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

How to Cite?: Trupti Mohite, "On Convexity of Fuzzy Sets and Fuzzy Relations", Volume 12 Issue 7, July 2023, International Journal of Science and Research (IJSR), Pages: 758-761, https://www.ijsr.net/getabstract.php?paperid=SR23710111006, DOI: https://dx.doi.org/10.21275/SR23710111006