On some correlation coefficients in Pythagorean fuzzy environment with applications

Abstract

A Pythagorean fuzzy set (PFS) is an extension of an intuitionistic FS that can be extended by relaxing the restriction on the grades of satisfaction and dissatisfaction. PFS is a powerful tool for dealing with uncertainty and vagueness. Correlation analysis of PFSs is a hot research topic in Pythagorean fuzzy (PF) theory and has practical applications in many areas, such as decision‐making, pattern recognition, medical diagnosis, engineering, and so forth. In this communication, we introduce some novel correlation coefficients in the PF‐environment satisfying the condition that the correlation coefficient of two PFSs is one if and only if the two sets are equal. We discuss the properties and applications of the proposed measures in pattern recognition, medical diagnosis, multicriteria decision‐making, and clustering analysis. Furthermore, the superiority of our proposed correlation coefficients over some existing ones is also established. We also extend the correlation coefficients to interval‐valued PFSs.

Directional correlation coefficient measures for Pythagorean fuzzy sets: their applications to medical diagnosis and cluster analysis

“…To the best of our knowledge, there are only four research studies reporting the correlation coefficients of PFSs, which are presented in the literatures [7,21,45,49]. Here, the drawbacks of these four research studies are analyzed as follows.…”

“…The existing studies have the drawback that the correlation coefficient value between two unequal PFSs may equal to 1. To address this issue, Singh et al [45] put forward some correlation coefficients for PFSs. To consider the inverse correlation relation between PFSs, Thao [49] proposed a novel correlation coefficient for PFSs, the value of which is in the interval [− 1, 1].…”

An innovative picture fuzzy distance measure and novel multi-attribute decision-making method

“…Atanassov [10] included the non-membership degree of an element to a FS with the condition that the sum of membership and non-membership degrees should be less or equal to one. Some prominent studies comprising the development and applications of intuitionistic fuzzy (IF)/ Pythagorean fuzzy (PF) compatibility/comparison measures are due to researches [20][21][22][23][24][25][26][27][28][29]. Recently, Niu et al [30] introduced two mentality-parameters and proposed a new method for solving some MADM problems in the intervalvalued IF environment.…”

Strategies on admissible total orders over typical hesitant fuzzy implications applied to decision making problems

“…The study of typical hesitant fuzzy connectives plays an indispensable role in logical systems, by enabling to model solutions for the hesitant fuzzy multicriteria decision-making (MCDM) problems, such as hesitant fuzzy linguistic information 8 and hesitant fuzzy linguistic terms sets. 9,10 As basic logical operations, implication operations have been widely used in the narrow sense to formalize concepts, such as similarity degrees, 11,12 coefficient correlation, 13,14 consensus measures, 15 and integrated to fuzzy subsethood measures. [16][17][18] In the broad sense, when a large amount of data are considered under hesitant fuzzy environments, the detailed study of fuzzy implication properties and their main classes provides a lot of different meanings and distinct applications.…”