The operations on intuitionistic fuzzy values in the framework of Dempster–Shafer theory

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. Two sets of operations on IFVs based on the interpretation of intuitionistic fuzzy sets in the framework of the Dempster–Shafer theory of evidence (DST) are proposed and analysed. This interpretation makes it possible to represent mathematical operations on IFVs as operations on belief intervals. The corresponding methods for aggregation of local criteria presented by IFVs in the framework of DST are proposed and analysed. 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.