Correlation Coefficients of Fermatean Fuzzy Sets with a Medical Application

The FFS is an influential extension of the available IFS and PFS, whose benefit is to better exhaustively characterize ambiguous information. For FFSs, the correlation between them is usually evaluated by the correlation coefficient. To reflect the perspective of professionals, in this paper, a new correlation coefficient of FFSs is proposed and investigated. The correlation coefficient is very important and frequently used in every field from engineering to economics, from technology to science. In this paper, we propose a new correlation coefficient and weighted correlation coefficient formularization to evaluate the affair between two FFSs. A numerical example of diagnosis has been gotten to represent the efficiency of the presented approximation. Outcomes calculated by the presented approximation are compared with the available indices

A decision-making framework based on the Fermatean hesitant fuzzy distance measure and TOPSIS

A particularly useful assessment tool for evaluating uncertainty and dealing with fuzziness is the Fermatean fuzzy set (FFS), which expands the membership and non-membership degree requirements. Distance measurement has been extensively employed in several fields as an essential approach that may successfully disclose the differences between fuzzy sets. In this article, we discuss various novel distance measures in Fermatean hesitant fuzzy environments as research on distance measures for FFS is in its early stages. These new distance measures include weighted distance measures and ordered weighted distance measures. This justification serves as the foundation for the construction of the generalized Fermatean hesitation fuzzy hybrid weighted distance (DGFHFHWD) scale, as well as the discussion of its weight determination mechanism, associated attributes and special forms. Subsequently, we present a new decision-making approach based on DGFHFHWD and TOPSIS, where the weights are processed by exponential entropy and normal distribution weighting, for the multi-attribute decision-making (MADM) issue with unknown attribute weights. Finally, a numerical example of choosing a logistics transfer station and a comparative study with other approaches based on current operators and FFS distance measurements are used to demonstrate the viability and logic of the suggested method. The findings illustrate the ability of the suggested MADM technique to completely present the decision data, enhance the accuracy of decision outcomes and prevent information loss