Abstract
We discuss properties of a class of real-valued functions on a set X 2 constructed as finite (real) linear combinations of functions denoted as [(X, ∗); μ], where (X, ∗) is a groupoid (binary system) and μ is a fuzzy subset of X and where [(X, ∗); μ](x, y): = μ(x∗y) − min{μ(x), μ(y)}. Many properties, for example, μ being a fuzzy subgroupoid of X, ∗), can be restated as some properties of [(X, ∗); μ]. Thus, the context provided opens up ways to consider well-known concepts in a new light, with new ways to prove known results as well as to provide new questions and new results. Among these are identifications of many subsemigroups and left ideals of (Bin(X), □) for example.
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. The present authors [6] introduced the notion of abelian fuzzy subgroupoids on a groupoid and discuss diagonal symmetric relations, convex sets, and fuzzy centers on Bin(X). The context provided opens up ways to consider wellknown concepts in a new light, with new ways to prove known results as well as to provide new questions and new results. Among these are identifications of many subsemigroups and left ideals of (Bin(X), ◻), for example
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
