Open AccessSTUDY OF CONVEXITY IN SETS AND FUZZY SETS
Author(s) -
Abubakar Abdulkarim,
I. F. Mukaila
Publication year - 2022
Publication title -
fudma journal of sciences
Language(s) - English
Resource type - Journals
ISSN - 2616-1370
DOI - 10.33003/fjs-2022-0601-852
Subject(s) - convexity , mathematics , fuzzy set , mathematical proof , regular polygon , fuzzy logic , algebraic number , set (abstract data type) , pure mathematics , discrete mathematics , algebra over a field , combinatorics , computer science , artificial intelligence , mathematical analysis , geometry , financial economics , economics , programming language
In this paper, we present an overview of both classical and fuzzy convexity, particularly, in conjunction with continuity5 and some topological concepts, and provide proofs of some of their algebraic properties along with suitable illustrations. We have extended the work of (Ammar E. E., 1999) by proving that if and are two convex fuzzy sets, then , , , and are also convex fuzzy sets. We have also shown that the convexity of a fuzzy set implies semistrict quasi-convexity