Q-rung orthopair fuzzy multiple attribute group decision-making method based on normalized bidirectional projection model and generalized knowledge-based entropy measure

Abstract

The q-rung orthopair fuzzy sets (q-ROFSs) can serve as a generalization of intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs). q-ROFSs provide more freedom for decision makers in describing their opinions than other ordinary orthopair fuzzy sets. In this paper, a novel multiple attribute group decision making(MAGDM) method is constructed under q-rung orthopair fuzzy (q-ROF) environment. First, considering the projection measure provides the distance and the angle between two alternatives simultaneously, this work investigates a new normalized bidirectional projection model (NBPM) of q-ROFSs. By combining the proposed NBPM with Jaynes maximum entropy method, a nonlinear programming model is constructed to calculate the objective attribute weight information. Second, we present a new entropy measure based on the proposed generalized p-norm knowledge-based measure which takes into account both the membership and non-membership functions and the inherent fuzziness of q-ROFSs. Then the weights of decision makers are given by the proposed entropy measure. Furthermore, an integrated MAGDM framework is presented by using the weight determination methods of decision makers and attributes under q-ROF environment. Finally, an illustrative example is given to illustrate the operation process of the proposed decision-making method, sensitivity analysis and comparison analysis are also performed to show the effectiveness and superiority of the proposed method.