id	sid	eid	entity	type
ejpam-5385	1	1	european journal	ORG
ejpam-5385	2	1	17	CARDINAL
ejpam-5385	2	2	4	CARDINAL
ejpam-5385	2	3	2024	DATE
ejpam-5385	2	4	3291	CARDINAL
ejpam-5385	3	1	new york	GPE
ejpam-5385	3	2	algebras shadi m. shaqaqha1,∗	ORG
ejpam-5385	3	3	mounther y. al-deiakeh1 1	PERSON
ejpam-5385	3	4	yarmouk university	ORG
ejpam-5385	3	5	shafiq irshidat street	PERSON
ejpam-5385	3	6	21163	DATE
ejpam-5385	3	7	jordan	PERSON
ejpam-5385	6	1	algebras	ORG
ejpam-5385	7	1	2020	DATE
ejpam-5385	7	2	17b99	CARDINAL
ejpam-5385	7	3	08a72	CARDINAL
ejpam-5385	7	4	03e72	CARDINAL
ejpam-5385	7	5	1	CARDINAL
ejpam-5385	8	1	lotfi zadeh	ORG
ejpam-5385	8	2	1965	DATE
ejpam-5385	8	3	22	CARDINAL
ejpam-5385	10	1	1986	DATE
ejpam-5385	10	2	atanassov	ORG
ejpam-5385	10	3	6	CARDINAL
ejpam-5385	11	1	10	CARDINAL
ejpam-5385	11	2	11	CARDINAL
ejpam-5385	12	1	2012	DATE
ejpam-5385	12	2	5	CARDINAL
ejpam-5385	14	1	s. shaqaqha	PERSON
ejpam-5385	14	2	m. al-deiakeh	PERSON
ejpam-5385	15	1	3291	PRODUCT
ejpam-5385	15	2	2024	CARDINAL
ejpam-5385	16	1	s. shaqaqha	PERSON
ejpam-5385	16	2	m. y. al-deiakeh	PERSON
ejpam-5385	17	1	j. pure	PERSON
ejpam-5385	17	2	17	CARDINAL
ejpam-5385	17	3	4	CARDINAL
ejpam-5385	17	4	2024	CARDINAL
ejpam-5385	17	5	3291-3303 3292	CARDINAL
ejpam-5385	19	1	3	CARDINAL
ejpam-5385	19	2	2	CARDINAL
ejpam-5385	21	1	roh et al	PERSON
ejpam-5385	22	1	12	CARDINAL
ejpam-5385	23	1	18	CARDINAL
ejpam-5385	25	1	21	CARDINAL
ejpam-5385	26	1	1	CARDINAL
ejpam-5385	26	2	13	CARDINAL
ejpam-5385	27	1	2	CARDINAL
ejpam-5385	28	1	2.1	CARDINAL
ejpam-5385	29	1	algebras	ORG
ejpam-5385	29	2	9	CARDINAL
ejpam-5385	30	1	algebras	ORG
ejpam-5385	31	1	wherem signifies	ORG
ejpam-5385	33	1	two	CARDINAL
ejpam-5385	33	2	∈	ORG
ejpam-5385	33	3	m1, m2	PRODUCT
ejpam-5385	35	1	m1, m2	PRODUCT
ejpam-5385	37	1	m3	CARDINAL
ejpam-5385	37	2	m1, m2	PRODUCT
ejpam-5385	41	1	0	CARDINAL
ejpam-5385	41	2	2	CARDINAL
ejpam-5385	41	3	m1, m2	PRODUCT
ejpam-5385	41	4	∈	ORG
ejpam-5385	43	1	s. shaqaqha	PERSON
ejpam-5385	43	2	m. y. al-deiakeh	PERSON
ejpam-5385	44	1	j. pure	PERSON
ejpam-5385	44	2	17	CARDINAL
ejpam-5385	44	3	4	CARDINAL
ejpam-5385	44	4	2024	CARDINAL
