The q‐rung orthopair fuzzy set, whose membership function and nonmembership function belong to the interval [0,1], is more powerful than both intuitionistic fuzzy set and Pythagorean fuzzy set in expressing imprecise information of decision‐makers. The aim of this paper is to investigate a method to determine the priority weights from individual or group q‐rung orthopair fuzzy preference relations (q‐ROFPRs). To do so, firstly, a new definition of additively consistent q‐ROFPR is presented based on the preference relation of alternatives given by decision‐makers. Afterward, according to individual and group q‐ROFPRs, two kinds of goal programming models are proposed, respectively, to generate the q‐rung orthopair fuzzy priority weight vector of the given q‐ROFPR(s). Finally, two numerical examples are given to illustrate the effectiveness and superiority of the method proposed in this paper.

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The q-rung orthopair fuzzy set is characterized by membership and nonmembership functions, and the sum of the qth power of them is less than or equal to one. Since it releases the constraints existed in both intuitionistic fuzzy set and Pythagorean fuzzy set, it has wide applications in real cases. However, so far, there is little research on the multiplicative consistency of q-rung orthopair fuzzy preference relation (q-ROFPR). To fill this vacancy, this paper provides a detailed analysis on the multiplicative consistency of q-ROFPR. First, we investigate the concept of multiplicative consistent q-ROFPR and its properties. Subsequently, two goal programming models are proposed to derive the priorities from individual and group q-ROFPRs, respectively. After that, a novel consistency-improving algorithm for q-ROFPR and a weight-generating method for decision-makers are discussed in detail, based on which, a novel group decision-making method is proposed. Finally, a case study concerning the evaluation of rehabilitation program selection is given to illustrate the applicability of the proposed method. The effectiveness and superiority of the proposed method are verified by comparing it with some existing methods. K E Y W O R D S multiple criteria decision making, multiplicative consistency, q-rung orthopair fuzzy preference relation, q-rung orthopair fuzzy priority weight, q-rung orthopair fuzzy set F I G U R E 1 The orthogonal projections of intuitionistic fuzzy set (IFS)/Pythagorean fuzzy set (PFS)/q-rung orthopair fuzzy set (q-ROFS) in μ and ν coordinates 2 ZHANG ET AL. | 39

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