基于一致性局部调整算法和DEA的语言偏好决策模型

设计一致性调整算法和计算可靠的方案排序权重向量已成为近年来备受关注的两个重要研究课题。针对决策信息为语言偏好关系的决策问题，提出一种基于一致性局部调整算法和数据包络分析（DEA）方法的语言偏好决策模型。首先，基于局部调整策略设计一种收敛的乘性一致性调整算法，该算法不仅使得调整后的语言偏好关系具有满意乘性一致性，而且能够尽可能多的保存原始决策信息；其次，基于提出的新型语言DEA模型构造一种语言偏好决策模型用以确定方案的排序权重向量，进而得到合理可靠的决策结果。最后，将提出的语言偏好决策模型用于供应商的选择实例，对比分析实验验证了模型的合理性和有效性。

Linguistic Preference Decision-Making Model Based on Consistency Local Adjustment Algorithm and DEA

The linguistic preference relations (LPRs) are useful tool to address situations in which the decision makers (DMs) are more comfortable providing their evaluation information linguistically rather than numerical values. Consistency improvement process and deriving the reliable priority weight vector for alternatives are two significant and challenging issues in decision-making with LPRs. In this paper, a linguistic preference decision-making model is investigated with consistency local adjustment algorithm and data envelopment analysis (DEA). Firstly, the concept of multiplicative consistent LPRs is reviewed. Then, a construction approach of multiplicative consistent LPRs is proposed, and a convergent consistency-improving algorithm for LPRs is designed to transform the unacceptable multiplicative consistent LPRs into the acceptable ones, in which the local adjustment strategy is presented to preserve the DM's original decision-making information as much as possible and use the DM's original information sufficiently. Subsequently, a novel linguistic DEA model is developed to explore the relationship between the relative efficiency scores and the priority weight vector of multiplicative consistent LPRs. Furthermore, the linguistic preference decision-making model is investigated to generate the reliable ranking of the alternatives. Finally, a numerical example of selecting the desirable supplier is provided, and the comparison with existing approaches is performed to validate the rationality and effectiveness of the proposed linguistic preference decision-making model.