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Issue:New measures of entropy for intuitionistic fuzzy sets

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Title of paper: New measures of entropy for intuitionistic fuzzy sets
Author(s):
Eulalia Szmidt
Systems Research lnstitute - Polish Academy of Sciences, ul. Newelska 6, OL-447 Warsaw, Poland
szmidt@ibspan.waw.pl
Janusz Kacprzyk
Systems Research lnstitute - Polish Academy of Sciences, ul. Newelska 6, OL-447 Warsaw, Poland
kacprzyk@ibspan.waw.pl
Presented at: 9th ICIFS, Sofia, 7-8 May 2005
Published in: Conference proceedings, "Notes on IFS", Volume 11 (2005) Number 2, pages 12—20
Download:  PDF (167  Kb, File info)
Abstract: We propose the new measures of entropy for intuitionistic fuzzy sets. This paper is in a sense a continuation of our previous paper on entropy of intuitionistic fuzzy sets — the inferences are based on the same two types of distances as previously — to the farer and to the nearer crisp elements. But instead of the ratio of these distances we examine their difference. The distances are calculated using the formulas for the normalized Hamming distance, and the normalized Euclidean distance. In the case of the Hamming distance we obtain simpler formulas than in our previous paper. We show some special properties for the formulas when Hamming distance is applied. We also suggest π-entropy, a function strongly accounting for the lack of knowledge as to the membership and non-membership.
Keywords: Fuzzy sets, Intuitionistic fuzzy sets, Entropy, Similarity
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