A picture fuzzy multi-criteria decision-making framework for evaluating urban planning proposals under uncertainty

The rapid growth of cities demands sophisticated decision support systems capable of simultaneously tackling social, economic, and environmental issues in urban planning. This research introduces a comprehensive decision-making framework that integrates machine learning to optimize urban infrastructure development. To improve the reliability of the analysis, recursive feature elimination paired with random forest (RF-RFE) is utilized to pinpoint the most critical factors, ensuring that the decision process emphasizes the features that matter most. To handle uncertainty and vagueness in expert evaluations, picture fuzzy sets are implemented, allowing a nuanced expression of hesitation, while the entropy method is employed to objectively determine the weights of social, economic, and environmental criteria, thereby reducing subjective influence. The evaluation based on the approach of relative utility and nonlinear standardization (ERUNS) is employed to rank urban planning alternatives, capturing the nonlinear interactions among criteria. This framework provides a comprehensive, data-driven decision support tool for urban planners and policymakers to address the intricate and dynamic challenges of modern urbanization.