Multiple attribute group decision‐making based on order‐α divergence and entropy measures under q‐rung orthopair fuzzy environment

Abstract

The q-rung orthopair fuzzy set ((ROPFS)-R-q), proposed by Yager, is a more effective and proficient tool to represent uncertain or vague information in real-life situations. Divergence and entropy are two important measures, which have been extensively studied in different information environments, including fuzzy, intuitionistic fuzzy, interval-valued fuzzy, and Pythagorean fuzzy. In the present communication, we study the divergence and entropy measures under the q-rung orthopair fuzzy environment. First, the work defines two new order-alpha divergence measures for (q)ROPFSs to quantify the information of discrimination between two (q)ROPFSs. We also examine several mathematical properties associated with order-alpha (ROPF)-R-q divergence measures in detail. Second, the paper introduces two new parametric entropy functions called "order-alpha (ROPF)-R-q entropy measures" to measure the degree of fuzziness associated with a (ROPFS)-R-q. We show that the proposed order-alpha divergence and entropy measures include several existing divergence and entropy measures as their particular cases. Further, the paper develops a new decision-making approach to solve multiple attribute group decision-making problems under the (ROPF)-R-q environment where the information about the attribute weights is completely unknown or partially known. Finally, an example of selecting the best enterprise resource planning system is provided to illustrate the decision-making steps and effectiveness of the proposed approach