A New Approach to the Fuzzification of Convex Structures

Abstract

A new approach to the fuzzification of convex structures is introduced. It is also called an M-fuzzifying convex structure. In the definition of M-fuzzifying convex structure, each subset can be regarded as a convex set to some degree. An M-fuzzifying convex structure can be characterized by means of its M-fuzzifying closure operator. An M-fuzzifying convex structure and its M-fuzzifying closure operator are one-to-one corresponding. The concepts of M-fuzzifying convexity preserving functions, substructures, disjoint sums, bases, subbases, joins, product, and quotient structures are presented and their fundamental properties are obtained in M-fuzzifying convex structure.