An Advanced Approach to Weighted Neutrosophic Soft Relations for Multi-Criteria Decision-Making for Apartment Selection, Macroeconomic Policy Evaluation, and Water Quality Assessment

Resumo

In this study, we propose the concept of Weighted Neutrosophic Soft Relations (WNSRs) and analyze their theoretical foundations, including fundamental definitions, properties, and operations. We establish the Cartesian product of Weighted Neutrosophic Soft Sets (WNSSs) and introduce a new class of WNSRs, providing a mathematical framework for their application. Additionally, we develop a novel Multi-Criteria Decision-Making Model (MCDMM) based on WNSRs, leveraging a weighted score function to enhance the stability and feasibility of decision analysis under uncertainty. Our approach allows decision-makers to incorporate parameter-specific weights, making the model more adaptable and precise in complex decision-making problems. To demonstrate the practical applicability of the proposed method, we solve a real-world Decision-Making Problem (DMP) and compare our model with the existing Dalkılıç method. The results indicate that our constructed MCDMM overcomes the limitations of previous models by offering greater flexibility and accuracy in ranking alternatives. Furthermore, the adjustability of our approach enables iterative refinements, ensuring optimal decision outcomes. This study contributes to multi-criteria decision-making (MCDM) by advancing the theoretical and applied aspects of WNSRs, making them a powerful tool for handling uncertainty in various domains.