Fuzzy congruence relation generated by a fuzzy relation in vector spaces

摘要

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.