A New Distance Measure to Rank Type-2 Intuitionistic Fuzzy Sets and Its Application to Multi-Criteria Group Decision Making

Abstract

The type 2 intuitionistic fuzzy sets (T2IFS) have a greater expressive power in representing the uncertainty involved in the information given by the experts. A very few ranking methods have been proposed to compare the T2IFS based on distance measure. This paper proposes a new distance measure called Jaccard distance for type 2 intuitionistic fuzzy set. This method ranks the T2IFS based on the dissimilarity of the given T2IFS to the ideal set. The properties of distance measure have been proved. The efficiency of proposed method is validate by comparing with existing methods. It is observed that the proposed ranking can rank the T2IFS more effectively when compared to existing methods in some tested contexts. The proposed ranking method is applied in solving a multi criteria group decision making method and the results are analyzed. From the analysis it is observed that the ordering the alternatives using proposed method agrees with the human intuition.