638	114	25	b	b	X
ap-638	115	1	k	k	PROPN
ap-638	115	2	k	k	PROPN
ap-638	116	1	k	k	PROPN
ap-638	116	2	k	k	PROPN
ap-638	116	3	k	k	PROPN
ap-638	116	4	k	k	PROPN
ap-638	116	5	(	(	PUNCT
ap-638	116	6	)	)	PUNCT
ap-638	116	7	(	(	PUNCT
ap-638	116	8	)	)	PUNCT
ap-638	116	9	(	(	PUNCT
ap-638	116	10	)	)	PUNCT
ap-638	116	11	(	(	PUNCT
ap-638	116	12	)	)	PUNCT
ap-638	116	13	(	(	PUNCT
ap-638	116	14	)	)	PUNCT
ap-638	116	15	(	(	PUNCT
ap-638	116	16	)	)	PUNCT
ap-638	116	17	(	(	PUNCT
ap-638	116	18	)	)	PUNCT
ap-638	116	19	�	�	PROPN
ap-638	116	20	�	�	PROPN
ap-638	116	21	�	�	PROPN
ap-638	116	22	�	�	PROPN
ap-638	116	23	�	�	PROPN
ap-638	116	24	�	�	PROPN
ap-638	116	25	�	�	PROPN
ap-638	116	26	1	1	NUM
ap-638	116	27	1	1	NUM
ap-638	116	28	2	2	NUM
ap-638	116	29	2	2	NUM
ap-638	116	30	3	3	NUM
ap-638	116	31	3	3	NUM
ap-638	116	32	4	4	NUM
ap-638	116	33	4	4	NUM
ap-638	116	34	5	5	NUM
ap-638	116	35	1	1	NUM
ap-638	116	36	�	�	PROPN
ap-638	116	37	6	6	NUM
ap-638	116	38	2	2	NUM
ap-638	116	39	7	7	NUM
ap-638	116	40	3	3	NUM
ap-638	116	41	8	8	NUM
ap-638	116	42	4	4	NUM
ap-638	116	43	9	9	NUM
ap-638	116	44	(	(	PUNCT
ap-638	116	45	)	)	PUNCT
ap-638	116	46	(	(	PUNCT
ap-638	116	47	)	)	PUNCT
ap-638	116	48	(	(	PUNCT
ap-638	116	49	)	)	PUNCT
ap-638	116	50	(	(	PUNCT
ap-638	116	51	)	)	PUNCT
ap-638	116	52	.k	.k	PROPN
ap-638	117	1	k	k	PROPN
ap-638	118	1	k	k	PROPN
ap-638	118	2	kb	kb	PROPN
ap-638	118	3	b	b	PROPN
ap-638	118	4	b	b	PROPN
ap-638	118	5	�	�	PROPN
ap-638	118	6	�	�	PROPN
ap-638	118	7	�	�	PROPN
ap-638	118	8	�	�	PROPN
ap-638	118	9	�	�	PROPN
ap-638	118	10	�	�	PROPN
ap-638	118	11	(	(	PUNCT
ap-638	118	12	6	6	NUM
ap-638	118	13	)	)	PUNCT
ap-638	118	14	the	the	DET
ap-638	118	15	first	first	ADJ
ap-638	118	16	five	five	NUM
ap-638	118	17	mode	mode	NOUN
ap-638	118	18	shapes	shape	NOUN
ap-638	118	19	are	be	AUX
ap-638	118	20	shown	show	VERB
ap-638	118	21	in	in	ADP
ap-638	118	22	figs	fig	NOUN
ap-638	118	23	.	.	PUNCT
ap-638	119	1	2	2	NUM
ap-638	119	2	to	to	ADP
ap-638	119	3	7	7	NUM
ap-638	119	4	,	,	PUNCT
ap-638	119	5	where	where	SCONJ
ap-638	119	6	the	the	DET
ap-638	119	7	dotted	dotted	ADJ
ap-638	119	8	lines	line	NOUN
ap-638	119	9	represent	represent	VERB
ap-638	119	10	all	all	DET
ap-638	119	11	possible	possible	ADJ
ap-638	119	12	envelopes	envelope	NOUN
ap-638	119	13	of	of	ADP
ap-638	119	14	response	response	NOUN
ap-638	119	15	,	,	PUNCT
ap-638	119	16	in	in	ADP
ap-638	119	17	other	other	ADJ
ap-638	119	18	words	word	NOUN
ap-638	119	19	,	,	PUNCT
ap-638	119	20	the	the	DET
ap-638	119	21	minimum	minimum	ADJ
ap-638	119	22	and	and	CCONJ
ap-638	119	23	maximum	maximum	ADJ
ap-638	119	24	values	value	NOUN
ap-638	119	25	,	,	PUNCT
ap-638	119	26	which	which	PRON
ap-638	119	27	correspond	correspond	VERB
ap-638	119	28	to	to	ADP
ap-638	119	29	the	the	DET
ap-638	119	30	values	value	NOUN
ap-638	119	31	obtained	obtain	VERB
ap-638	119	32	for	for	ADP
ap-638	119	33	�	�	NOUN
ap-638	119	34	-cuts	-cut	NOUN
ap-638	119	35	(	(	PUNCT
ap-638	119	36	�	�	PROPN
ap-638	119	37	�	�	PROPN
ap-638	119	38	0	0	NUM
ap-638	119	39	)	)	PUNCT
ap-638	119	40	.	.	PUNCT
ap-638	120	1	the	the	DET
ap-638	120	2	finite	finite	PROPN
ap-638	120	3	element	element	NOUN
ap-638	120	4	model	model	NOUN
ap-638	120	5	of	of	ADP
ap-638	120	6	this	this	DET
ap-638	120	7	frame	frame	NOUN
ap-638	120	8	discretized	discretize	VERB
ap-638	120	9	each	each	DET
ap-638	120	10	frame	frame	NOUN
ap-638	120	11	section	section	NOUN
ap-638	120	12	(	(	PUNCT
ap-638	120	13	beam	beam	NOUN
ap-638	120	14	and	and	CCONJ
ap-638	120	15	column	column	NOUN
ap-638	120	16	)	)	PUNCT
ap-638	120	17	by	by	ADP
ap-638	120	18	five	five	NUM
ap-638	120	19	beam	beam	NOUN
ap-638	120	20	elements	element	NOUN
ap-638	120	21	,	,	PUNCT
ap-638	120	22	however	however	ADV
ap-638	120	23	,	,	PUNCT
ap-638	120	24	only	only	ADV
ap-638	120	25	the	the	DET
ap-638	120	26	joint	joint	ADJ
ap-638	120	27	displacements	displacement	NOUN
ap-638	120	28	are	be	AUX
ap-638	120	29	shown	show	VERB
ap-638	120	30	.	.	PUNCT
ap-638	121	1	this	this	PRON
ap-638	121	2	is	be	AUX
ap-638	121	3	why	why	SCONJ
ap-638	121	4	no	no	DET
ap-638	121	5	significant	significant	ADJ
ap-638	121	6	difference	difference	NOUN
ap-638	121	7	is	be	AUX
ap-638	121	8	distinguishable	distinguishable	ADJ
ap-638	121	9	in	in	ADP
ap-638	121	10	figs	fig	NOUN
ap-638	121	11	.	.	PUNCT
ap-638	122	1	6	6	NUM
ap-638	122	2	and	and	CCONJ
ap-638	122	3	7	7	NUM
ap-638	122	4	.	.	PUNCT
ap-638	123	1	in	in	ADP
ap-638	123	2	fig	fig	NOUN
ap-638	123	3	.	.	PUNCT
ap-638	124	1	3	3	NUM
ap-638	124	2	,	,	PUNCT
ap-638	124	3	a	a	DET
ap-638	124	4	section	section	NOUN
ap-638	124	5	of	of	ADP
ap-638	124	6	the	the	DET
ap-638	124	7	frame	frame	NOUN
ap-638	124	8	is	be	AUX
ap-638	124	9	enlarged	enlarge	VERB
ap-638	124	10	and	and	CCONJ
ap-638	124	11	the	the	DET
ap-638	124	12	vertical	vertical	ADJ
ap-638	124	13	displacements	displacement	NOUN
ap-638	124	14	are	be	AUX
ap-638	124	15	1000	1000	NUM
ap-638	124	16	times	time	NOUN
ap-638	124	17	increased	increase	VERB
ap-638	124	18	compared	compare	VERB
ap-638	124	19	to	to	ADP
ap-638	124	20	the	the	DET
ap-638	124	21	horizontal	horizontal	ADJ
