Weighted IndetermSoft Set for Prioritized Decision-Making with Indeterminacy and Its Application to Green Competitiveness Evaluation in Equipment Manufacturing Enterprises

Soft set theory, introduced by Molodtsov in 1999, is a versatile tool for modeling uncertainty in decision-making. This paper proposes the Weighted IndetermSoft Set, a novel extension that integrates attribute prioritization with indeterminacy handling, building on the Weighted Soft Set and IndetermSoft Set. By assigning weights to attributes and accommodating uncertain or incomplete data, it addresses limitations of existing models like HyperSoft Set, IndetermHyperSoft Set, and TreeSoft Set. We formally define the Weighted IndetermSoft Set, present its operations with proofs, and provide a detailed methodology for implementation. A case study on green competitiveness evaluation in equipment manufacturing enterprises demonstrates its practical utility in assessing sustainability under uncertainty. A real-world comparative analysis on supply chain risk assessment highlights its advantages. The paper concludes with recommendations for future research, positioning the Weighted IndetermSoft Set as a powerful framework for complex decision-making scenarios.