A Ratio-Based Method to Solve Multiple Criteria Decision-Making Problems with Interval-Valued Fuzzy Numbers

This paper addresses multiple-criteria decision-making (MCDM) under interval-valued fuzzy numbers (IVFNs) by introducing a ratio-based approach that jointly considers closeness to the positive ideal solution (PIS) and remoteness from the negative ideal solution (NIS). The method constructs the normalized and weighted decision matrix, identifies the ideal and anti-ideal points, and then computes a combined closeness index along with a relative ratio to provide a balanced and interpretable ranking of alternatives. A real-world case study on selecting an R&D manager in a telecommunication company illustrates the applicability of the method. The proposed approach identifies [Formula: see text] as the best alternative, yielding the final ordering [Formula: see text]. Comparative experiments using IVF-TOPSIS and IVF-VIKOR arrive at the same ordering, thereby confirming the robustness, consistency, and reduced redundancy of the proposed method. Overall, the approach is simple to implement, enhances flexibility in handling uncertainty, and provides reliable support for real-world decision-making under imprecise information.