Intuitionistic Fuzzy Set Functions, Mass Assignment Theory, Possibility Theory and Histograms

Abstract

The idea of describing imprecise information taking independently into account both positive and negative aspects lies in the core of intuitionistic fuzzy sets which are generalization of fuzzy sets. But to apply intuitionistic fuzzy sets which seem to be a very good tool for representation and processing of imperfect information, one should be able to assign their membership and non-membership functions. In this paper we propose two ways of assigning the membership and non-membership functions for intuitionistic fuzzy sets: a) -by asking experts; b) -from relative frequency distributions (histograms). To justify the second (automatic) method, we show some similarities/parallels between intuitionistic fuzzy set theory and mass assignment theory -a well known tool for dealing with both probabilistic and fuzzy uncertainties. We also recall a semantic for membership functions -the interpretation having its roots in the possibility theory. Finally, we propose the automatic algorithm assigning the functions describing intuitionistic fuzzy sets.

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