A new approach to the fuzzification of convex structures (Q2336259)

Summary: 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.