ejpam-5385	44	5	3291-3303 3293	PERCENT
ejpam-5385	45	1	∈	ORG
ejpam-5385	46	1	algebras	ORG
ejpam-5385	47	1	algebras	ORG
ejpam-5385	47	2	∈	ORG
ejpam-5385	47	3	n ∈ n	ORG
ejpam-5385	49	1	z(m	ORG
ejpam-5385	51	1	∈	ORG
ejpam-5385	53	1	∈	ORG
ejpam-5385	53	2	∈	ORG
ejpam-5385	53	3	∈	ORG
ejpam-5385	53	4	two	CARDINAL
ejpam-5385	53	5	m1 and m2	PRODUCT
ejpam-5385	53	6	m1 → m2	PRODUCT
ejpam-5385	56	1	one	CARDINAL
ejpam-5385	58	1	∈	ORG
ejpam-5385	59	1	adm	PERSON
ejpam-5385	59	2	adm	PERSON
ejpam-5385	59	3	∈	ORG
ejpam-5385	60	1	m. moreover	PERSON
ejpam-5385	60	2	ker(f	GPE
ejpam-5385	62	1	ker(f	GPE
ejpam-5385	63	1	2.2	CARDINAL
ejpam-5385	63	2	ψe(x	NORP
ejpam-5385	65	1	ψe(x	NORP
ejpam-5385	66	1	ψe(x	NORP
ejpam-5385	66	2	|≤ 1	DATE
ejpam-5385	67	1	−1	DATE
ejpam-5385	67	2	ψe(x	NORP
ejpam-5385	67	3	iζe(x	ORG
ejpam-5385	67	4	ρ̂e(x)e iζ̂e(x	PRODUCT
ejpam-5385	68	1	0	CARDINAL
ejpam-5385	68	2	1	CARDINAL
ejpam-5385	68	3	0	CARDINAL
ejpam-5385	68	4	2π	CARDINAL
ejpam-5385	70	1	0	CARDINAL
ejpam-5385	70	2	s. shaqaqha	PERSON
ejpam-5385	70	3	m. y. al-deiakeh	PERSON
ejpam-5385	71	1	j. pure	PERSON
ejpam-5385	71	2	17	CARDINAL
ejpam-5385	71	3	4	CARDINAL
ejpam-5385	71	4	2024	CARDINAL
ejpam-5385	71	5	3291-3303	CARDINAL
ejpam-5385	72	1	ψe(x	NORP
ejpam-5385	72	2	1−ρe(x))ei(2π−ζe(x	CARDINAL
ejpam-5385	73	1	two	CARDINAL
ejpam-5385	77	1	z2ρ2e iζ2 (ρ1	ORG
ejpam-5385	78	1	0	CARDINAL
ejpam-5385	78	2	1	CARDINAL
ejpam-5385	79	1	0	CARDINAL
ejpam-5385	79	2	2π	CARDINAL
ejpam-5385	79	3	two	CARDINAL
ejpam-5385	80	1	1	CARDINAL
ejpam-5385	81	1	18	CARDINAL
ejpam-5385	81	2	three	CARDINAL
ejpam-5385	81	3	k ∈	PERSON
ejpam-5385	83	1	+m2	QUANTITY
ejpam-5385	84	1	ϕe([m1,m2	ORG
ejpam-5385	84	2	m. 3	PERSON
ejpam-5385	85	1	algebras	ORG
ejpam-5385	85	2	m1 and m2	PRODUCT
ejpam-5385	92	1	1	CARDINAL
ejpam-5385	93	1	algebras	ORG
ejpam-5385	95	1	s. shaqaqha	PERSON
ejpam-5385	95	2	m. y. al-deiakeh	PERSON
ejpam-5385	96	1	j. pure	PERSON
ejpam-5385	96	2	17	CARDINAL
ejpam-5385	96	3	4	CARDINAL
ejpam-5385	96	4	2024	CARDINAL
ejpam-5385	96	5	3291-3303	CARDINAL
ejpam-5385	104	1	two	CARDINAL
ejpam-5385	111	1	k ∈ k	PERSON
ejpam-5385	112	1	1	CARDINAL
ejpam-5385	115	1	+m2	PERSON
ejpam-5385	117	1	1	CARDINAL
