基于概率语言术语集的多属性环境下三支决策方法研究

Three-Way Decisions Approach to Multiple Attribute Group Decision Making with Probabilistic Linguistic Information

摘要: 相对于语言术语集，概率语言术语集要求决策者利用语言术语评价方案的同时，给出其对各语言术语的偏好，为后续的决策分析提供更多的判断信息。针对属性值为概率语言术语集的多属性决策问题，本文提出了基于三支决策的多属性群决策方法，在求得方案排序的同时给出每个方案应采取的行动策略。首先，为了确定属性权重及正、负理想解，构建了以决策者评价非一致度最小化为目标的优化模型；然后，基于求得的属性权重和正、负理想解，通过计算每个属性下各方案在不同状态下采取不同行动时的损失值，构建综合损失矩阵；最后，利用TOPSIS思想在根据相对贴近度对方案进行排序的同时确定各方案属于不同状态的条件概率，求得各方案采取不同行动的期望损失值，并以此为基础利用三支决策规则确定各方案应采取的行动策略。

Abstract: Compared with linguistic term set, the probabilistic linguistic term set (PLTS) allows the decision makers (DMs) to give the weight of each linguistic term as a probability, which is useful to DMs to provide their preference more completely and accurately. The aim of this paper is to propose a three-way decisions method for multiple attribute group decision making in which the DMs’ pref-erence over alternatives with respect to the given attribute is expressed by PLTSs. Firstly, a liner programming model aiming to minimize inconsistency index of all DMs is constructed to derive the weights of attributes and positive/negative ideal solution (PIS/NIS). Then, based on the obtained weights of attributes, PIS and NIS, the method to determine the collective loss matrix is proposed. Furthermore, the relative closeness degrees are calculated to estimate the conditional probabilities of each alternative under different states, while the ranking of alternatives is obtained. Finally, the expected loss values of each alternative adopting different actions are calculated, and thus according to the decision rule, the best action for each alternative is determined.