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Issue:A "family" of similarity measures for intuitionistic fuzzy set theory and mass assignment theory

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Title of paper: A "family" of similarity measures for intuitionistic fuzzy set theory and mass assignment theory
Author(s):
Eulalia Szmidt
Systems Research Institute - Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
szmidt@ibspan.waw.pl
Jim F. Baldwin
Department of Engineering Mathematics, University of Bristol, Bristol BS8 1TR, England
Jim.Baldwin@bristol.ac.uk
Published in: "Notes on IFS", Volume 12 (2006) Number 1, pages 1—23
Download:  PDF (199  Kb, File info)
Abstract: We remind some similarities/parallels between two of the theories dealing with widely understood (not only as randomness) uncertainty — mass assignment theory and intuitionistic fuzzy set theory. Mass assignment theory is well known tool for dealing with both probabilistic and fuzzy uncertainties whereas intuitionistic fuzzy set theory is an extension of fuzzy set theory which makes it possible to describe imprecise information. Next, we recall the measures of similarity which we have proposed for both theories. The proposed measures take into account not only a pure distance between compared elements but answer the questions if the considered elements/objects are more similar or more dissimilar (the measures take into account and compare two types of distances). It is shown that even if a distance between compared objects is small, it can happen that the objects are completely dissimilar. The disadvantage of the measures is the range of their values — not consistent with the tradition as far as the similarity measures are concerned. In this paper we propose the whole array of the new similarity measures preserving the advantages of the previously proposed similarity measures and the same time following the commonly assumed number values.
AMS Classification: 03E72
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