ap-638	124	22	displacements	displacement	NOUN
ap-638	124	23	so	so	SCONJ
ap-638	124	24	that	that	SCONJ
ap-638	124	25	we	we	PRON
ap-638	124	26	can	can	AUX
ap-638	124	27	see	see	VERB
ap-638	124	28	the	the	DET
ap-638	124	29	distribution	distribution	NOUN
ap-638	124	30	of	of	ADP
ap-638	124	31	possible	possible	ADJ
ap-638	124	32	displacements	displacement	NOUN
ap-638	124	33	of	of	ADP
ap-638	124	34	the	the	DET
ap-638	124	35	frame	frame	NOUN
ap-638	124	36	.	.	PUNCT
ap-638	125	1	the	the	DET
ap-638	125	2	distribution	distribution	NOUN
ap-638	125	3	of	of	ADP
ap-638	125	4	the	the	DET
ap-638	125	5	first	first	ADJ
ap-638	125	6	five	five	NUM
ap-638	125	7	natural	natural	ADJ
ap-638	125	8	frequencies	frequency	NOUN
ap-638	125	9	is	be	AUX
ap-638	125	10	shown	show	VERB
ap-638	125	11	in	in	ADP
ap-638	125	12	fig	fig	NOUN
ap-638	125	13	.	.	PUNCT
ap-638	126	1	8	8	X
ap-638	126	2	.	.	PUNCT
ap-638	127	1	it	it	PRON
ap-638	127	2	was	be	AUX
ap-638	127	3	observed	observe	VERB
ap-638	127	4	that	that	SCONJ
ap-638	127	5	the	the	DET
ap-638	127	6	response	response	NOUN
ap-638	127	7	function	function	NOUN
ap-638	127	8	gives	give	VERB
ap-638	127	9	very	very	ADV
ap-638	127	10	good	good	ADJ
ap-638	127	11	results	result	NOUN
ap-638	127	12	for	for	ADP
ap-638	127	13	the	the	DET
ap-638	127	14	dominant	dominant	ADJ
ap-638	127	15	displacements	displacement	NOUN
ap-638	127	16	(	(	PUNCT
ap-638	127	17	at	at	ADP
ap-638	127	18	point	point	NOUN
ap-638	127	19	a	a	PRON
ap-638	127	20	,	,	PUNCT
ap-638	127	21	which	which	PRON
ap-638	127	22	is	be	AUX
ap-638	127	23	the	the	DET
ap-638	127	24	top	top	ADJ
ap-638	127	25	left	left	ADJ
ap-638	127	26	joint	joint	NOUN
ap-638	127	27	)	)	PUNCT
ap-638	127	28	in	in	ADP
ap-638	127	29	the	the	DET
ap-638	127	30	lower	low	ADJ
ap-638	127	31	natural	natural	ADJ
ap-638	127	32	mode	mode	NOUN
ap-638	127	33	shapes	shape	NOUN
ap-638	127	34	,	,	PUNCT
ap-638	127	35	which	which	PRON
ap-638	127	36	are	be	AUX
ap-638	127	37	important	important	ADJ
ap-638	127	38	for	for	ADP
ap-638	127	39	seismic	seismic	ADJ
ap-638	127	40	design	design	NOUN
ap-638	127	41	.	.	PUNCT
ap-638	128	1	for	for	ADP
ap-638	128	2	vertical	vertical	ADJ
ap-638	128	3	displacements	displacement	NOUN
ap-638	128	4	,	,	PUNCT
ap-638	128	5	which	which	PRON
ap-638	128	6	do	do	AUX
ap-638	128	7	not	not	PART
ap-638	128	8	play	play	VERB
ap-638	128	9	an	an	DET
ap-638	128	10	important	important	ADJ
ap-638	128	11	role	role	NOUN
ap-638	128	12	in	in	ADP
ap-638	128	13	seismic	seismic	ADJ
ap-638	128	14	design	design	NOUN
ap-638	128	15	(	(	PUNCT
ap-638	128	16	at	at	ADP
ap-638	128	17	point	point	NOUN
ap-638	128	18	b	b	NOUN
ap-638	128	19	,	,	PUNCT
ap-638	128	20	which	which	PRON
ap-638	128	21	is	be	AUX
ap-638	128	22	the	the	DET
ap-638	128	23	intermediate	intermediate	ADJ
ap-638	128	24	joint	joint	NOUN
ap-638	128	25	of	of	ADP
ap-638	128	26	the	the	DET
ap-638	128	27	first	first	ADJ
ap-638	128	28	floor	floor	NOUN
ap-638	128	29	)	)	PUNCT
ap-638	128	30	,	,	PUNCT
ap-638	128	31	the	the	DET
ap-638	128	32	response	response	NOUN
ap-638	128	33	function	function	NOUN
ap-638	128	34	could	could	AUX
ap-638	128	35	not	not	PART
ap-638	128	36	fit	fit	VERB
ap-638	128	37	the	the	DET
ap-638	128	38	proper	proper	ADJ
ap-638	128	39	shape	shape	NOUN
ap-638	128	40	of	of	ADP
ap-638	128	41	the	the	DET
ap-638	128	42	membership	membership	NOUN
ap-638	128	43	function	function	NOUN
ap-638	128	44	,	,	PUNCT
ap-638	128	45	which	which	PRON
ap-638	128	46	is	be	AUX
ap-638	128	47	evidenced	evidence	VERB
ap-638	128	48	in	in	ADP
ap-638	128	49	figs	fig	NOUN
ap-638	128	50	.	.	PUNCT
ap-638	129	1	9	9	NUM
ap-638	129	2	and	and	CCONJ
ap-638	129	3	10	10	NUM
ap-638	129	4	.	.	X
ap-638	129	5	5	5	NUM
ap-638	129	6	possible	possible	ADJ
ap-638	129	7	applications	application	NOUN
ap-638	129	8	in	in	ADP
ap-638	129	9	the	the	DET
ap-638	129	10	design	design	NOUN
ap-638	129	11	of	of	ADP
ap-638	129	12	earthquake	earthquake	NOUN
ap-638	129	13	resistant	resistant	ADJ
ap-638	129	14	structures	structure	NOUN
ap-638	129	15	,	,	PUNCT
ap-638	129	16	it	it	PRON
ap-638	129	17	is	be	AUX
ap-638	129	18	essential	essential	ADJ
ap-638	129	19	not	not	PART
ap-638	129	20	to	to	PART
ap-638	129	21	neglect	neglect	VERB
ap-638	129	22	any	any	DET
ap-638	129	23	uncertainty	uncertainty	NOUN
ap-638	129	24	as	as	SCONJ
ap-638	129	25	it	it	PRON
ap-638	129	26	may	may	AUX
ap-638	129	27	lead	lead	VERB
ap-638	129	28	to	to	ADP
ap-638	129	29	an	an	DET
ap-638	129	30	erroneous	erroneous	ADJ
ap-638	129	31	conclusion	conclusion	NOUN
ap-638	129	32	due	due	ADP
ap-638	129	33	to	to	ADP
ap-638	129	34	the	the	DET
ap-638	129	35	dynamic	dynamic	ADJ
ap-638	129	36	simulation	simulation	NOUN
ap-638	129	37	which	which	PRON
ap-638	129	38	may	may	AUX
ap-638	129	39	amplify	amplify	VERB
ap-638	129	40	such	such	ADJ
ap-638	129	41	uncertainty	uncertainty	NOUN
ap-638	129	42	beyond	beyond	ADP
ap-638	129	43	all	all	DET
ap-638	129	44	limits	limit	NOUN
ap-638	129	45	.	.	PUNCT
ap-638	130	1	for	for	ADP
ap-638	130	2	these	these	DET
ap-638	130	3	reasons	reason	NOUN
ap-638	130	4	,	,	PUNCT
ap-638	130	5	it	it	PRON
