ABSTRACT This study introduces novel q‐ fractional hesitant fuzzy multicriteria decision‐making (MCDM) approaches aimed at optimizing power system performance under uncertain and imprecise conditions. We extend hesitant fuzzy set theory by formulating q‐ fractional hesitant fuzzy sets ( q‐ FHFSs), integrating with the concept of q‐ fractional fuzzy sets for more flexible and nuanced decision scenarios. Operational rules for q‐ fractional hesitant fuzzy numbers ( q‐ FHFNs) are established, and then averaging and geometric aggregation operators dedicated to q‐ FHFNs are developed. For efficient decision‐making, score and accuracy functions are defined to rank alternatives and estimate their relative effectiveness. Moreover, we define a weighted generalized distance measure between multiple q‐ FHFNs to enable a more accurate assessment of alternatives in intricate decision‐making settings. On the basis of these assumptions, two new algorithms for MCDM are formulated; namely, q ‐fractional hesitant fuzzy weighted average and q‐ FHF technique for order preference by similarity to ideal solution methods. Their applicability is demonstrated through an illustrative numerical example involving the selection of power systems based on their performance, followed by a sensitivity analysis of the influence of the q and parameters. Then, comparative analysis confirms the superiority of the developed methods to existing MCDM methods. The results highlight the efficiency and reliability of the q‐ FHFS‐based method in dealing with uncertainty in power system decision‐making.
Ameen et al. (Thu,) studied this question.