Some t-conorm-based distance measures and knowledge measures for Pythagorean fuzzy sets with their application in decision-making

Abstract

The Pythagorean fuzzy sets are more robust than fuzzy sets and intuitionistic fuzzy sets in dealing with the problems involving uncertainty. To compare two Pythagorean fuzzy sets, distance measures play a crucial role. In this paper, we have proposed some novel distance measures for Pythagorean fuzzy sets using t-conorms. We have also discussed their various desirable properties. With the help of suggested distance measures, we have introduced some new knowledge measures for Pythagorean fuzzy sets. Through numerical comparison and linguistic hedges, we have established the effectiveness of the suggested distance measures and knowledge measures, respectively, over the existing measures in the Pythagorean fuzzy setting. At last, we have demonstrated the application of the suggested measures in pattern analysis and multi-attribute decision-making.

Circular Pythagorean Fuzzy Hamacher Aggregation Operators With Application in the Assessment of Goldmines

“…Yager and Abbasov [11] exposed Pythagorean FSs (PyFSs), where PyFSs have the same structure as IFSs, but changed its condition with 0 ≤ 𝕋 𝒞 ℱ 2 (𝓍) + 𝔽 𝒞 ℱ 2 (𝓍) ≤ 1 . PyFSs become the extensions of FSs and IFSs with various applications, such as [12][13][14]. These different types of FSs extensions had taken the truth and falsity grades, but they avoided the angle between truth and falsity grades.…”

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.…”