The Foundations of Homotopic Fuzzy Sets

Abstract

Fuzzy sets are determined by membership functions. Many methods have been developed when determining the membership function of a fuzzy set. However, a fuzzy set can be specified with more than one membership function. Therefore, the membership function fitting problem is a well-known problem in fuzzy set theory. In this article, we have introduced the concepts of topologically continuous fuzzy set and homotopic fuzzy set whose membership functions are topologically continuous and homotopic, using the basic concepts of topology to overcome this problem. We have studied its basic structural properties. Finally, we proposed a solution method to the membership function fitting problem in fuzzy set theory using the homotopic fuzzy set concept.

Keywords

• Fuzzy set
• Homotopy
• Homotopic fuzzy set
• Topology

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