An Innovative Decision-Making Approach Based on Correlation Coefficients of Complex Picture Fuzzy Sets and Their Applications in Cluster Analysis

Abstract

In modern times, the organizational managements greatly depend on decision-making (DM). DM is considered the management’s fundamental function that helps the businesses and organizations to accomplish their targets. Several techniques and processes are proposed for the efficient DM. Sometimes, the situations are unclear and several factors make the process of DM uncertain. Fuzzy set theory has numerous tools to tackle such tentative and uncertain events. The complex picture fuzzy set (CPFS) is a super powerful fuzzy-based structure to cope with the various types of uncertainties. In this article, an innovative DM algorithm is designed which runs for several types of fuzzy information. In addition, a number of new notions are defined which act as the building blocks for the proposed algorithm, such as information energy of a CPFS, correlation between CPFSs, correlation coefficient of CPFSs, matrix of correlation coefficients, and composition of these matrices. Furthermore, some useful results and properties of the novel definitions have been presented. As an illustration, the proposed algorithm is applied to a clustering problem where a company intends to classify its products on the basis of features. Moreover, some experiments are performed for the purpose of comparison. Finally, a comprehensive analysis of the experimental results has been carried out, and the proposed technique is validated.

Linear Diophantine Fuzzy Clustering Algorithm Based on Correlation Coefficient and Analysis on Logistic Efficiency of Food Products

“…The CC between the IVIFSs are constructed by Nguyen and build a clustering analysis. Qu [37] introduced a new clustering algorithm that utilizes CC for complex picture fuzzy sets to classify products by features. Park [36] demonstrated the use of CC of IVIFS in MCDM.…”

“…The range of data limits the DM to certain bound Qu et.al [37] CPFS Clustering Algorithm based on CPF CC…”

An optimized multi-attribute decision-making approach to construction supply chain management by using complex picture fuzzy soft set

“…( Akram, Bashir & Garg, 2020a ; Qu et al, 2022 ) If , and are positive, neutral and negative membership grades of then cpFS is defined as where are complex fuzzy membership mappings such that , and provided that and . The , are called the amplitude terms and , and are known as phase terms.…”

“…As information-based periodicity is often observed in raw data embedded with uncertainties. To cope with such situation, the idea of pFS has been extended to complex picture fuzzy set (cpFS) ( Akram, Bashir & Garg, 2020a ; Qu et al, 2022 ) which is the generalization of complex fuzzy set (cFS) ( Ramot et al, 2002 ) and complex intuitionistic fuzzy set (cIFS) ( Alkouri & Salleh, 2012 ). In cpFS, the codomain of a three dimensional function is a unit circle in the complex plane which is characterized by two terms: amplitude term and phase term.…”