A New Approach to the Fuzzification of Convex Structures

الملخص EN

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.