(p,q,r)-Fractional Fuzzy Similarity and Dissimilarity Measures with an Inferior Ratio Decision Framework

This paper develops novel similarity and dissimilarity measures for (p,q,r)-fractional fuzzy sets to enhance information discrimination and decision-making under complex uncertainty. We first introduce axiomatic dissimilarity measures and establish their fundamental mathematical properties, including boundedness, symmetry, monotonicity, and identity conditions. Based on these, we derive corresponding similarity measures that improve discrimination capability. We further propose a multi-criteria group decision-making framework to facilitate robust, accurate ranking of alternatives by integrating the developed measures into a (p,q,r)-fractional fuzzy inferior ratio method. The approach evaluates alternatives using relative inferiority relationships and provides stable, reliable rankings in uncertain environments. Illustrative examples demonstrate the proposed method’s effectiveness and applicability, and sensitivity analysis examines decision robustness. Comparative analysis with existing methods confirms the superiority of the proposed framework, showing that it offers stronger discrimination ability and serves as a flexible, reliable tool for complex multi-criteria group decision problems under (p,q,r)-fractional fuzzy environments.