ejpam-5385	120	1	ϕf−1(p)(m1	GPE
ejpam-5385	122	1	+m2	PERSON
ejpam-5385	123	1	1	CARDINAL
ejpam-5385	126	1	+m2	QUANTITY
ejpam-5385	127	1	2.	CARDINAL
ejpam-5385	127	2	k ∈ k	PERSON
ejpam-5385	127	3	ϕf−1(p)(km1	PERSON
ejpam-5385	128	1	ϕp(kf(m1	PERSON
ejpam-5385	128	2	1	CARDINAL
ejpam-5385	129	1	ϕf−1(p)(km1	PERSON
ejpam-5385	129	2	ϕf−1(p)(m1	GPE
ejpam-5385	130	1	s. shaqaqha	PERSON
ejpam-5385	130	2	m. y. al-deiakeh	PERSON
ejpam-5385	131	1	j. pure	PERSON
ejpam-5385	131	2	17	CARDINAL
ejpam-5385	131	3	4	CARDINAL
ejpam-5385	131	4	2024	CARDINAL
ejpam-5385	131	5	3291-3303	CARDINAL
ejpam-5385	132	1	ψp(kf(m1	PERSON
ejpam-5385	132	2	1	CARDINAL
ejpam-5385	133	1	3	CARDINAL
ejpam-5385	134	1	1	CARDINAL
ejpam-5385	134	2	ϕf−1(p)(m1	GPE
ejpam-5385	135	1	1	CARDINAL
ejpam-5385	137	1	1	CARDINAL
ejpam-5385	138	1	algebras	ORG
ejpam-5385	141	1	1	CARDINAL
ejpam-5385	142	1	third	ORDINAL
ejpam-5385	142	2	1	CARDINAL
ejpam-5385	143	1	two	CARDINAL
ejpam-5385	146	1	s. shaqaqha	PERSON
ejpam-5385	146	2	m. y. al-deiakeh	PERSON
ejpam-5385	147	1	j. pure	PERSON
ejpam-5385	147	2	17	CARDINAL
ejpam-5385	147	3	4	CARDINAL
ejpam-5385	147	4	2024	CARDINAL
ejpam-5385	147	5	3291-3303 3297	CARDINAL
ejpam-5385	147	6	second	ORDINAL
ejpam-5385	148	1	1	CARDINAL
ejpam-5385	150	1	ϕf−1(p)(m1	GPE
ejpam-5385	158	1	1	CARDINAL
ejpam-5385	159	1	1	CARDINAL
ejpam-5385	161	1	2	CARDINAL
ejpam-5385	162	1	14	CARDINAL
ejpam-5385	164	1	∈	ORG
ejpam-5385	164	2	m. theorem 2.	ORG
ejpam-5385	164	3	algebras	ORG
ejpam-5385	168	1	s. shaqaqha	PERSON
ejpam-5385	168	2	m. y. al-deiakeh	PERSON
ejpam-5385	169	1	j. pure	PERSON
ejpam-5385	169	2	17	CARDINAL
ejpam-5385	169	3	4	CARDINAL
ejpam-5385	169	4	2024	CARDINAL
ejpam-5385	169	5	3291-3303 3298	CARDINAL
ejpam-5385	169	6	ρe(m)}ei(supn	ORG
ejpam-5385	172	1	supn2	PERSON
ejpam-5385	173	1	supn2	PERSON
ejpam-5385	174	1	supn2	PERSON
ejpam-5385	177	1	supn2	PERSON
ejpam-5385	179	1	supn2	PERSON
ejpam-5385	180	1	infn1	PERSON
ejpam-5385	180	2	infn1	GPE
ejpam-5385	182	1	lemma 2	ORG
ejpam-5385	182	2	∈	ORG
ejpam-5385	183	1	lemma 1	ORG
ejpam-5385	184	1	ρef(e	GPE
ejpam-5385	185	1	k ∈ k	PERSON
ejpam-5385	185	2	n1)∨	NORP