ap-638	130	6	seems	seem	VERB
ap-638	130	7	reasonable	reasonable	ADJ
ap-638	130	8	to	to	PART
ap-638	130	9	express	express	VERB
ap-638	130	10	uncertain	uncertain	ADJ
ap-638	130	11	numerical	numerical	ADJ
ap-638	130	12	data	datum	NOUN
ap-638	130	13	in	in	ADP
ap-638	130	14	terms	term	NOUN
ap-638	130	15	of	of	ADP
ap-638	130	16	fuzzy	fuzzy	ADJ
ap-638	130	17	numbers	number	NOUN
ap-638	130	18	and	and	CCONJ
ap-638	130	19	to	to	PART
ap-638	130	20	use	use	VERB
ap-638	130	21	them	they	PRON
ap-638	130	22	as	as	ADP
ap-638	130	23	such	such	ADJ
ap-638	130	24	in	in	ADP
ap-638	130	25	analyses	analysis	NOUN
ap-638	130	26	to	to	PART
ap-638	130	27	cover	cover	VERB
ap-638	130	28	all	all	DET
ap-638	130	29	possible	possible	ADJ
ap-638	130	30	solutions	solution	NOUN
ap-638	130	31	.	.	PUNCT
ap-638	131	1	in	in	ADP
ap-638	131	2	the	the	DET
ap-638	131	3	previous	previous	ADJ
ap-638	131	4	section	section	NOUN
ap-638	131	5	,	,	PUNCT
ap-638	131	6	an	an	DET
ap-638	131	7	approach	approach	NOUN
ap-638	131	8	to	to	ADP
ap-638	131	9	natural	natural	ADJ
ap-638	131	10	vibration	vibration	NOUN
ap-638	131	11	analysis	analysis	NOUN
ap-638	131	12	was	be	AUX
ap-638	131	13	shown	show	VERB
ap-638	131	14	which	which	PRON
ap-638	131	15	provides	provide	VERB
ap-638	131	16	input	input	NOUN
ap-638	131	17	data	datum	NOUN
ap-638	131	18	for	for	ADP
ap-638	131	19	further	further	ADJ
ap-638	131	20	analyses	analysis	NOUN
ap-638	131	21	considering	consider	VERB
ap-638	131	22	,	,	PUNCT
ap-638	131	23	e.g.	e.g.	ADV
ap-638	131	24	earthquake	earthquake	NOUN
ap-638	131	25	induced	induce	VERB
ap-638	131	26	vibrations	vibration	NOUN
ap-638	131	27	.	.	PUNCT
ap-638	132	1	spectral	spectral	ADJ
ap-638	132	2	-	-	PUNCT
ap-638	132	3	analysis	analysis	NOUN
ap-638	132	4	based	base	VERB
ap-638	132	5	methods	method	NOUN
ap-638	132	6	require	require	VERB
ap-638	132	7	only	only	ADV
ap-638	132	8	the	the	DET
ap-638	132	9	maximum	maximum	ADJ
ap-638	132	10	values	value	NOUN
ap-638	132	11	obtained	obtain	VERB
ap-638	132	12	for	for	ADP
ap-638	132	13	each	each	DET
ap-638	132	14	natural	natural	ADJ
ap-638	132	15	mode	mode	NOUN
ap-638	132	16	in	in	ADP
ap-638	132	17	order	order	NOUN
ap-638	132	18	to	to	PART
ap-638	132	19	evaluate	evaluate	VERB
ap-638	132	20	the	the	DET
ap-638	132	21	excited	excited	ADJ
ap-638	132	22	vibration	vibration	NOUN
ap-638	132	23	.	.	PUNCT
ap-638	133	1	therefore	therefore	ADV
ap-638	133	2	,	,	PUNCT
ap-638	133	3	it	it	PRON
ap-638	133	4	is	be	AUX
ap-638	133	5	desirable	desirable	ADJ
ap-638	133	6	to	to	PART
ap-638	133	7	verify	verify	VERB
ap-638	133	8	whether	whether	SCONJ
ap-638	133	9	these	these	DET
ap-638	133	10	values	value	NOUN
ap-638	133	11	can	can	AUX
ap-638	133	12	be	be	AUX
ap-638	133	13	satisfactorily	satisfactorily	ADV
ap-638	133	14	expressed	express	VERB
ap-638	133	15	by	by	ADP
ap-638	133	16	surface	surface	NOUN
ap-638	133	17	response	response	NOUN
ap-638	133	18	functions	function	NOUN
ap-638	133	19	which	which	PRON
ap-638	133	20	were	be	AUX
ap-638	133	21	obtained	obtain	VERB
ap-638	133	22	only	only	ADV
ap-638	133	23	by	by	ADP
ap-638	133	24	binary	binary	ADJ
ap-638	133	25	combinations	combination	NOUN
ap-638	133	26	of	of	ADP
ap-638	133	27	material	material	NOUN
ap-638	133	28	parameters	parameter	NOUN
ap-638	133	29	with	with	ADP
ap-638	133	30	three	three	NUM
ap-638	133	31	values	value	NOUN
ap-638	133	32	(	(	PUNCT
ap-638	133	33	minimum	minimum	ADJ
ap-638	133	34	,	,	PUNCT
ap-638	133	35	modal	modal	ADJ
ap-638	133	36	value	value	NOUN
ap-638	133	37	,	,	PUNCT
ap-638	133	38	maximum	maximum	ADJ
ap-638	133	39	)	)	PUNCT
ap-638	133	40	.	.	PUNCT
ap-638	134	1	the	the	DET
ap-638	134	2	resulting	result	VERB
ap-638	134	3	surface	surface	NOUN
ap-638	134	4	response	response	NOUN
ap-638	134	5	function	function	NOUN
ap-638	134	6	was	be	AUX
ap-638	134	7	also	also	ADV
ap-638	134	8	obtained	obtain	VERB
ap-638	134	9	for	for	ADP
ap-638	134	10	five	five	NUM
ap-638	134	11	values	value	NOUN
ap-638	134	12	,	,	PUNCT
ap-638	134	13	corresponding	correspond	VERB
ap-638	134	14	to	to	ADP
ap-638	134	15	the	the	DET
ap-638	134	16	�	�	PROPN
ap-638	134	17	-cut	-cut	ADJ
ap-638	134	18	values	value	NOUN
ap-638	134	19	with	with	ADP
ap-638	134	20	a	a	DET
ap-638	134	21	equal	equal	ADJ
ap-638	134	22	to	to	ADP
ap-638	134	23	0	0	NUM
ap-638	134	24	,	,	PUNCT
ap-638	134	25	0.5	0.5	NUM
ap-638	134	26	and	and	CCONJ
ap-638	134	27	1	1	NUM
ap-638	134	28	.	.	PUNCT
ap-638	135	1	however	however	ADV
ap-638	135	2	,	,	PUNCT
ap-638	135	3	this	this	PRON
ap-638	135	4	meant	mean	VERB
ap-638	135	5	52×4	52×4	PROPN
ap-638	135	6	(	(	PUNCT
ap-638	135	7	�	�	PROPN
ap-638	135	8	390625	390625	NUM
ap-638	135	9	)	)	PUNCT
ap-638	135	10	independent	independent	ADJ
ap-638	135	11	runs	run	NOUN
ap-638	135	12	of	of	ADP
ap-638	135	13	the	the	DET
ap-638	135	14	dynamic	dynamic	ADJ
ap-638	135	15	finite	finite	NOUN
ap-638	135	16	element	element	NOUN
ap-638	135	17	analysis	analysis	NOUN
ap-638	135	18	.	.	PUNCT
ap-638	136	1	the	the	DET
ap-638	136	2	improvement	improvement	NOUN
ap-638	136	3	was	be	AUX
ap-638	136	4	negligible	negligible	ADJ
ap-638	136	5	,	,	PUNCT
