A quantum probability theory-based method for heterogeneous multi-criteria group decision making with incomplete probabilistic linguistic preference relations considering the interference effect among decision makers
提出一种基于量子概率理论的方法，处理决策者间干扰效应下的异质多准则群决策问题，利用不完全概率语言偏好关系表达评价信息，并通过优化模型估计缺失信息、确定权重和排序方案。
Quantum probability theory (QPT) reveals that decision makers (DMs) can interfere with each other and thus affect the decision result. However, existing methods of heterogeneous multi-criteria group decision making (HMCGDM) seldom consider the interference effect among DMs. This paper defines an interference degree based on the phase angle difference obtained by QPT to address HMCGDM problems in which the alternative and criteria sets provided by DMs may be different. In addition, the incomplete probabilistic linguistic preference relations (InPLPRs) are introduced to express the evaluation information of DMs. Considering that the same linguistic term may has different meanings for DMs, we construct a consistency-driven optimization model based on the personalized individual semantics (PISs) to estimate the missing information in InPLPR on each criterion provided by DMs and the corresponding complete PLPR (CPLPR). Then, for each DM, the individual weights of criteria and the comprehensive CPLPR on all criteria in the individual criteria set can be obtained by an optimization model. Subsequently, a novel QPT-based model is erected to derive the weights of DMs and the ranking order of alternatives. Finally, an example of tourism evaluation and several sensitivity and comparative analyses are offered to examine the applicability of the proposed method.