Some Improved Correlation Coefficients for q-Rung Orthopair Fuzzy Sets and Their Applications in Cluster Analysis

Abstract

The structure of q-rung orthopair fuzzy sets (q-ROFSs) is a generalization of fuzzy sets (FSs), intuitionistic FSs (IFSs), and Pythagorean FSs (PFSs). The notion of q-ROFSs has the proficiency of coping with uncertainty without any restrictions. In addition, the structure of q-ROFSs can effectively cope with the situations involving dual opinions without any restrictions, instead of dealing with only single opinion or dual opinions under certain restrictions. In clustering problems, the correlation coefficients are worthwhile because they provide the degree of similarity or correlation between two elements or sets. The theme of this study is to formulate the correlation coefficients for q-ROFSs that are basically the generalization of correlation coefficients of IFSs and PFSs. Moreover, an application of these correlation coefficients to a clustering problem is proposed. Also, an analysis of the outcomes is carried out. Furthermore, a comparison is carried out among the correlation coefficients for q-ROFSs and the existing ones. Finally, the downsides of the existing works and benefits of the correlation coefficients for q-ROFSs are discussed.