A large group decision-making method based on a generalized Shapley probabilistic linguistic Choquet average operator and the TODIM method

Abstract

The probabilistic linguistic term set (PLTS) is an effective tool for properly modelling the uncertainty and complexity of participants’ linguistic preferences. Considering that some participants do not give evaluation information in the large group decision-making (LGDM) problem, PLTS can express many participants’ preferences with incompleteness more appropriately. Due to the existence of interest subgroups and non-independent criteria in the LGDM problem, this paper proposes a new probabilistic linguistic LGDM method to analyse the interactions among interest subgroups and the interrelationships among criteria. First, a transformation model that converts many scattered linguistic terms into probabilistic linguistic term sets (PLTSs) is proposed, and it can keep participants’ true feelings as complete as possible. Then, the probabilistic linguistic Choquet average (PLCA) operator and the generalized Shapley probabilistic linguistic Choquet average (GS-PLCA) operator are proposed to aggregate the PLTSs from different subgroups for different alternatives with respect to various criteria. These proposed operators can appropriately handle the games played among the different interest subgroups. Moreover, the generalized Shapely probabilistic linguistic TODIM (GS-PLTODIM) method is developed, and it considers the heterogeneous relationships among the criteria. In addition, the novel LGDM method is constructed based on the GS-PLCA operator and the GS-PLTODIM method to solve LGDM problems with interacting subgroups and interrelated criteria. Last, as one of the LGDM problems, the Beijing subway pricing case is used to illustrate the effectiveness and superiority of the proposed LGDM method compared to some other existing methods. The proposed LGDM method will be shown to be applicable not only to this case but also to other LGDM problems.