A Novel Cosine Similarity for Interval-Valued Fermatean Fuzzy Set and Its Application in MADM

Multi-attribute decision making (MADM) often involves uncertainty, and Interval-Valued Fermatean Fuzzy Set (IVFFS) is a powerful tool for handling such vagueness. However, existing research lacks a geometrically intuitive similarity measure for IVFFS. Therefore, this paper proposes a novel cosine similarity measure for IVFFS, which captures directional consistency of interval-valued membership and non-membership degrees. Next, to address attribute weighting in MADM, we integrate this cosine similarity into the DEMATEL method to derive attribute weights by analyzing interrelationships under interval uncertainty. Finally, TOPSIS is extended based on the proposed cosine similarity to implement MADM. A case study on supplier selection illustrates the practicality of the proposed method. Through comparison with existing methods, the proposed method yields a similar ranking result (A1 ≻ A3 ≻ A4 ≻ A5 ≻ A2), there by confirming its validity.