ejpam-5385	185	3	n1)∨	NORP
ejpam-5385	187	1	8	CARDINAL
ejpam-5385	189	1	2	CARDINAL
ejpam-5385	191	1	s. shaqaqha	PERSON
ejpam-5385	191	2	m. y. al-deiakeh	PERSON
ejpam-5385	192	1	j. pure	PERSON
ejpam-5385	192	2	17	CARDINAL
ejpam-5385	192	3	4	CARDINAL
ejpam-5385	192	4	2024	CARDINAL
ejpam-5385	192	5	3291-3303	CARDINAL
ejpam-5385	193	1	im(f	GPE
ejpam-5385	196	1	0	CARDINAL
ejpam-5385	196	2	1	CARDINAL
ejpam-5385	199	1	f(q	GPE
ejpam-5385	202	1	f(s	GPE
ejpam-5385	212	1	0	CARDINAL
ejpam-5385	212	2	1	CARDINAL
ejpam-5385	216	1	infn1	PERSON
ejpam-5385	216	2	f(q	GPE
ejpam-5385	220	1	f(s	GPE
ejpam-5385	226	1	2	CARDINAL
ejpam-5385	227	1	2	CARDINAL
ejpam-5385	227	2	algebras	ORG
ejpam-5385	228	1	3	CARDINAL
ejpam-5385	231	1	s. shaqaqha	PERSON
ejpam-5385	231	2	m. y. al-deiakeh	PERSON
ejpam-5385	232	1	j. pure	PERSON
ejpam-5385	232	2	17	CARDINAL
ejpam-5385	232	3	4	CARDINAL
ejpam-5385	232	4	2024	CARDINAL
ejpam-5385	232	5	3291-3303	MONEY
ejpam-5385	233	1	two	CARDINAL
ejpam-5385	234	1	chen	PERSON
ejpam-5385	236	1	ϕe+p	ORG
ejpam-5385	236	2	ψe+p	PERSON
ejpam-5385	239	1	ϕq	ORG
ejpam-5385	239	2	two	CARDINAL
ejpam-5385	239	3	ρ̂qe	PERSON
ejpam-5385	242	1	3	CARDINAL
ejpam-5385	243	1	14	CARDINAL
ejpam-5385	243	2	two	CARDINAL
ejpam-5385	245	1	two	CARDINAL
ejpam-5385	248	1	3	CARDINAL
ejpam-5385	250	1	4	CARDINAL
ejpam-5385	258	1	s. shaqaqha	PERSON
ejpam-5385	258	2	m. y. al-deiakeh	PERSON
ejpam-5385	259	1	j. pure	PERSON
ejpam-5385	259	2	17	CARDINAL
ejpam-5385	259	3	4	CARDINAL
ejpam-5385	259	4	2024	CARDINAL
ejpam-5385	259	5	3291-3303	CARDINAL
ejpam-5385	264	1	iζe(x	ORG
ejpam-5385	264	2	ψe(x	NORP
ejpam-5385	265	1	ρ̂e(x)e iζ̂e(x	PRODUCT
ejpam-5385	265	2	ψe(x	NORP
ejpam-5385	266	1	α̂ ∈	CARDINAL
ejpam-5385	267	1	0	CARDINAL
ejpam-5385	267	2	1	CARDINAL
ejpam-5385	268	1	0	CARDINAL
ejpam-5385	268	2	2π	CARDINAL
ejpam-5385	271	1	α>,β	NORP
ejpam-5385	272	1	s. shaqaqha	PERSON
ejpam-5385	273	1	13	CARDINAL
ejpam-5385	275	1	5	CARDINAL
ejpam-5385	278	1	α̂ ∈	CARDINAL
ejpam-5385	279	1	0	CARDINAL
ejpam-5385	279	2	1	CARDINAL
ejpam-5385	280	1	0	CARDINAL
ejpam-5385	280	2	2π	CARDINAL
ejpam-5385	281	1	α̂,β̂	ORG
ejpam-5385	281	2	α>,β	NORP
ejpam-5385	281	3	α>,β	NORP
