Decision Analysis Algorithm Using Frank Aggregation in the SWARA Framework with [sup.p,q]Rung Orthopair Fuzzy Information

The present study introduces an innovative approach to multi-criteria decision making (MCDM) aimed at handling decision analysis involving [sup.p,q]rung orthopair fuzzy ([sup.p,q]ROF) data, where the criteria weights are completely unknown. To achieve this objective, we formulate generalized operational rules referred to as Frank operational rules, tailored for [sup.p,q]ROF numbers ([sup.p,q]ROFNs) utilizing the Frank t-norm and t-conorm. With these newly devised operations as a foundation, we create a variety of [sup.p,q]ROF aggregation operators (AOs) to effectively aggregate [sup.p,q]ROF information. Furthermore, we examine specific instances of these operators and rigorously establish their desirable properties, including idempotency, monotonicity, boundedness, and symmetry. Subsequently, we adapt the SWARA technique to the realm of [sup.p,q]ROF fuzzy data and this adapted technique becomes instrumental in determining criteria weights within the proposed MCDM framework centered around proposed AOs. We furnish a descriptive example to exemplify the practicality of the developed approach. Lastly, the effectiveness and soundness of our approach are underscored through both parameter analysis and a comparative evaluation.