ap-638	136	6	and	and	CCONJ
ap-638	136	7	compared	compare	VERB
ap-638	136	8	with	with	ADP
ap-638	136	9	the	the	DET
ap-638	136	10	computational	computational	ADJ
ap-638	136	11	effort	effort	NOUN
ap-638	136	12	it	it	PRON
ap-638	136	13	proved	prove	VERB
ap-638	136	14	truly	truly	ADV
ap-638	136	15	unnecessary	unnecessary	ADJ
ap-638	136	16	.	.	PUNCT
ap-638	137	1	120	120	NUM
ap-638	137	2	©	©	PROPN
ap-638	137	3	czech	czech	PROPN
ap-638	137	4	technical	technical	PROPN
ap-638	137	5	university	university	PROPN
ap-638	137	6	publishing	publishing	NOUN
ap-638	137	7	house	house	NOUN
ap-638	137	8	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-638	137	9	acta	acta	PROPN
ap-638	137	10	polytechnica	polytechnica	PROPN
ap-638	137	11	vol	vol	NOUN
ap-638	137	12	.	.	PROPN
ap-638	138	1	44	44	NUM
ap-638	138	2	no	no	NOUN
ap-638	138	3	.	.	PUNCT
ap-638	139	1	5–6/2004	5–6/2004	NUM
ap-638	139	2	fig	fig	NOUN
ap-638	139	3	.	.	PUNCT
ap-638	140	1	8	8	NUM
ap-638	140	2	:	:	PUNCT
ap-638	140	3	distribution	distribution	NOUN
ap-638	140	4	of	of	ADP
ap-638	140	5	natural	natural	ADJ
ap-638	140	6	frequencies	frequency	NOUN
ap-638	140	7	fig	fig	NOUN
ap-638	140	8	.	.	PUNCT
ap-638	141	1	9	9	NUM
ap-638	141	2	:	:	PUNCT
ap-638	141	3	distribution	distribution	NOUN
ap-638	141	4	of	of	ADP
ap-638	141	5	horizontal	horizontal	ADJ
ap-638	141	6	displacement	displacement	ADJ
ap-638	141	7	fig	fig	NOUN
ap-638	141	8	.	.	PUNCT
ap-638	142	1	10	10	NUM
ap-638	142	2	:	:	PUNCT
ap-638	142	3	distribution	distribution	NOUN
ap-638	142	4	of	of	ADP
ap-638	142	5	vertical	vertical	ADJ
ap-638	142	6	displacement	displacement	NOUN
ap-638	142	7	6	6	NUM
ap-638	142	8	conclusions	conclusion	NOUN
ap-638	142	9	the	the	DET
ap-638	142	10	fuzzy	fuzzy	ADJ
ap-638	142	11	approach	approach	NOUN
ap-638	142	12	has	have	AUX
ap-638	142	13	been	be	AUX
ap-638	142	14	applied	apply	VERB
ap-638	142	15	to	to	ADP
ap-638	142	16	dynamic	dynamic	ADJ
ap-638	142	17	analysis	analysis	NOUN
ap-638	142	18	of	of	ADP
ap-638	142	19	a	a	DET
ap-638	142	20	2d	2d	NUM
ap-638	142	21	concrete	concrete	ADJ
ap-638	142	22	frame	frame	NOUN
ap-638	142	23	with	with	ADP
ap-638	142	24	uncertainties	uncertainty	NOUN
ap-638	142	25	.	.	PUNCT
ap-638	143	1	the	the	DET
ap-638	143	2	natural	natural	ADJ
ap-638	143	3	frequencies	frequency	NOUN
ap-638	143	4	and	and	CCONJ
ap-638	143	5	the	the	DET
ap-638	143	6	natural	natural	ADJ
ap-638	143	7	mode	mode	NOUN
ap-638	143	8	shapes	shape	NOUN
ap-638	143	9	have	have	AUX
ap-638	143	10	been	be	AUX
ap-638	143	11	computed	compute	VERB
ap-638	143	12	and	and	CCONJ
ap-638	143	13	described	describe	VERB
ap-638	143	14	by	by	ADP
ap-638	143	15	fuzzy	fuzzy	ADJ
ap-638	143	16	numbers	number	NOUN
ap-638	143	17	.	.	PUNCT
ap-638	144	1	the	the	DET
ap-638	144	2	response	response	NOUN
ap-638	144	3	surface	surface	NOUN
ap-638	144	4	function	function	NOUN
ap-638	144	5	has	have	AUX
ap-638	144	6	been	be	AUX
ap-638	144	7	applied	apply	VERB
ap-638	144	8	in	in	ADP
ap-638	144	9	order	order	NOUN
ap-638	144	10	to	to	PART
ap-638	144	11	reduce	reduce	VERB
ap-638	144	12	the	the	DET
ap-638	144	13	number	number	NOUN
ap-638	144	14	of	of	ADP
ap-638	144	15	required	require	VERB
ap-638	144	16	computations	computation	NOUN
ap-638	144	17	.	.	PUNCT
ap-638	145	1	the	the	DET
ap-638	145	2	results	result	NOUN
ap-638	145	3	have	have	AUX
ap-638	145	4	been	be	AUX
ap-638	145	5	compared	compare	VERB
ap-638	145	6	with	with	ADP
ap-638	145	7	a	a	DET
ap-638	145	8	full	full	ADJ
ap-638	145	9	analysis	analysis	NOUN
ap-638	145	10	based	base	VERB
ap-638	145	11	on	on	ADP
ap-638	145	12	an	an	DET
ap-638	145	13	evaluation	evaluation	NOUN
ap-638	145	14	of	of	ADP
ap-638	145	15	all	all	DET
ap-638	145	16	combinations	combination	NOUN
ap-638	145	17	(	(	PUNCT
ap-638	145	18	in	in	ADP
ap-638	145	19	the	the	DET
ap-638	145	20	order	order	NOUN
ap-638	145	21	of	of	ADP
ap-638	145	22	thousands	thousand	NOUN
ap-638	145	23	)	)	PUNCT
ap-638	145	24	and	and	CCONJ
ap-638	145	25	very	very	ADV
ap-638	145	26	good	good	ADJ
ap-638	145	27	accordance	accordance	NOUN
ap-638	145	28	has	have	AUX
ap-638	145	29	been	be	AUX
ap-638	145	30	obtained	obtain	VERB
ap-638	145	31	.	.	PUNCT
ap-638	146	1	the	the	DET
ap-638	146	2	first	first	ADJ
ap-638	146	3	lower	low	ADJ
ap-638	146	4	natural	natural	ADJ
ap-638	146	5	mode	mode	NOUN
ap-638	146	6	shapes	shape	NOUN
ap-638	146	7	are	be	AUX
ap-638	146	8	naturally	naturally	ADV
ap-638	146	9	described	describe	VERB
ap-638	146	10	more	more	ADV
ap-638	146	11	precisely	precisely	ADV
ap-638	146	12	than	than	ADP
ap-638	146	13	the	the	DET
ap-638	146	14	higher	high	ADJ
ap-638	146	15	ones	one	NOUN
ap-638	146	16	.	.	PUNCT
ap-638	147	1	the	the	DET
ap-638	147	2	errors	error	NOUN
ap-638	147	3	of	of	ADP
ap-638	147	4	the	the	DET
ap-638	147	5	obtained	obtain	VERB
ap-638	147	6	results	result	NOUN
ap-638	147	7	for	for	ADP
ap-638	147	8	lower	low	ADJ
ap-638	147	9	natural	natural	ADJ
ap-638	147	10	mode	mode	NOUN
ap-638	147	11	shapes	shape	NOUN
ap-638	147	12	are	be	AUX
ap-638	147	13	less	less	ADJ
ap-638	147	14	than	than	ADP
ap-638	147	15	5	5	NUM
ap-638	147	16	%	%	NOUN
