Development of Non-linear Diophantine Linguistic Term Sets and Their Application in Decision-Making Problems

Abstract

In this study, we introduce a new notion called non-linear Diophantine linguistic term sets, which is a hybrid of the non-linear Diophantine fuzzy set and linguistic term sets. Initially, we will go over the fundamental idea of fuzzy sets and its generalization. Discuss both linear and nonlinear Diophantine fuzzy sets. Following that, we describe the non-linear Diophantine linguistic term sets, as well as their score and accuracy functions. Next, we define the operational rules and aggregation operator for the proposed notion using the Hamacher t-norm and t-conorm. Furthermore, we modify the TOPSIS approach for non-linear Diophantine linguistic term sets using the Hamacher aggregation operator. Next, we apply the proposed approach to the selection of mathematical thinking tools, gathering reliable guidance from three experts. To aggregate these experts' data, we use the Hamacher aggregation operator, followed by the modified TOPSIS approach for the final data. According to the presented framework, Abstraction is the most effective mathematical tool. Finally, we compare the proposed model to existing approaches to ensure its accuracy and applicability. Comparative study shows that the proposed framework appears to be accurate and flexible to real-world decision-making challenges.