The Spherical q-Linear Diophantine Fuzzy Multiple-Criteria Group Decision-Making Based on Differential Measure

Abstract

Spherical q-linear Diophantine fuzzy sets (Sq-LDFSs) proved more effective for handling uncertainty and vagueness in multi-criteria decision-making (MADM). It does not only cover the data in two variable parameters but is also beneficial for three parametric data. By Pythagorean fuzzy sets, the difference is calculated only between two parameters (membership and non-membership). According to human thoughts, fuzzy data can be found in three parameters (membership uncertainty, and non-membership). So, to make a compromise decision, comparing Sq-LDFSs is essential. Existing measures of different fuzzy sets do, however, can have several flaws that can lead to counterintuitive results. For instance, they treat any increase or decrease in the membership degree as the same as the non-membership degree because the uncertainty does not change, even though each parameter has a different implication. In the Sq-LDFSs comparison, this research develops the differential measure (DFM). The main goal of the DFM is to cover the unfair arguments that come from treating different types of FSs opposing criteria equally. Due to their relative positions in the attribute space and the similarity of their membership and non-membership degrees, two Sq-LDFSs form this preference connection when the uncertainty remains same in both sets. According to the degree of superiority or inferiority, two Sq-LDFSs are shown as identical, equivalent, superior, or inferior over one another. The suggested DFM's fundamental characteristics are provided. Based on the newly developed DFM, a unique approach to multiple criterion group decision-making is offered. Our suggested method verifies the novel way of calculating the expert weights for Sq-LDFSS as in PFSs. Our proposed technique in three parameters is applied to evaluate solid-state drives and choose the optimum photovoltaic cell in two applications by taking uncertainty parameter zero. The method's applicability and validity shown by the findings are contrasted with those obtained using various other existing approaches. To assess its stability and usefulness, a sensitivity analysis is done.