Filter theory on hyper equality algebras
In this paper, some results related to properties of various versions in equality algebras are given by using the notion of hyper equality algebras. We introduce some types of filters such as implicative, positive implicative and fantastic filters on hyper equality algebras and prove some results de...
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Published in | Soft computing (Berlin, Germany) Vol. 25; no. 11; pp. 7257 - 7269 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.06.2021
Springer Nature B.V |
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Abstract | In this paper, some results related to properties of various versions in equality algebras are given by using the notion of hyper equality algebras. We introduce some types of filters such as implicative, positive implicative and fantastic filters on hyper equality algebras and prove some results determining the relation between these filters. Further, it is shown that every (
S
∼
-reflexive) positive implicative filter of a hyper equality algebra
H
is a weak (strong) filter of
H
. Finally, we prove that every
S
∼
-reflexive implicative filter of
H
is a (fantastic filter) positive implicative filter of
H
. |
---|---|
AbstractList | In this paper, some results related to properties of various versions in equality algebras are given by using the notion of hyper equality algebras. We introduce some types of filters such as implicative, positive implicative and fantastic filters on hyper equality algebras and prove some results determining the relation between these filters. Further, it is shown that every (
S
∼
-reflexive) positive implicative filter of a hyper equality algebra
H
is a weak (strong) filter of
H
. Finally, we prove that every
S
∼
-reflexive implicative filter of
H
is a (fantastic filter) positive implicative filter of
H
. In this paper, some results related to properties of various versions in equality algebras are given by using the notion of hyper equality algebras. We introduce some types of filters such as implicative, positive implicative and fantastic filters on hyper equality algebras and prove some results determining the relation between these filters. Further, it is shown that every (S∼-reflexive) positive implicative filter of a hyper equality algebra H is a weak (strong) filter of H. Finally, we prove that every S∼-reflexive implicative filter of H is a (fantastic filter) positive implicative filter of H. |
Author | Borzooei, R. A. Hashemi, M. A. Kologani, M. Aaly |
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Cites_doi | 10.3233/JIFS-191112 10.1007/s11225-012-9457-0 10.1007/s00153-013-0325-z 10.29252/hatef.jahla.1.2.5 10.29252/hatef.jahla.1.3.3 10.1007/s00500-014-1494-3 10.1016/j.ins.2016.11.027 10.1007/s00153-014-0380-0 10.1016/j.fss.2009.04.010 |
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Keywords | Implicative filter Positive implicative filter Filter Equality algebra Hyper equality algebra Fantastic filter |
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References | Hashemi, Borzooei (CR12) 2020; 14 Jenei (CR13) 2012; 100 Cheng, Xin, Yong (CR7) 2017; 37 Yang, Zhu, Xin (CR18) 2020; 38 Borzooei, Aaly Kologani (CR1) 2020; 1 Borzooei, Ganji Saffar, Ameri (CR3) 2013; 31 Paad, Bakhshi (CR17) 2020; 1 Cheng, Xin (CR4) 2015; 35 Cheng, Xin (CR5) 2019; 54 CR15 Cheng, Xin, Jun (CR6) 2016; 510 CR10 Borzooei, Bakhshi, Zahiri (CR2) 2014; 22 Novák, De Baets (CR16) 2009; 160 Jenei, Kóródi (CR14) 2013; 52 Zebardast, Borzooei, Aaly Kologani (CR19) 2017; 381 Ciungu (CR8) 2014; 53 Ciungu (CR9) 2015; 19 Hashemi, Borzooei (CR11) 2020; 13 RA Borzooei (5832_CR1) 2020; 1 RA Borzooei (5832_CR3) 2013; 31 MA Hashemi (5832_CR12) 2020; 14 Y Yang (5832_CR18) 2020; 38 5832_CR15 A Paad (5832_CR17) 2020; 1 RA Borzooei (5832_CR2) 2014; 22 LC Ciungu (5832_CR8) 2014; 53 MA Hashemi (5832_CR11) 2020; 13 S Jenei (5832_CR13) 2012; 100 LC Ciungu (5832_CR9) 2015; 19 XY Cheng (5832_CR4) 2015; 35 XY Cheng (5832_CR5) 2019; 54 XY Cheng (5832_CR7) 2017; 37 F Zebardast (5832_CR19) 2017; 381 XY Cheng (5832_CR6) 2016; 510 S Jenei (5832_CR14) 2013; 52 V Novák (5832_CR16) 2009; 160 5832_CR10 |
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SubjectTerms | Algebra Artificial Intelligence Computational Intelligence Control Engineering Equality Foundations Fuzzy sets Mathematical Logic and Foundations Mechatronics Robotics |
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Title | Filter theory on hyper equality algebras |
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