ejpam-5385	282	1	α̂,β̂	ORG
ejpam-5385	282	2	α>,β	NORP
ejpam-5385	285	1	α>,β	NORP
ejpam-5385	287	1	∈	ORG
ejpam-5385	291	1	∈	ORG
ejpam-5385	291	2	α̂,β̂	ORG
ejpam-5385	293	1	3302 5	DATE
ejpam-5385	296	1	21	CARDINAL
ejpam-5385	297	1	1	CARDINAL
ejpam-5385	298	1	13	CARDINAL
ejpam-5385	299	1	14	CARDINAL
ejpam-5385	299	2	15	CARDINAL
ejpam-5385	300	1	16	CARDINAL
ejpam-5385	300	2	17	CARDINAL
ejpam-5385	302	1	19	CARDINAL
ejpam-5385	302	2	20	CARDINAL
ejpam-5385	303	1	mounther al-deiakeh	PERSON
ejpam-5385	304	1	4	CARDINAL
ejpam-5385	307	1	1	CARDINAL
ejpam-5385	307	2	m. akram	PERSON
ejpam-5385	309	1	southeast asian	NORP
ejpam-5385	309	2	31:843–855	CARDINAL
ejpam-5385	309	3	2007	DATE
ejpam-5385	310	1	2	CARDINAL
ejpam-5385	310	2	m. akram	PERSON
ejpam-5385	311	1	algebras	ORG
ejpam-5385	312	1	quasigroups	ORG
ejpam-5385	312	2	21:1–10	CARDINAL
ejpam-5385	312	3	2013	DATE
ejpam-5385	313	1	3	CARDINAL
ejpam-5385	313	2	m. akram	PERSON
ejpam-5385	314	1	algebras	ORG
ejpam-5385	315	1	infosys science foundation series	ORG
ejpam-5385	316	1	2018	DATE
ejpam-5385	317	1	4	CARDINAL
ejpam-5385	317	2	m. al-deiakeh	PERSON
ejpam-5385	318	1	algebras	ORG
ejpam-5385	319	1	yarmouk university	ORG
ejpam-5385	319	2	jordan	GPE
ejpam-5385	319	3	2019	DATE
ejpam-5385	320	1	5	CARDINAL
ejpam-5385	320	2	a. s.	PERSON
ejpam-5385	320	3	a. salleh	PERSON
ejpam-5385	322	1	12	CARDINAL
ejpam-5385	322	2	1482:464	CARDINAL
ejpam-5385	322	3	470	CARDINAL
ejpam-5385	322	4	2012	DATE
ejpam-5385	323	1	3303	CARDINAL
ejpam-5385	323	2	6	CARDINAL
ejpam-5385	323	3	k. t. atanassov	PERSON
ejpam-5385	325	1	20:87–96	CARDINAL
ejpam-5385	325	2	1986	DATE
ejpam-5385	326	1	7	CARDINAL
ejpam-5385	327	1	algebras	ORG
ejpam-5385	328	1	vnu science press	ORG
ejpam-5385	328	2	utrecht	GPE
ejpam-5385	328	3	1987	DATE
ejpam-5385	329	1	8	CARDINAL
ejpam-5385	329	2	w. chen	PERSON
ejpam-5385	329	3	s. zhang	PERSON
ejpam-5385	331	1	58:1645–1661	CARDINAL
ejpam-5385	331	2	2009	DATE
ejpam-5385	332	1	9	CARDINAL
ejpam-5385	332	2	n. jacobson	PERSON
ejpam-5385	333	1	algebras	ORG
ejpam-5385	334	1	wiley	PERSON
ejpam-5385	334	2	new york	GPE
ejpam-5385	334	3	1962	DATE
ejpam-5385	335	1	10	CARDINAL
