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 inSoft computing (Berlin, Germany) Vol. 25; no. 11; pp. 7257 - 7269
Main Authors Borzooei, R. A., Kologani, M. Aaly, Hashemi, M. A.
Format Journal Article
LanguageEnglish
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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10.1016/j.ins.2016.11.027
10.1007/s00153-014-0380-0
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Issue 11
Keywords Implicative filter
Positive implicative filter
Filter
Equality algebra
Hyper equality algebra
Fantastic filter
Language English
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Snippet 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...
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StartPage 7257
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
URI https://link.springer.com/article/10.1007/s00500-021-05832-z
https://www.proquest.com/docview/2917979351/abstract/
Volume 25
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