On Generalized Correlation Coefficients of Picture Fuzzy Sets With Their Applications

1. Introduction

In an uncertain environment, expert-based decision-making is quite easily handled by the fuzzy set (FS) theory introduced by Zadeh (1965). Thereafter various generalizations of fuzzy sets (FSs) have been introduced by various researchers and they have been applied successfully in various problems in day to day life. One of the important extensions of FSs is Atanassov’s (1986) intuitionistic fuzzy sets (IFSs) which consider both membership and non-membership values of an element with the condition that their sum should not exceed one. Various researchers have applied IFSs in different fields. It is observed that IFSs lack an important concept i.e., degree of neutrality. This concept plays an important role in the situations which require more answers of the type yes, no, refusal, abstain e.g., In human voting, people can be divided into four groups (1) people who vote for (2) people who vote against (3) people who refuse (4) people who abstain. The group of people who abstain consists of the people who cast their votes but reject all the candidates. Degree of neutrality also plays an important role in medical diagnosis e.g., the symptoms headache, temperature may have a null effect on the diseases chest problem and stomach problem. Similarly, the effect of the symptoms chest and stomach pain may be neutral on the disease malaria, viral fever, typhoid, etc. So, the concept of picture fuzzy set (PFS), which takes into consideration the degree of membership, degree of non-membership, and degree of neutrality of an element was introduced by Cuong and Kreinovich(2013). Cuong(2014) introduced some basic operations for PFSs and also introduced picture fuzzy soft set (PFSS) and interval-valued picture fuzzy sets (IVPFSs). Cuong(2014) also suggested some picture fuzzy (PF) distance measures. A new PFS distance measure with its application in fuzzy clustering was introduced by Son (2016). The fuzzy inference system on PFSs was introduced by Son et al.(2017). A PFS algorithm based on a new distance measure with its application in decision-making was proposed by Peng and Dai (2017). Some process for measuring the similarity of PFSs was presented by Wei (2017). Aggregation operations for PFSs were studied by Garg (2017) and also applied them to multi-criteria decision-making (MCDM). Janna et al. (2019) introduced some picture fuzzy Dombi arithmetic/geometric aggregation operators with some desired properties and demonstrated their application in MADM involving PF information.