ejpam-5385	335	2	t. tanaka	PERSON
ejpam-5385	337	1	nihonkai mathematical journal	ORG
ejpam-5385	337	2	34:1–18	CARDINAL
ejpam-5385	337	3	2023	CARDINAL
ejpam-5385	338	1	11	CARDINAL
ejpam-5385	338	2	l. c. platil	PERSON
ejpam-5385	338	3	g. c. petalcorin	PERSON
ejpam-5385	340	1	journal of analysis & applications	ORG
ejpam-5385	340	2	15:71–83	DATE
ejpam-5385	340	3	2017	DATE
ejpam-5385	341	1	12	CARDINAL
ejpam-5385	341	2	e. h. roh	PERSON
ejpam-5385	341	3	e. yang	PERSON
ejpam-5385	341	4	y. b. jun.	PERSON
ejpam-5385	343	1	european journal	ORG
ejpam-5385	343	2	16(3):1342–1358	CARDINAL
ejpam-5385	343	3	2023	CARDINAL
ejpam-5385	344	1	13	CARDINAL
ejpam-5385	345	1	algebras	ORG
ejpam-5385	346	1	jordan j.	PERSON
ejpam-5385	347	1	13(2):231–247	ORG
ejpam-5385	347	2	2020	DATE
ejpam-5385	348	1	14	CARDINAL
ejpam-5385	350	1	palestine	GPE
ejpam-5385	350	2	2022	CARDINAL
ejpam-5385	351	1	15	CARDINAL
ejpam-5385	353	1	missouri	GPE
ejpam-5385	353	2	34(2):196–207	DATE
ejpam-5385	353	3	2022	CARDINAL
ejpam-5385	354	1	16	CARDINAL
ejpam-5385	356	1	jordan j.	PERSON
ejpam-5385	357	1	15(3a):523	DATE
ejpam-5385	357	2	540	CARDINAL
ejpam-5385	357	3	2022	CARDINAL
ejpam-5385	358	1	17	CARDINAL
ejpam-5385	359	1	algebras	ORG
ejpam-5385	360	1	12(7):630	CARDINAL
ejpam-5385	360	2	2023	CARDINAL
ejpam-5385	361	1	18	CARDINAL
ejpam-5385	361	2	s. shaqaqha	PERSON
ejpam-5385	361	3	m. al-deiakeh	PERSON
ejpam-5385	362	1	algebras	ORG
ejpam-5385	363	1	2023	CARDINAL
ejpam-5385	364	1	19	CARDINAL
ejpam-5385	364	2	r. r. yager	PERSON
ejpam-5385	367	1	ifsa world congr	ORG
ejpam-5385	368	1	nafips annu	PERSON
ejpam-5385	369	1	ifsa/nafips	ORG
ejpam-5385	369	2	edmonton	GPE
ejpam-5385	369	3	ab	GPE
ejpam-5385	369	4	canada	GPE
ejpam-5385	369	5	2013	DATE
ejpam-5385	370	1	20	CARDINAL
ejpam-5385	370	2	r. r. yager	PERSON
ejpam-5385	371	1	pythagorean	ORG
ejpam-5385	371	2	multicriteria	GPE
ejpam-5385	372	1	syst	LOC
ejpam-5385	372	2	22(4):958–965, 2014	DATE
ejpam-5385	373	1	21	CARDINAL
ejpam-5385	373	2	s. e. yehia	PERSON
ejpam-5385	374	1	80:237–244	CARDINAL
ejpam-5385	374	2	1996	DATE
ejpam-5385	375	1	22	CARDINAL
ejpam-5385	375	2	l. zadeh	PERSON
ejpam-5385	377	1	1965	DATE