Linear Diophantine Fuzzy Weighted Hamy Mean Operator with Application to Multi-Attribute Decision-Making Problems

Abstract

Existing multi-attribute decision-making methods often fail to adequately capture complex uncertainty and attribute interrelationships in real-world problems, potentially leading to suboptimal outcomes. To overcome this, we develop a robust linear Diophantine fuzzy sets based framework and introduce four novel Hamy mean operators such as linear Diophantine fuzzy Hamy mean, linear Diophantine fuzzy weighted Hamy mean, linear Diophantine fuzzy dual Hamy mean, and linear Diophantine fuzzy weighted dual Hamy mean operators, which empower decision-makers through reference parameters and effectively model interdependent attributes. The practical impact of our approach is demonstrated through a critical emergency shelter material selection case study, where the proposed operators successfully identified "3D Printed Recycled Materials" as the optimal choice, validating its decision alignment with expert judgment. A detailed comparative analysis confirms the superiority of our model, showing a higher ranking consistency and significantly better performance in handling high hesitancy and conflicting criteria compared to existing methods. This research provides a more reliable and robust decision-making tool for practical applications in emergency management, supply chain logistics, and strategic planning, where managing complex uncertainty is crucial.