A Cosine Similarity Measure Based on the Choquet Integral for Intuitionistic Fuzzy Sets and Its Applications to Pattern Recognition

Abstract

There exist various types of similarity measures for intuitionistic fuzzy sets in the literature. However, in many studies the interactions among the elements are ignored in the construction of the similarity measure. This paper presents a cosine similarity measure for intuitionistic fuzzy sets by using a Choquet integral model in which the interactions between elements are considered. The proposed similarity measure is applied to some pattern recognition problems and the results are compared with some existing results to demonstrate the effectiveness of this new similarity measure.

An Intuitionistic Fuzzy based Intelligent System for Semantic Interoperability and Privacy Preservation in Healthcare Systems

“…The Choquet Cosine Similarity Measure in fuzzy set theory [32] is a variation of the Choquet Cosine Similarity Measure that specifically deals with fuzzy sets. It is defined as follows:…”

Multi-attribute decision-making based on novel Fermatean fuzzy similarity measure and entropy measure

“…Singh and Ganie ( 2020 ) developed a few PF metrics of correlation with their utility. PFSs have been examined and implemented by numerous researchers (Garg 2019a , b ; Khan et al 2019a , b ; Akram and Ali 2020 ; Ejegwa 2020a , b ; Rahman et al 2020 ; Zhang et al 2021 ; Olgun et al 2021 ; Mishra et al 2021 ; Zeb et al 2022 ; Wang et al 2022 ; Ganie 2022 , 2023 ; Ganie et al 2022 ; Akram and Bibi 2023 ; Ejegwa et al 2023 ; Aldring and Ajay 2023 ; Kirişci 2023 ; Akram et al 2023b ; Akram et al 2023a , c ) in various uncertain situations. Chen and Chiou ( 2015 ) and Zeng et al ( 2020 ) discussed the applicability of interval-valued IFSs to MADM problems.…”

“…Thus, there is no technique that can be applied repeatedly to assess similarity. The five FF entropy measurements (Olgun et al 2021 ) are worthless from the standpoint of linguistic hedging, and there is no standard method for creating the FF entropy measurements. The conventional MADM technique i.e., TOPSIS provides a compromise solution that is most similar to the PIS (positive ideal solution), but not the least similar to the NIS (negative ideal solution).…”

“…The five FF entropy measurements (Olgun et al 2021 ) are worthless from the standpoint of linguistic hedging, and there is no standard method for creating the FF entropy measurements.…”

An information measure based extended VIKOR method in intuitionistic fuzzy valued neutrosophic value setting for multi-criteria group decision making

“…These extensions have been widely used by the researchers to address the problems such as multi-criteria decision making (MCDM), multi-criteria group decision making (MCGDM), classification and pattern recognition etc. (see, e.g., [8][9][10][11][12][13][14][15][16][17][18]).…”