Multi-Criteria Decision-Making Method Based on Probabilistic Uncertain Linguistic T-Spherical Fuzzy ARAS

Based on the need to address the uncertainty and fuzziness of evaluation information in multi-criteria decision-making while reflecting probability distributions, a novel Probabilistic Uncertain Linguistic T-Spherical Fuzzy Set (PULTSFS) is proposed by integrating the probabilistic expression advantages of PULTS with the three-dimensional evaluation characteristics of TSFS. Firstly, the related concepts and fundamental operational rules of PULTSFS are defined, including the score function, accuracy function, Hamming distance measure, and the Probabilistic Uncertain Linguistic T-Spherical Fuzzy Weighted Averaging (PULTSFWA) operator, with properties such as monotonicity, idempotency, and boundedness being analyzed. Subsequently, the ARAS method is extended to establish a multi-criteria decision-making model based on PULTSF-ARAS. In this model, the criterion weights are determined by integrating subjective weights and objective distance-based weights, and the relative closeness of alternatives is calculated using the positive ideal solution to rank the alternatives. Finally, a case study on green supplier selection for new energy vehicle enterprises is conducted to demonstrate the validity and feasibility of the proposed method