ap-638	147	17	.	.	PUNCT
ap-638	148	1	there	there	PRON
ap-638	148	2	are	be	VERB
ap-638	148	3	some	some	DET
ap-638	148	4	quantities	quantity	NOUN
ap-638	148	5	belonging	belong	VERB
ap-638	148	6	to	to	ADP
ap-638	148	7	higher	high	ADJ
ap-638	148	8	modes	mode	NOUN
ap-638	148	9	where	where	SCONJ
ap-638	148	10	the	the	DET
ap-638	148	11	response	response	NOUN
ap-638	148	12	surface	surface	NOUN
ap-638	148	13	function	function	NOUN
ap-638	148	14	gives	give	VERB
ap-638	148	15	results	result	NOUN
ap-638	148	16	unacceptable	unacceptable	ADJ
ap-638	148	17	from	from	ADP
ap-638	148	18	the	the	DET
ap-638	148	19	point	point	NOUN
ap-638	148	20	of	of	ADP
ap-638	148	21	the	the	DET
ap-638	148	22	fuzzy	fuzzy	ADJ
ap-638	148	23	set	set	NOUN
ap-638	148	24	theory	theory	NOUN
ap-638	148	25	.	.	PUNCT
ap-638	149	1	these	these	DET
ap-638	149	2	difficulties	difficulty	NOUN
ap-638	149	3	should	should	AUX
ap-638	149	4	be	be	AUX
ap-638	149	5	studied	study	VERB
ap-638	149	6	in	in	ADP
ap-638	149	7	future	future	NOUN
ap-638	149	8	.	.	PUNCT
ap-638	150	1	7	7	NUM
ap-638	150	2	acknowledgment	acknowledgment	NOUN
ap-638	150	3	this	this	DET
ap-638	150	4	work	work	NOUN
ap-638	150	5	was	be	AUX
ap-638	150	6	supported	support	VERB
ap-638	150	7	by	by	ADP
ap-638	150	8	project	project	NOUN
ap-638	150	9	no	no	NOUN
ap-638	150	10	.	.	PUNCT
ap-638	151	1	103/04/1320	103/04/1320	NUM
ap-638	151	2	of	of	ADP
ap-638	151	3	the	the	DET
ap-638	151	4	grant	grant	NOUN
ap-638	151	5	agency	agency	NOUN
ap-638	151	6	of	of	ADP
ap-638	151	7	the	the	DET
ap-638	151	8	czech	czech	PROPN
ap-638	151	9	republic	republic	NOUN
ap-638	151	10	,	,	PUNCT
ap-638	151	11	which	which	PRON
ap-638	151	12	is	be	AUX
ap-638	151	13	gratefully	gratefully	ADV
ap-638	151	14	acknowledged	acknowledge	VERB
ap-638	151	15	.	.	PUNCT
ap-638	152	1	references	reference	NOUN
ap-638	152	2	[	[	X
ap-638	152	3	1	1	X
ap-638	152	4	]	]	PUNCT
ap-638	152	5	zadeh	zadeh	PROPN
ap-638	152	6	l.	l.	PROPN
ap-638	152	7	a.	a.	PROPN
ap-638	152	8	:	:	PUNCT
ap-638	152	9	“	"	PUNCT
ap-638	152	10	fuzzy	fuzzy	ADJ
ap-638	152	11	sets	set	NOUN
ap-638	152	12	.	.	PUNCT
ap-638	152	13	”	"	PUNCT
ap-638	153	1	information	information	NOUN
ap-638	153	2	control	control	NOUN
ap-638	153	3	,	,	PUNCT
ap-638	153	4	vol	vol	NOUN
ap-638	153	5	.	.	PROPN
ap-638	153	6	8	8	NUM
ap-638	153	7	(	(	PUNCT
ap-638	153	8	1965	1965	NUM
ap-638	153	9	)	)	PUNCT
ap-638	154	1	no	no	INTJ
ap-638	154	2	.	.	NOUN
ap-638	155	1	3	3	NUM
ap-638	155	2	,	,	PUNCT
ap-638	155	3	p.	p.	NOUN
ap-638	155	4	338–352	338–352	NUM
ap-638	155	5	.	.	PUNCT
ap-638	156	1	[	[	X
ap-638	156	2	2	2	X
ap-638	156	3	]	]	PUNCT
ap-638	156	4	valliappan	valliappan	PROPN
ap-638	156	5	s.	s.	PROPN
ap-638	156	6	,	,	PUNCT
ap-638	156	7	pham	pham	PROPN
ap-638	156	8	t.	t.	PROPN
ap-638	156	9	d.	d.	PROPN
ap-638	156	10	:	:	PUNCT
ap-638	156	11	“	"	PUNCT
ap-638	156	12	construction	construction	VERB
ap-638	156	13	the	the	DET
ap-638	156	14	membership	membership	NOUN
ap-638	156	15	function	function	NOUN
ap-638	156	16	of	of	ADP
ap-638	156	17	a	a	DET
ap-638	156	18	fuzzy	fuzzy	ADJ
ap-638	156	19	set	set	VERB
ap-638	156	20	with	with	ADP
ap-638	156	21	objective	objective	ADJ
ap-638	156	22	and	and	CCONJ
ap-638	156	23	subjective	subjective	ADJ
ap-638	156	24	information	information	NOUN
ap-638	156	25	.	.	PUNCT
ap-638	156	26	”	"	PUNCT
ap-638	156	27	microcomputers	microcomputer	NOUN
ap-638	156	28	in	in	ADP
ap-638	156	29	civil	civil	ADJ
ap-638	156	30	engineering	engineering	NOUN
ap-638	156	31	,	,	PUNCT
ap-638	156	32	vol	vol	NOUN
ap-638	156	33	.	.	NOUN
ap-638	156	34	8	8	NUM
ap-638	156	35	(	(	PUNCT
ap-638	156	36	1993	1993	NUM
ap-638	156	37	)	)	PUNCT
ap-638	156	38	,	,	PUNCT
ap-638	156	39	p.	p.	NOUN
ap-638	156	40	75–82	75–82	NUM
ap-638	156	41	.	.	PUNCT
ap-638	157	1	[	[	X
ap-638	157	2	3	3	X
ap-638	157	3	]	]	X
ap-638	157	4	kaufman	kaufman	PROPN
ap-638	157	5	a.	a.	PROPN
ap-638	157	6	,	,	PUNCT
ap-638	157	7	gupta	gupta	PROPN
ap-638	157	8	m.	m.	PROPN
ap-638	157	9	m.	m.	NOUN
ap-638	157	10	:	:	PUNCT
ap-638	157	11	“	"	PUNCT
ap-638	157	12	introduction	introduction	NOUN
ap-638	157	13	to	to	ADP
ap-638	157	14	fuzzy	fuzzy	ADJ
ap-638	157	15	arithmetic	arithmetic	ADJ
ap-638	157	16	:	:	PUNCT
ap-638	157	17	theory	theory	NOUN
ap-638	157	18	and	and	CCONJ
ap-638	157	19	application	application	NOUN
ap-638	157	20	.	.	PUNCT
ap-638	157	21	”	"	PUNCT
ap-638	158	1	new	new	PROPN
ap-638	158	2	york	york	PROPN
ap-638	158	3	,	,	PUNCT
ap-638	158	4	van	van	PROPN
ap-638	158	5	nostrand	nostrand	PROPN
ap-638	158	6	reinhold	reinhold	PROPN
ap-638	158	7	company	company	PROPN
ap-638	158	8	,	,	PUNCT
ap-638	158	9	inc.1985	inc.1985	X
ap-638	158	10	.	.	PUNCT
ap-638	159	1	[	[	X
ap-638	159	2	4	4	X
ap-638	159	3	]	]	PUNCT
ap-638	159	4	akpan	akpan	PROPN
ap-638	159	5	u.	u.	PROPN
ap-638	159	6	o.	o.	PROPN
ap-638	159	7	,	,	PUNCT
ap-638	159	8	koko	koko	PROPN
ap-638	159	9	t.	t.	PROPN
ap-638	159	10	s.	s.	PROPN
ap-638	159	11	,	,	PUNCT
ap-638	159	12	orisamolu	orisamolu	PROPN
ap-638	159	13	i.	i.	PROPN
ap-638	159	14	r.	r.	PROPN
ap-638	159	15	,	,	PUNCT
ap-638	159	16	gallant	gallant	PROPN
