## A new approach to the fuzzification of convex structures.(English)Zbl 1449.54018

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.

### MSC:

 54A40 Fuzzy topology

### Keywords:

$$M$$-fuzzifying convex structure
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### References:

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