TOPSIS Multi-Attribute Decision-Making Model Utilizing Novel Distance Measure of Picture Fuzzy Sets and Its Application in Power Battery Recycling Evaluation.

The recycling of power batteries is a key measure for improving the new energy industry chain and achieving green circular economy goals. However, the process of evaluating and selecting recycling schemes is influenced by multiple complex factors and often involves a significant amount of ambiguous and uncertain decision-making information. As an important extension of intuitionistic fuzzy sets, picture fuzzy sets characterize fuzzy information through three distinct dimensions: membership, neutrality, and non-membership. This three-dimensional structure offers unique advantages in addressing uncertain and ambiguous decision-making problems, where traditional fuzzy sets may lose valuable information. Drawing on the Bray-Curtis distance measure, this paper proposes a novel picture fuzzy distance measure that captures differences across all three dimensions more comprehensively. By combining the weighted form of the proposed picture fuzzy distance measure with the classical TOPSIS method, a new multi-attribute decision-making model is established under the picture fuzzy framework. The effectiveness and feasibility of the proposed method are demonstrated through a case study on the recycling of power batteries for electric vehicles. A sensitivity analysis of relevant parameters is conducted, confirming the stability of the model against variations in parameter settings. Comparative results indicate that the proposed novel picture fuzzy distance measure exhibits superior robustness compared to existing similar distance measures. Furthermore, the constructed decision-making model can provide reliable and practical support for uncertain multi-attribute decision-making problems in real-world applications.