A New Similarity Measure for Intuitionistic Fuzzy Sets: Straightforward Approaches may not work

This paper is a continuation of our previous works on similarity measures of Atanassov intuitionistic fuzzy sets (to be called A-IFSs, for short). The similarity measures we considered used all three functions (membership, non-membership and hesitation) to represent A-IFSs, and examined two kinds of distances - one to an object to be compared, and one to its complement. The disadvantage of those measures is the range of their values - not consistent with the tradition adopted so far for the similarity measures. In this paper we propose a new similarity measure preserving all the advantages of the previously proposed similarity measures and the same time following the commonly assumed number values. We compare the measure proposed with other measure (by Zeng and Li, 2006), and analyze the reasons of the differences (in favour of our measure) in the results.