Fuzzy congruence relation generated by a fuzzy relation in vector spaces

In this paper, we introduce the concepts of fuzzy congruence relation and fuzzy coset relation on vector spaces and find some their properties. We define some operations on fuzzy coset relations and show that the set of all fuzzy coset relations on a vector space is a vector space, too. We study the...

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Bibliographic Details
Published inJournal of intelligent & fuzzy systems Vol. 35; no. 5; pp. 5635 - 5645
Main Authors Khosravi Shoar, S., Borzooei, R.A., Moradian, R.
Format Journal Article
LanguageEnglish
Published Amsterdam IOS Press BV 01.01.2018
Subjects
Fuzzy sets
Vector space
Vector spaces
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Summary:In this paper, we introduce the concepts of fuzzy congruence relation and fuzzy coset relation on vector spaces and find some their properties. We define some operations on fuzzy coset relations and show that the set of all fuzzy coset relations on a vector space is a vector space, too. We study the union of two fuzzy congruence relations and investigate some its properties. Finally, by using the concepts of a generated subspace of a set and a congruence relation on a vector space, we introduce the notion of a fuzzy congruence relation generated by a fuzzy relation in a vector space.
ISSN:1064-1246
1875-8967
DOI:10.3233/JIFS-17088