p, q, r-Fractional Fuzzy Frank Aggregation Operators and Their Application in Multi-Criteria Group Decision-Making

This paper presents new aggregation operators for p,q,r-fractional fuzzy sets based on the Frank t-norm and t-conorm. We introduce the p,q,r-fractional fuzzy Frank weighted average and p,q,r-fractional fuzzy Frank weighted geometric operators and discuss their algebraic properties, including closure, boundedness, idempotency, and monotonicity. Based on new operations, we develop a multi-criteria group decision-making framework that integrates the evaluations of multiple experts via the proposed Frank operators and ranks the alternatives under p,q,r-fractional fuzzy information. The model is applied to a cryptocurrency stability assessment problem, where four coins are evaluated with respect to six criteria. The results show that both aggregation operators yield consistent rankings with good discriminatory power among the alternatives. A sensitivity analysis is conducted to check the stability of the model under parameter variations. A comparative study further demonstrates the compatibility and advantages of the proposed method over several existing decision-making approaches. The proposed framework is well suited to decision-making scenarios in which multiple experts’ opinions must be integrated within a complex fuzzy information environment.