Abstract
We introduce the notion of abelian fuzzy subsets on a groupoid, and we observe a variety of consequences which follow. New notions include, among others, diagonal symmetric relations, several types of quasi orders, convex sets, and fuzzy centers, some of whose properties are also investigated.
Highlights
The notion of a fuzzy subset of a set was introduced by Zadeh [1]
Rosenfeld [2] used the notion of a fuzzy subset to set down corner stone papers in several areas of mathematics
The book included all the important work that has been done on L-subspaces of a vector space and on Lsubfields of a field
Summary
The notion of a fuzzy subset of a set was introduced by Zadeh [1]. His seminal paper in 1965 has opened up new insights and applications in a wide range of scientific fields. Fayoumi [5] introduced the notion of the center ZBin(X) in the semigroup Bin(X) of all binary systems on a set X and showed that a groupoid (X, ∙) ∈ ZBin(X) if and only if it is a locally zero groupoid. We introduce the notion of abelian fuzzy subgroupoids on a groupoid and discuss diagonal symmetric relations, convex sets, and fuzzy centers on Bin(X)
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