Abstract
A cubic m -polar fuzzy set (CmPFS) is a new hybrid extension of m -polar fuzzy set and cubic set. A CmPFS is a robust model to express multipolar information in terms of m fuzzy intervals representing membership grades and m fuzzy numbers representing nonmembership grades. In this article, we explore some new operational laws of CmPFSs, produce some related results, and discuss their consequences. We propose relative informational coefficients and relative noninformational coefficients for CmPFSs. These coefficients are analyzed to investigate further properties of CmPFSs. Based on these coefficients, we introduce new correlation measures and their weighted versions for CmPFSs. The value of proposed correlation measures is symmetrical and lies between −1 and 1. Moreover, the applications of the proposed correlation in pattern recognition and medical diagnosis are developed. The feasibility and efficiency of suggested correlation measures is determined by respective illustrative examples.
Highlights
Modern systems and logic are the schematic study of the rules that can lead to the acceptance of a certain proposition on the basis of preassumed hypothesis. e development of the modern systems owes to the advancement of set theory and logic
Fuzzy logic and fuzzy sets have a large number of applications in computational intelligence, robotics, neural networks, data sciences, and pattern recognition. e idea of fuzzification proved to be an open end for the scientists
Its positive membership value μ+ lies in the interval [0, 1] and negative membership value μ− lies in the interval [− 1, 0]. e positive scores depict the consent of a certain property, and the negative scores assigned reflect the consent of a counter property
Summary
Modern systems and logic are the schematic study of the rules that can lead to the acceptance of a certain proposition on the basis of preassumed hypothesis. e development of the modern systems owes to the advancement of set theory and logic. Erefore, bipolar fuzzy theory cannot answer this sort of problem and there is a need to invent a new extension To address this limitation, m-polar fuzzy set (mPFS) theory has been. E development of fuzzy set theories give rise to new extension of correlation and similarity measures. Erefore, there is a need to introduce correlation measures in every environment because a real problem may be diverse in its uncertain nature To address this issue, Ejegwa et al [32], Gerstenkorn and Manko [33], and Szmidt and Kacprzyk [34] proposed some correlation measures for IFSs. Garg et al [35] presented the correlation coefficient for cubic intuitionistic fuzzy set and presented a decision-making algorithm.
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