An extended multi-attribute decision making method based on novel information measures and its application

Information measures and decision-making methods are key tools in addressing multi-attribute group decision-making (MAGDM) problems. This paper first introduces an uncertainty measure for q-rung orthopair fuzzy sets (q-ROFSs), supported by an axiomatic framework. Compared with existing entropy measures, the proposed measure considers both fuzziness and hesitation simultaneously, enabling more precise quantification of uncertainty information. Secondly, a new score function is developed that incorporates hesitation degrees, improving the ability to distinguish among different q-ROFSs. Based on these two measures, we propose a MAGDM method under a q-ROF environment, integrating the Criteria Importance Through Intercriteria Correlation (CRITIC) model, an optimization model, and the Weighted Aggregated Sum Product Assessment (WASPAS) method. Q-ROFSs allow more flexible expression of membership, non-membership, and hesitation, enhancing their capacity to handle uncertain information in real-world decision-making. In the proposed framework, the CRITIC method and the new score function are used to determine expert weights, accounting for dependence and hesitation of experts. Attribute weights are derived by combining the uncertainty measure and optimization model, considering both objective and subjective factors. The WASPAS method is then employed to rank alternative solutions. Finally, a case study on the selection of food waste treatment technologies (FWTTs) is conducted to verify the universality and superiority of the established framework and the effectiveness and robustness are further validated through comparative analysis and sensitivity analysis.