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

Abstract

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. 

DOI: 10.5281/zenodo.15420579