Group decision making based on multiplicative consistency-and-consensus preference analysis for incomplete q-rung orthopair fuzzy preference relations

Abstract

The q-rung orthopair fuzzy preference relations are useful tools to represent hesitant and uncertain judgments of decision makers. In this paper, we propose a new group decision making method based on multiplicative consistency-and-consensus preference analysis for incomplete q-rung orthopair fuzzy preference relations. First, we provide a novel concept of multiplicative consistency for q-rung orthopair fuzzy preference relations. Then, a multiplicative consistency index is offered, by which we derive the concept of acceptable multiplicative consistency for q-rung orthopair fuzzy preference relations. Following this concept, optimization models for ascertaining unknown values in an incomplete q-rung orthopair fuzzy preference relation are built. Furthermore, optimization models for obtaining acceptable multiplicative q-rung orthopair fuzzy preference relation are proposed. Then, an optimization model for group decision making is proposed to attain an enough consensus. Afterward, a group decision making method with incomplete and unacceptable multiplicative consistent q-rung orthopair fuzzy preference relations is proposed. Finally, we use an application example to show the practicality of the proposed group decision making method. The proposed group decision making method outperforms the existing group decision making methods for group decision making in incomplete q-rung orthopair fuzzy environments.