ap-638	159	17	b.	b.	PROPN
ap-638	159	18	k.	k.	PROPN
ap-638	159	19	:	:	PUNCT
ap-638	159	20	“	"	PUNCT
ap-638	159	21	practical	practical	ADJ
ap-638	159	22	fuzzy	fuzzy	ADJ
ap-638	159	23	finite	finite	ADJ
ap-638	159	24	element	element	NOUN
ap-638	159	25	analysis	analysis	NOUN
ap-638	159	26	of	of	ADP
ap-638	159	27	structures	structure	NOUN
ap-638	159	28	.	.	PUNCT
ap-638	159	29	”	"	PUNCT
ap-638	160	1	finite	finite	ADJ
ap-638	160	2	elements	element	NOUN
ap-638	160	3	in	in	ADP
ap-638	160	4	analysis	analysis	NOUN
ap-638	160	5	and	and	CCONJ
ap-638	160	6	design	design	NOUN
ap-638	160	7	,	,	PUNCT
ap-638	160	8	vol	vol	NOUN
ap-638	160	9	.	.	PROPN
ap-638	161	1	38	38	NUM
ap-638	161	2	(	(	PUNCT
ap-638	161	3	2001	2001	NUM
ap-638	161	4	)	)	PUNCT
ap-638	161	5	,	,	PUNCT
ap-638	161	6	p.	p.	NOUN
ap-638	161	7	93–111	93–111	NUM
ap-638	161	8	.	.	PUNCT
ap-638	162	1	[	[	X
ap-638	162	2	5	5	NUM
ap-638	162	3	]	]	PUNCT
ap-638	162	4	bucher	bucher	PROPN
ap-638	162	5	c.	c.	PROPN
ap-638	162	6	g.	g.	PROPN
ap-638	162	7	,	,	PUNCT
ap-638	162	8	chen	chen	PROPN
ap-638	162	9	y.	y.	PROPN
ap-638	162	10	m.	m.	PROPN
ap-638	162	11	,	,	PUNCT
ap-638	162	12	schueler	schueler	PROPN
ap-638	162	13	g.	g.	PROPN
ap-638	162	14	i.	i.	PROPN
ap-638	162	15	:	:	PUNCT
ap-638	162	16	“	"	PUNCT
ap-638	162	17	time	time	NOUN
ap-638	162	18	variant	variant	ADJ
ap-638	162	19	reliability	reliability	NOUN
ap-638	162	20	analysis	analysis	NOUN
ap-638	162	21	utilizing	utilize	VERB
ap-638	162	22	response	response	NOUN
ap-638	162	23	surface	surface	NOUN
ap-638	162	24	approach	approach	NOUN
ap-638	162	25	.	.	PUNCT
ap-638	162	26	”	"	PUNCT
ap-638	163	1	in	in	ADP
ap-638	163	2	:	:	PUNCT
ap-638	163	3	reliability	reliability	NOUN
ap-638	163	4	and	and	CCONJ
ap-638	163	5	optimization	optimization	NOUN
ap-638	163	6	of	of	ADP
ap-638	163	7	structural	structural	ADJ
ap-638	163	8	systems	system	NOUN
ap-638	163	9	,	,	PUNCT
ap-638	163	10	88	88	NUM
ap-638	163	11	.	.	PUNCT
ap-638	164	1	(	(	PUNCT
ap-638	164	2	editor	editor	NOUN
ap-638	164	3	p.	p.	PROPN
ap-638	164	4	thoft	thoft	PROPN
ap-638	164	5	-	-	PUNCT
ap-638	164	6	christensen	christensen	PROPN
ap-638	164	7	)	)	PUNCT
ap-638	164	8	,	,	PUNCT
ap-638	164	9	1988	1988	NUM
ap-638	164	10	.	.	PUNCT
ap-638	165	1	[	[	X
ap-638	165	2	6	6	NUM
ap-638	165	3	]	]	PUNCT
ap-638	165	4	rajashekhar	rajashekhar	ADJ
ap-638	165	5	m.	m.	PROPN
ap-638	165	6	r.	r.	PROPN
ap-638	165	7	,	,	PUNCT
ap-638	165	8	ellingwood	ellingwood	PROPN
ap-638	165	9	b.	b.	PROPN
ap-638	165	10	r.	r.	PROPN
ap-638	165	11	:	:	PUNCT
ap-638	165	12	“	"	PUNCT
ap-638	165	13	a	a	DET
ap-638	165	14	new	new	ADJ
ap-638	165	15	look	look	NOUN
ap-638	165	16	at	at	ADP
ap-638	165	17	the	the	DET
ap-638	165	18	response	response	NOUN
ap-638	165	19	surface	surface	NOUN
ap-638	165	20	approach	approach	NOUN
ap-638	165	21	for	for	ADP
ap-638	165	22	reliability	reliability	NOUN
ap-638	165	23	analysis	analysis	NOUN
ap-638	165	24	.	.	PUNCT
ap-638	165	25	”	"	PUNCT
ap-638	166	1	structural	structural	ADJ
ap-638	166	2	safety	safety	NOUN
ap-638	166	3	,	,	PUNCT
ap-638	166	4	vol	vol	NOUN
ap-638	166	5	.	.	PROPN
ap-638	166	6	12	12	NUM
ap-638	166	7	(	(	PUNCT
ap-638	166	8	1993	1993	NUM
ap-638	166	9	)	)	PUNCT
ap-638	166	10	,	,	PUNCT
ap-638	166	11	p.	p.	NOUN
ap-638	166	12	205–220	205–220	NUM
ap-638	166	13	.	.	PUNCT
ap-638	167	1	[	[	X
ap-638	167	2	7	7	X
ap-638	167	3	]	]	X
ap-638	167	4	bathe	bathe	NOUN
ap-638	167	5	k.	k.	PROPN
ap-638	167	6	j.	j.	PROPN
ap-638	167	7	:	:	PUNCT
ap-638	167	8	“	"	PUNCT
ap-638	167	9	finite	finite	ADJ
ap-638	167	10	element	element	NOUN
ap-638	167	11	procedures	procedure	NOUN
ap-638	167	12	.	.	PUNCT
ap-638	167	13	”	"	PUNCT
ap-638	167	14	prentice	prentice	NOUN
ap-638	167	15	-	-	PUNCT
ap-638	167	16	hall	hall	PROPN
ap-638	167	17	,	,	PUNCT
ap-638	167	18	inc	inc	PROPN
ap-638	167	19	.	.	PROPN
ap-638	167	20	1996	1996	NUM
ap-638	167	21	.	.	PUNCT
ap-638	168	1	[	[	X
ap-638	168	2	8	8	NUM
ap-638	168	3	]	]	PUNCT
ap-638	168	4	bittnar	bittnar	PROPN
ap-638	168	5	z.	z.	PROPN
ap-638	168	6	,	,	PUNCT
ap-638	168	7	šejnoha	šejnoha	PROPN
ap-638	168	8	j.	j.	PROPN
ap-638	168	9	:	:	PUNCT
ap-638	168	10	“	"	PUNCT
ap-638	168	11	numerical	numerical	ADJ
ap-638	168	12	methods	method	NOUN
ap-638	168	13	in	in	ADP
ap-638	168	14	structural	structural	ADJ
ap-638	168	15	mechanics	mechanic	NOUN
ap-638	168	16	.	.	PUNCT
ap-638	168	17	”	"	PUNCT
ap-638	169	1	asce	asce	PROPN
ap-638	169	2	press	press	PROPN
ap-638	169	3	1996	1996	NUM
ap-638	169	4	.	.	PUNCT
ap-638	170	1	[	[	X
ap-638	170	2	9	9	NUM
ap-638	170	3	]	]	PUNCT
ap-638	170	4	buckley	buckley	PROPN
ap-638	170	5	j.	j.	PROPN
ap-638	170	6	j.	j.	PROPN
ap-638	170	7	,	,	PUNCT
ap-638	170	8	qu	qu	PROPN
ap-638	170	9	y.	y.	PROPN
ap-638	170	10	:	:	PUNCT
ap-638	170	11	“	"	PUNCT
ap-638	170	12	solving	solve	VERB
ap-638	170	13	systems	system	NOUN
ap-638	170	14	of	of	ADP
ap-638	170	15	linear	linear	ADJ
ap-638	170	16	fuzzy	fuzzy	ADJ
ap-638	170	17	equations	equation	NOUN
ap-638	170	18	.	.	PUNCT
ap-638	170	19	”	"	PUNCT
ap-638	171	1	fuzzy	fuzzy	ADJ
ap-638	171	2	sets	set	NOUN
ap-638	171	3	and	and	CCONJ
ap-638	171	4	systems	system	NOUN
