The use of belief intervals in operations on intuitionistic fuzzy values

Authors:
Ludmila Dymova;Pavel Sevastjanov;Kamil Tkacz
Affiliations:
Institute of Comp. & Information Sci., Czestochowa University of Technology, Czestochowa, Poland;Institute of Comp. & Information Sci., Czestochowa University of Technology, Czestochowa, Poland;Institute of Comp. & Information Sci., Czestochowa University of Technology, Czestochowa, Poland
Venue:
ICAISC'12 Proceedings of the 11th international conference on Artificial Intelligence and Soft Computing - Volume Part I
Year:
2012

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Abstract

This paper presents a critical analysis of conventional operations on intuitionistic fuzzy values (IFVs ) and their applicability to the solution of multiple criteria decision making (MCDM ) problems in the intuitionistic fuzzy setting. A set of operations on IFVs based on the interpretation of intuitionistic fuzzy sets in the framework of the Dempster-Shafer theory of evidence (DST ) is proposed and analyzed. This interpretation makes it possible to represent mathematical operations on IFVs as operations on belief intervals. The corresponding method for aggregation of local criteria presented by IFVs in the framework of DST is proposed and analyzed. The proposed approach allows us to solve MCDM problems without intermediate defuzzification when not only criteria, but their weights are IFVs . The advantages of the proposed approach are illustrated by numerical examples.