A framework for group decision making with multiplicative trapezoidal fuzzy preference relations

Abstract Trapezoidal fuzzy numbers are efficient to represent the quantitative vagueness and ambiguity of decision makers (DMs). Preference relations are powerful to express pairwise judgments of DMs with respect to alternatives. Combining their advantages, this paper focuses on group decision making (GDM) with multiplicative trapezoidal fuzzy preference relations (MTrFPRs) and proposes a new consistency-consensus based GDM method. To achieve this goal, a new consistency concept for MTrFPRs is proposed by analyzing the drawbacks of the previous ones. By utilizing this concept, optimal models for judging the consistency of MTrFPRs are built. Meanwhile, a consistency index is proposed to measure the consistency level of any given MTrFPR. After that, an algorithm for ranking alternatives from acceptable consistent MTrFPRs is proposed. For GDM, a central-derivation model for determining the fuzzy measure on a set of DMs is proposed. Furthermore, an optimal model for reaching the consensus threshold is constructed. Finally, a GDM method with MTrFPRs is proposed and an application example is utilized to show the efficiency of the proposed GDM method and to compare with the existing GDM methods. The proposed GDM method outperforms the existing GDM methods. It provides us with a very useful way for GDM based on MTrFPRs.