Arya Bhatta Journal of Mathematics and Informatics

This research develops a novel mathematical framework that addresses multi-criteria decision making (MCDM) challenges in uncertain environments through interval-valued fuzzy sets (IVFSs). Our approach enhances traditional fuzzy MCDM methodologies by incorporating interval-valued membership functions within TOPSIS, VIKOR, and ELECTRE frameworks, thereby improving the representation of imprecision and uncertainty inherent in complex decision scenarios. The theoretical groundwork encompasses comprehensive mathematical formulations, convergence analysis for interval-valued fuzzy aggregation operators, and rigorous proofs demonstrating the algebraic characteristics of interval-valued fuzzy computations. Our findings establish that interval-valued fuzzy MCDM algorithms preserve computational efficiency with complexity O(mn + m log m), where m denotes alternatives and n represents criteria, ensuring scalability for real-world applications. Empirical comparisons demonstrate enhanced robustness and precision of interval-valued methodologies compared to conventional fuzzy approaches, especially when addressing expert consensus challenges and data incompleteness scenarios. Validation across three distinct application domains-healthcare waste management, automotive supplier evaluation, and maritime risk assessment-confirms the framework's practical utility, with interval-valued techniques exhibiting greater decision consistency and reduced susceptibility to ranking reversals relative to traditional methodologies.