Interval-Valued Linear Diophantine Fuzzy Frank Aggregation Operators with Multi-Criteria Decision-Making

We introduce the notion of the interval-valued linear Diophantine fuzzy set, which is a generalized fuzzy model for providing more accurate information, particularly in emergency decision-making, with the help of intervals of membership grades and non-membership grades, as well as reference parameters that provide freedom to the decision makers to analyze multiple objects and alternatives in the universe. The accuracy of interval-valued linear Diophantine fuzzy numbers is analyzed using Frank operations. We first extend the Frank t-conorm and t-norm (FT c T n ) to interval-valued linear Diophantine fuzzy information and then offer new operations such as the Frank product, Frank sum, Frank exponentiation, and Frank scalar multiplication. Based on these operations, we develop novel interval-valued linear Diophantine fuzzy aggregation operators (AOs), including the “interval-valued linear Diophantine fuzzy Frank weighted averaging operator and the interval-valued linear Diophantine fuzzy Frank weighted geometric operator”. We also demonstrate various features of these AOs and examine the interactions between the proposed AOs. FT c T n s offer two significant advantages. Firstly, they function in the same way as algebraic, Einstein, and Hamacher t-conorms and t-norms. Secondly, they have an additional parameter that results in a more dynamic and reliable aggregation process, making them more effective than other general t-conorm and t-norm approaches. Furthermore, we use these operators to design a method for dealing with multi-criteria decision-making with IVLDFNs. Finally, a numerical case study of the novel carnivorous issue is shown as an application for emergency decision-making based on the proposed AOs. The purpose of this numerical example is to demonstrate the practicality and viability of the provided AOs.