A FCM-TODIM-STWD Method for Large-Group Multi-Attribute Decision Making with Probabilistic Linguistic Term Sets

Abstract

Probabilistic linguistic term sets (PLTSs) can flexibly express uncertain evaluation information provided by decision makers (DMs). Large-group multi-attribute decision making (LGMADM) problems usually involve uncertainty, heterogeneity, and strong subjectivity, which makes it difficult for conventional methods to simultaneously achieve effective classification, behavioral modeling, and sequential information utilization. This study investigates LGMADM problems in the context of PLTSs and proposes a FCM-TODIM-STWD method. First, to deal with the structural heterogeneity of large-scale expert groups, FCM is introduced to cluster experts and generate cluster-level preference information. Second, a novel deviation-range entropy of PLTSs is developed to determine attribute weights objectively. Third, according to the obtained attribute weights, a sequential three-way decision framework is constructed, in which attributes are incorporated into the decision process one by one, and alternatives in the boundary region are progressively refined until all alternatives are classified. Meanwhile, TODIM is introduced to calculate dominance degrees and conditional probabilities, so that the psychological behavior of DMs can be incorporated into the decision process. Therefore, behavioral rationality and sequential discrimination can be considered in a unified framework. Finally, an air-quality case study based on the 2024 data of 20 cities is provided to demonstrate the feasibility of the proposed method. Comparative analysis, sensitivity analysis, and ablation experiments are further conducted to verify its effectiveness, interpretability, and superiority. The results show that the proposed method not only maintains high consistency with several classical methods in ranking results, but also provides additional classification information and better decision support. Hence, the proposed method provides an effective and interpretable framework for solving LGMADM problems in a PLTS environment.