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Issue:Analysis of similarity measures for Atanassov's intuitionistic fuzzy sets

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http://ifigenia.org/wiki/issue:eusflat-2009-1416-1421
Title of paper: Analysis of similarity measures for Atanassov's intuitionistic fuzzy sets
Author(s):
Eulalia Szmidt
Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01—447 Warsaw, Poland
szmidt@ibspan.waw.pl
Janusz Kacprzyk
Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01—447 Warsaw, Poland
kacprzyk@ibspan.waw.pl
Presented at: Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, Portugal, July 20-24, 2009
Published in: Conference proceedings, pages 1416-1421
Download:  PDF (138  Kb, File info)
Abstract: We consider some existing similarity measures for Atanassov's intuitionistic fuzzy sets (A-IFSs, for short). We show that neither similarity measures treating an A-IF as a simple interval values fuzzy set, nor straightforward generalizations of the similarity measures well-known for the classic fuzzy sets work under reasonable circumstances. Next, expanding upon our previous works, we consider a family of similarity measures constructed by taking into account both all the three functions (the membership, non-membership and hesitation) describing an A-IF, and the complements of the elements we compare to each other. That is, we use all kinds and fine shades of information available. We point out their proper behavior and an intuitive appeal.
Keywords: Atanassov's intuitionistic fuzzy sets, similarity measures.
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Citations:
  1. Szmidt E. and Kreinovich V. Symmetry between true, false and uncertain: An explanation, Proc. of 5th International Workshop on Intuitionistic Fuzzy Sets, 19 October 2009, Banská Bystrica, Slovakia. Published in: Notes on Intuitionistic Fuzzy Sets, Volume 15, Number 4, pages 1—8

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