关键词: 群决策, 区间互补偏好关系, 一致性, 共识性, 规划模型

Abstract: Interval fuzzy preference relations have the advantages of intervals and preference relations, which have been widely concerned. Interval is one type of the simplest fuzzy evaluation information, which can easily represent the upper and lower bounds of the decision makers’ uncertain judgment. Preference relation reduces the requirement for the decision makers that only needs decision makers to provide the pairwise comparative value of objects. However, the current consistency research on interval fuzzy preference relationships still has some shortcomings. For example, the complementarity and order invariance cannot be guaranteed.
This paper first summarizes the limitations of previous additive consistency concepts of interval complementary preference relations. Then, a new group decision making method is developed based on the additive consistency and consensus analysis. The main contributions are as follows: a new additive consistency concept based on the median and deviation of the interval judgment matrix is proposed and its properties are discussed. For the incomplete interval complementary preference relations, a programming model is built to determine the missing value. or the inconsistent interval complementary preference relations, this paper establishes several models to judge and adjust its inconsistency. Based on the interval distance measure, a consensus index is proposed and the consensus analysis of additive consistent interval complementary preference relations is carried out.
The new approach is implemented in a practical scenario: assessing and choosing suppliers of spare parts. Upon conducting a sensitivity analysis of decision outcomes, the new method shows good robustness. Moreover, the effectiveness and superiority of the new method are demonstrated, compared with other decision-making methods. Notably, the new method eliminates their theoretical limitations.
The new method is based on complete additive consistency, which is difficult to achieve in practical decision making. Thus, the subsequent research can be based on satisfactory additive consistency. Considering the difference in the characteristics of decision makers, the preference relationship with heterogeneous information is worth further study. It is worth noting that the theoretical results of this paper can be extended to other types of preference relationships, such as triangular complementary preference relationship, intuitive complementary preference relationship, hesitant complementary preference relationship, and double-hierarchical linguistic preference relationship.

Key words: group decision making, interval complementary preference relations, additive consistency, consensus, programming model