On Convexity of Fuzzy Sets and Fuzzy Relations

Trupti Mohite

Abstract: This paper explores the convexity of fuzzy sets and fuzzy relations defined on the set of real numbers and their cartesian product respectively. Using the concept of ?-cut, we establish that a fuzzy set is convex if and only if the ?-cut of the fuzzy set is convex. The paper further extends this concept to fuzzy relations. The findings have significant implications for the application of convexity in various fields.

Keywords: Fuzzy sets, Convex fuzzy sets, Fuzzy relations, Convex fuzzy relations, ?-cuts