Geometric similarity measures for the intuitionistic fuzzy sets

Abstract

This paper is a continuation of our previous works on geometric similarity measures between Atanassov's intuitionistic fuzzy sets (A-IFSs for short). We consider some traps of the straightforward approach in the case of A-ISs while similarity is understood as a dual concept of a distance. The difficulties are a result of, first, the symmetry of the three terms (the membership, nonmembership and hesitation margin) in an A-IFS element description, and second, of an important role played by those three terms in the definition of the complement of the A-IFS which should be taken into account in the similarity measures.

Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications

“…Szimidt and Kacprzyk [21] defined a similarity measure using a distance measure which involves both similarity and dissimilarity. Expanding upon this work, Szimidt and Kacprzyk in [25] considered a family of similarity measures and compared with some existing similarity measures. Hong and Kim [10], Hung and Yang [15], Xu [31] defined independently some similarity measures based on different distance measures for IFSs.…”

Local Divergences for Atanassov Intuitionistic Fuzzy Sets

“…This divergence is known as the Hamming distance for fuzzy sets (see [28]), and it is usually denoted by l F S . Moreover, as the Hong and Kim AIF-divergence satisfies the local property, applying Proposition 5.3 the Hamming distance for fuzzy sets is also a local divergence.…”

On generalized similarity measures for Pythagorean fuzzy sets and their applications to multiple attribute decision‐making

“…Then, corresponding to (18), (41), and (43), we define the following similarity measures between PFSs P and Q as…”

“…In 2003, Liang and Shi developed several similarity measures to distinguish different IFSs and discussed the relationship between these measures. Szimidt and Kacprzyk defined a similarity measure for IFSs based on Humming distance. Hung and Yang proposed a distance measure between IFSs based on the Hausdorff distance and further used it to develop several intuitionistic fuzzy similarity measures.…”