A novel multicriteria decision‐making approach with unknown weight information under q‐ rung orthopair fuzzy environment

Abstract

The Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) method has been developed as one of the effective techniques to accomplish the best alternative selection of multicriteria decision-making (MCDM) problems. However, the existing PROMETHEE methods fail to adjust the representation range of uncertain information. Moreover, the weight determination and information aggregation in the PROMETHEE model still suffer from an excessive dependence of decision makers' (DMs') subjective judgments and the lack of considering the interrelationship among criteria. To solve the aforementioned drawbacks and provide DMs with a reliable and robust method of MCDM, a novel PROMETHEE method based on the q-rung orthopair fuzzy sets, that is, q-ROF-PROMETHEE model, is presented herein. First, the PROMETHEE-II method is extended to q-rung orthopair fuzzy (q-ROF) environment, which not only handles the uncertainty of human cognition but also provides DMs with a broader space to represent their decisions information. Second, a new optimization model is constructed based on the proposed cross entropy and q-ROF entropy, which is capable of leveraging the preference of DMs to obtain the optimal objective weights among criteria. In addition, the q-ROF weighted Hamy mean operator is embedded in the preference information aggregation of the PROMETHEE method so as to deal with the interrelationship among criteria. Finally, q-ROF-PROMETHEE is applied to a hospital performance evaluation case to demonstrate the proposed method's superiority, validity, and feasibility.