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.

A New Concept of a Similarity Measure for Intuitionistic Fuzzy Sets and Its Use in Group Decision Making

“…In Szmidt [16], Szmidt and Baldwin [17,18], Szmidt and Kacprzyk [24] it is shown why when calculating distances between intuitionistic fuzzy sets it is expedient to take into account all three parameters describing intuitionistic fuzzy sets. One of the reasons is that when taking into account two parameters only, for elements from classical fuzzy sets (which are a special case of intuitionistic fuzzy sets) we obtain distances from a different interval than for elements belonging to intuitionistic fuzzy sets.…”

“…We use a geometric interpretation of intuitionistic fuzzy sets which was described in details by Szmidt ([16]), Szmidt and Baldwin ( [17,18]), Szmidt and Kacprzyk ([24], [27]). …”

Intuitionistic Fuzzy Decision Tree: A New Classifier

“…(An approach to the assigning memberships and non-memberships for A-IFSs from data is proposed by Szmidt and Baldwin [29]). Obviously, each fuzzy set may be represented by the following A-IFS:…”

Managing contradictory evidence

“…Later work by Hinde (6) explored the relationship between inconsistent intuitionistic fuzzy sets and mass assignment. Following and extending the work by (7) it developed a prototype relationship between the two representations extending both. In Hinde (5) the operators ∩ and ∪ were defined such that they are t-norms and s-norms respectively within the context of intuitionistic fuzzy sets.…”