ap-638	171	5	,	,	PUNCT
ap-638	171	6	vol	vol	NOUN
ap-638	171	7	.	.	PROPN
ap-638	171	8	39	39	NUM
ap-638	171	9	(	(	PUNCT
ap-638	171	10	1991	1991	NUM
ap-638	171	11	)	)	PUNCT
ap-638	171	12	,	,	PUNCT
ap-638	171	13	p.	p.	NOUN
ap-638	171	14	33–43	33–43	NUM
ap-638	171	15	.	.	PUNCT
ap-638	172	1	ing	ing	PROPN
ap-638	172	2	.	.	PUNCT
ap-638	173	1	petr	petr	PROPN
ap-638	173	2	štemberk	štemberk	PROPN
ap-638	173	3	,	,	PUNCT
ap-638	173	4	ph.d	ph.d	PROPN
ap-638	173	5	.	.	PUNCT
ap-638	173	6	phone	phone	NOUN
ap-638	173	7	:	:	PUNCT
ap-638	173	8	+420	+420	PROPN
ap-638	173	9	224	224	NUM
ap-638	173	10	354	354	NUM
ap-638	173	11	634	634	NUM
ap-638	173	12	fax	fax	NOUN
ap-638	173	13	:	:	PUNCT
ap-638	173	14	+420	+420	NUM
ap-638	173	15	233	233	NUM
ap-638	173	16	335	335	NUM
ap-638	173	17	797	797	NUM
ap-638	173	18	e	e	NOUN
ap-638	173	19	-	-	NOUN
ap-638	173	20	mail	mail	NOUN
ap-638	173	21	:	:	PUNCT
ap-638	173	22	stemberk@fsv.cvut.cz	stemberk@fsv.cvut.cz	VERB
ap-638	173	23	department	department	NOUN
ap-638	173	24	of	of	ADP
ap-638	173	25	concrete	concrete	ADJ
ap-638	173	26	structures	structure	NOUN
ap-638	173	27	ing	ing	ADJ
ap-638	173	28	.	.	PUNCT
ap-638	174	1	jaroslav	jaroslav	PROPN
ap-638	174	2	kruis	kruis	PROPN
ap-638	174	3	,	,	PUNCT
ap-638	174	4	ph.d	ph.d	PROPN
ap-638	174	5	.	.	PUNCT
ap-638	174	6	phone	phone	NOUN
ap-638	174	7	:	:	PUNCT
ap-638	174	8	+420	+420	PROPN
ap-638	174	9	224	224	NUM
ap-638	174	10	354	354	NUM
ap-638	174	11	369	369	NUM
ap-638	174	12	fax	fax	NOUN
ap-638	174	13	:	:	PUNCT
ap-638	174	14	+420	+420	PROPN
ap-638	174	15	224	224	NUM
ap-638	174	16	310	310	NUM
ap-638	174	17	775	775	NUM
ap-638	174	18	e	e	NOUN
ap-638	174	19	-	-	NOUN
ap-638	174	20	mail	mail	NOUN
ap-638	174	21	:	:	PUNCT
ap-638	174	22	jk@cml.fsv.cvut.cz	jk@cml.fsv.cvut.cz	PROPN
ap-638	174	23	department	department	PROPN
ap-638	174	24	of	of	ADP
ap-638	174	25	structural	structural	ADJ
ap-638	174	26	mechanics	mechanic	NOUN
ap-638	174	27	czech	czech	PROPN
ap-638	174	28	technical	technical	PROPN
ap-638	174	29	university	university	PROPN
ap-638	174	30	in	in	ADP
ap-638	174	31	prague	prague	PROPN
ap-638	174	32	faculty	faculty	NOUN
ap-638	174	33	of	of	ADP
ap-638	174	34	civil	civil	ADJ
ap-638	174	35	engineering	engineering	NOUN
ap-638	174	36	thákurova	thákurova	VERB
ap-638	174	37	7	7	NUM
ap-638	174	38	166	166	NUM
ap-638	174	39	29	29	NUM
ap-638	174	40	praha	praha	NOUN
ap-638	174	41	6	6	NUM
ap-638	174	42	,	,	PUNCT
ap-638	174	43	czech	czech	PROPN
ap-638	174	44	republic	republic	NOUN
ap-638	174	45	©	©	PROPN
ap-638	174	46	czech	czech	PROPN
ap-638	174	47	technical	technical	PROPN
ap-638	174	48	university	university	PROPN
ap-638	174	49	publishing	publishing	NOUN
ap-638	174	50	house	house	NOUN
ap-638	174	51	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-638	174	52	121	121	NUM
ap-638	174	53	acta	acta	PROPN
ap-638	174	54	polytechnica	polytechnica	PROPN
ap-638	174	55	vol	vol	NOUN
ap-638	174	56	.	.	PROPN
ap-638	175	1	44	44	NUM
ap-638	175	2	no	no	NOUN
ap-638	175	3	.	.	PUNCT
ap-638	176	1	5–6/2004	5–6/2004	NUM
ap-638	176	2	table	table	NOUN
ap-638	176	3	of	of	ADP
ap-638	176	4	contents	content	NOUN
ap-638	176	5	section	section	NOUN
ap-638	176	6	1	1	NUM
ap-638	176	7	z.	z.	PROPN
ap-638	176	8	p.	p.	NOUN
ap-638	176	9	bažant	bažant	PROPN
ap-638	176	10	,	,	PUNCT
ap-638	176	11	q.	q.	PROPN
ap-638	176	12	yu	yu	PROPN
ap-638	176	13	nonlocal	nonlocal	ADJ
ap-638	176	14	theories	theory	NOUN
ap-638	176	15	in	in	ADP
ap-638	176	16	continuum	continuum	ADJ
ap-638	176	17	mechanics	mechanic	NOUN
ap-638	176	18	16	16	NUM
ap-638	176	19	m.	m.	NOUN
ap-638	176	20	jirásek	jirásek	NOUN
ap-638	176	21	modelling	modelling	NOUN
ap-638	176	22	of	of	ADP
ap-638	176	23	size	size	NOUN
ap-638	176	24	effect	effect	NOUN
ap-638	176	25	with	with	ADP
ap-638	176	26	regularised	regularise	VERB
ap-638	176	27	continua	continua	X
ap-638	176	28	35	35	NUM
ap-638	176	29	h.	h.	NOUN
ap-638	176	30	askes	ask	VERB
ap-638	176	31	,	,	PUNCT
ap-638	176	32	a.	a.	NOUN
ap-638	176	33	simone	simone	PROPN
ap-638	176	34	,	,	PUNCT
ap-638	176	35	l.	l.	PROPN
ap-638	176	36	j.	j.	PROPN
ap-638	176	37	sluys	sluys	PROPN
ap-638	176	38	a	a	DET
ap-638	176	39	discontinuous	discontinuous	ADJ
ap-638	176	40	model	model	NOUN
ap-638	176	41	to	to	PART
ap-638	176	42	study	study	VERB
ap-638	176	43	fracture	fracture	NOUN
ap-638	176	44	of	of	ADP
ap-638	176	45	brittle	brittle	ADJ
ap-638	176	46	materials	material	NOUN
ap-638	176	47	42	42	NUM
ap-638	176	48	k.	k.	PROPN
ap-638	176	49	de	de	PROPN
ap-638	176	50	proft	proft	PROPN
ap-638	176	51	,	,	PUNCT
ap-638	176	52	w.	w.	PROPN
ap-638	176	53	p.	p.	PROPN
ap-638	176	54	de	de	PROPN
ap-638	176	55	wilde	wilde	PROPN
ap-638	176	56	section	section	NOUN
ap-638	176	57	2	2	NUM
ap-638	176	58	p.	p.	NOUN
ap-638	176	59	krysl	krysl	NOUN
ap-638	176	60	oofem	oofem	PROPN
ap-638	176	61	–	–	PUNCT
ap-638	176	62	an	an	DET
ap-638	176	63	object	object	NOUN
ap-638	176	64	oriented	orient	VERB
ap-638	176	65	framework	framework	NOUN
ap-638	176	66	for	for	ADP
ap-638	176	67	finite	finite	ADJ
ap-638	176	68	element	element	NOUN
ap-638	176	69	analysis	analysis	NOUN
