Fuzzy entropy on intuitionistic fuzzy sets

TLDR

The article defines fuzzy entropy for intuitionistic fuzzy sets using probability and proposes two families of entropy measures. The authors construct axiom definitions and properties, and compare their measures with two existing entropy definitions by Burillo & Bustince (1996) and Szmidt & Kacprzyk (2001) through numerical comparisons. The proposed entropy measures appear more reliable for quantifying the degree of fuzziness of an IFS. © 2006 Wiley Periodicals, Inc., Int J Int Syst 21:443–451.

Abstract

In this article we exploit the concept of probability for defining the fuzzy entropy of intuitionistic fuzzy sets (IFSs). We then propose two families of entropy measures for IFSs and also construct the axiom definition and properties. Two definitions of entropy for IFSs proposed by Burillo and Bustince in 1996 and Szmidt and Kacprzyk in 2001 are used. The first one allows us to measure the degree of intuitionism of an IFS, whereas the second one is a nonprobabilistic-type entropy measure with a geometric interpretation of IFSs used in comparison with our proposed entropy of IFSs in the numerical comparisons. The results show that the proposed entropy measures seem to be more reliable for presenting the degree of fuzziness of an IFS. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 443–451, 2006.