Abstract
In this paper we study the relations among similarity measure, subsethood measure and fuzzy entropy and present several propositions that similarity measure, subsethood measure and fuzzy entropy ca...
Highlights
In fuzzy set theory, similarity measure, subsethood measure and fuzzy entropy are three basic concepts
Zeng et al 32 investigated the relations among subsethood measure, similarity measure, and fuzzy entropy based on their axiomatic definitions
We propose several propositions to show that these three concepts can be transformed by each other based on their axiomatic definitions
Summary
Similarity measure, subsethood measure and fuzzy entropy are three basic concepts. The subsethood measure ( called inclusion measure) is a relation between fuzzy sets A and B, which indicates the degree to which A is contained in B. Burillo and Bustince 2 studied the concepts of entropy for intuitionistic fuzzy sets and intervalvalued fuzzy sets In addition to their concepts, many researchers have contributed to discussing the relations among the above-mentioned three concepts. Zeng et al 32 investigated the relations among subsethood measure, similarity measure, and fuzzy entropy based on their axiomatic definitions. The present paper is related to, but different from the above-mentioned works, it focuses on discussing the relationships among subsethood measure, similarity measure, and fuzzy entropy in a more general setting and can be thought of as an extension of the above works.
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