ap-638	176	70	54	54	NUM
ap-638	176	71	b.	b.	NOUN
ap-638	176	72	patzák	patzák	PROPN
ap-638	176	73	,	,	PUNCT
ap-638	176	74	z.	z.	PROPN
ap-638	176	75	bittnar	bittnar	PROPN
ap-638	176	76	triangulation	triangulation	NOUN
ap-638	176	77	of	of	ADP
ap-638	176	78	3d	3d	PROPN
ap-638	176	79	surfaces	surface	NOUN
ap-638	176	80	recovered	recover	VERB
ap-638	176	81	from	from	ADP
ap-638	176	82	stl	stl	PROPN
ap-638	176	83	grids	grid	NOUN
ap-638	176	84	61	61	NUM
ap-638	176	85	d.	d.	PROPN
ap-638	176	86	rypl	rypl	PROPN
ap-638	176	87	,	,	PUNCT
ap-638	176	88	z.	z.	PROPN
ap-638	176	89	bittnar	bittnar	PROPN
ap-638	176	90	solution	solution	NOUN
ap-638	176	91	of	of	ADP
ap-638	176	92	nonlinear	nonlinear	ADJ
ap-638	176	93	coupled	couple	VERB
ap-638	176	94	heat	heat	NOUN
ap-638	176	95	and	and	CCONJ
ap-638	176	96	moisture	moisture	NOUN
ap-638	176	97	transport	transport	NOUN
ap-638	176	98	using	use	VERB
ap-638	176	99	finite	finite	PROPN
ap-638	176	100	element	element	NOUN
ap-638	176	101	method	method	NOUN
ap-638	176	102	68	68	NUM
ap-638	176	103	t.	t.	NOUN
ap-638	176	104	krejèí	krejèí	PROPN
ap-638	176	105	membrane	membrane	NOUN
ap-638	176	106	triangles	triangle	NOUN
ap-638	176	107	with	with	ADP
ap-638	176	108	drilling	drilling	NOUN
ap-638	176	109	degrees	degree	NOUN
ap-638	176	110	of	of	ADP
ap-638	176	111	freedom	freedom	NOUN
ap-638	176	112	75	75	NUM
ap-638	176	113	p.	p.	NOUN
ap-638	176	114	fajman	fajman	NOUN
ap-638	176	115	section	section	NOUN
ap-638	176	116	3	3	NUM
ap-638	176	117	p.	p.	NOUN
ap-638	176	118	tesárek	tesárek	PROPN
ap-638	176	119	,	,	PUNCT
ap-638	176	120	j.	j.	PROPN
ap-638	176	121	drchalová	drchalová	PROPN
ap-638	176	122	,	,	PUNCT
ap-638	176	123	j.	j.	PROPN
ap-638	176	124	kolísko	kolísko	PROPN
ap-638	176	125	,	,	PUNCT
ap-638	176	126	p.	p.	PROPN
ap-638	176	127	rovnaníková	rovnaníková	PROPN
ap-638	176	128	,	,	PUNCT
ap-638	176	129	r.	r.	PROPN
ap-638	176	130	èerný	èerný	PROPN
ap-638	176	131	experimental	experimental	ADJ
ap-638	176	132	analysis	analysis	NOUN
ap-638	176	133	of	of	ADP
ap-638	176	134	sandstone	sandstone	NOUN
ap-638	176	135	and	and	CCONJ
ap-638	176	136	travertine	travertine	NOUN
ap-638	176	137	89	89	NUM
ap-638	176	138	t.	t.	PROPN
ap-638	176	139	doležel	doležel	PROPN
ap-638	176	140	,	,	PUNCT
ap-638	176	141	m.	m.	NOUN
ap-638	176	142	drdácký	drdácký	PROPN
ap-638	176	143	,	,	PUNCT
ap-638	176	144	p.	p.	PROPN
ap-638	176	145	konvalinka	konvalinka	PROPN
ap-638	176	146	,	,	PUNCT
ap-638	176	147	l.	l.	PROPN
ap-638	176	148	kopecký	kopecký	PROPN
ap-638	176	149	mohr	mohr	PROPN
ap-638	176	150	-	-	PUNCT
ap-638	176	151	coulomb	coulomb	PROPN
ap-638	176	152	failure	failure	NOUN
ap-638	176	153	condition	condition	NOUN
ap-638	176	154	and	and	CCONJ
ap-638	176	155	the	the	DET
ap-638	176	156	direct	direct	ADJ
ap-638	176	157	shear	shear	NOUN
ap-638	176	158	test	test	NOUN
ap-638	176	159	revisited	revisit	VERB
ap-638	176	160	93	93	NUM
ap-638	176	161	p.	p.	NOUN
ap-638	176	162	øeøicha	øeøicha	NUM
ap-638	177	1	efficient	efficient	ADJ
ap-638	177	2	analytical	analytical	ADJ
ap-638	177	3	model	model	NOUN
ap-638	177	4	for	for	ADP
ap-638	177	5	calculation	calculation	NOUN
ap-638	177	6	of	of	ADP
ap-638	177	7	the	the	DET
ap-638	177	8	influence	influence	NOUN
ap-638	177	9	zone	zone	NOUN
ap-638	177	10	inside	inside	ADP
ap-638	177	11	the	the	DET
ap-638	177	12	subsoil	subsoil	NOUN
ap-638	177	13	below	below	ADP
ap-638	177	14	foundations	foundation	NOUN
ap-638	177	15	slabs	slab	VERB
ap-638	177	16	97	97	NUM
ap-638	177	17	p.	p.	NOUN
ap-638	177	18	kuklík	kuklík	NOUN
ap-638	177	19	,	,	PUNCT
ap-638	177	20	m.	m.	NOUN
ap-638	177	21	kopáèková	kopáèková	PROPN
ap-638	177	22	section	section	PROPN
ap-638	177	23	4	4	NUM
ap-638	177	24	b.	b.	NOUN
ap-638	177	25	teplý	teplý	NOUN
ap-638	177	26	,	,	PUNCT
ap-638	177	27	p.	p.	PROPN
ap-638	177	28	rovnaník	rovnaník	PROPN
ap-638	177	29	,	,	PUNCT
ap-638	177	30	z.	z.	PROPN
ap-638	177	31	keršner	keršner	PROPN
ap-638	177	32	,	,	PUNCT
ap-638	177	33	p.	p.	PROPN
ap-638	177	34	rovnaníková	rovnaníková	PROPN
ap-638	177	35	neural	neural	PROPN
ap-638	177	36	network	network	NOUN
ap-638	177	37	based	base	VERB
ap-638	177	38	identification	identification	NOUN
ap-638	177	39	of	of	ADP
ap-638	177	40	material	material	NOUN
ap-638	177	41	model	model	NOUN
ap-638	177	42	parameters	parameter	NOUN
ap-638	177	43	to	to	PART
ap-638	177	44	capture	capture	VERB
ap-638	177	45	experimental	experimental	ADJ
ap-638	177	46	load	load	NOUN
ap-638	177	47	-	-	PUNCT
ap-638	177	48	deflection	deflection	NOUN
ap-638	177	49	curve	curve	NOUN
ap-638	177	50	110	110	NUM
ap-638	177	51	d.	d.	PROPN
ap-638	177	52	novák	novák	PROPN
ap-638	177	53	,	,	PUNCT
ap-638	177	54	d.	d.	PROPN
ap-638	177	55	lehký	lehký	PROPN
ap-638	178	1	fuzzy	fuzzy	ADJ
ap-638	178	2	dynamic	dynamic	ADJ
ap-638	178	3	analysis	analysis	NOUN
ap-638	178	4	of	of	ADP
ap-638	178	5	a	a	DET
ap-638	178	6	2d	2d	NUM
ap-638	178	7	frame	frame	NOUN
ap-638	178	8	117	117	NUM
ap-638	178	9	p.	p.	NOUN
ap-638	178	10	štemberk	štemberk	NOUN
ap-638	178	11	,	,	PUNCT
ap-638	178	12	j.	j.	PROPN
ap-638	178	13	kruis	kruis	PROPN