Multi-attribute decision-making with (p, q)-rung orthopair fuzzy sets

(p, q)-rung orthopair fuzzy sets can provide more ambiguous scenarios since they can exhibit membership grades across a larger range than Fermatean fuzzy sets, Pythagorean fuzzy sets, and intuitionistic fuzzy sets. In this work, Yager t-norm and t-conorm are used to investigate the correctness of (p, q)-rung orthopair fuzzy numbers. Initially, the Yager operational laws are extended to the (p, q)-rung orthopair fuzzy data. The goal of this study paper is to provide a decision-making strategy related to the great tendencies of the conventional TOPSIS method in the context of (p, q)-rung orthopair fuzzy sets. The TOPSIS method, which employs a system to identify alternatives that acquire beneficial distances from optimal solutions, is recognized as one of the legitimate approaches to multi-attribute decision making. Novel Yager’s operational rules for (p, q)-rung orthopair fuzzy numbers have been developed utilizing Yager norms and the flexibility of (p, q)-rung orthopair fuzzy sets. To further show the viability and use of the created technique, we carry out a case study of the specific carnivorous issue and an application for emergency decision making. The following are this article’s primary contributions: (1) Yager norms have been used to study the aggregation operators for (p, q)-rung orthopair fuzzy numbers and their properties. (2) Under (p, q)-rung orthopair fuzzy sets, the TOPSIS technique is established. An algorithm that explains the suggested method step-by-step is provided. (3) The created technique is then used as a case study of a carnivorous concern. (4) The outcomes have been compared to the rankings attained using different methods that are currently in use.