Modification of the Ranking of Alternatives with Weights of Criterion (RAWEC) Method and Improvement with Fermatean Fuzzy numbers

This paper presents a modified version of the Ranking of Alternatives with Weights of Criterion (RAWEC) method, improved by the application of Fermatean fuzzy (FF) numbers, with the aim of solving decision-making problems under conditions of uncertainty. As a contribution to the field of multi-criteria decision making (MCDM), the FF-RAWEC method offers a solid mathematical foundation and shows flexibility through different decision scenarios—when the criteria are of benefit, cost, or mixed type. Numerical examples illustrate the practical application of the method, while sensitivity analysis confirms its stability. In addition, the comparative analysis shows a high correlation of ranks with other methods, which further confirms the validity and reliability of the proposed method. FF-RAWEC successfully integrates the advantages of FF logic, making it suitable for solving real-world problems involving imprecise or subjective information. Its adaptability and consistency indicate great potential for further application and development in engineering and social decision-making contexts.