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

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.