Improved cosine similarity and distance measures-based TOPSIS method for cubic Fermatean fuzzy sets

Similarity and distance measures play important roles in fuzzy environments, helping to quantify the degree of similarity or concepts that may not have clear limits. They are used in various fields, including fuzzy logic, fuzzy clustering, and fuzzy decision-making. The cubic Fermatean fuzzy set (CFFS), which is a type of fuzzy set (FS), is highly favoured as an extension for expressing uncertainty through degrees of membership (η) and non-membership (υ). This article introduces novel measures for cosine similarity and distance in CFFSs. These measures are designed to improve the accuracy and efficiency of similarity and distance calculations in CFFSs. Also, a novel method is introduced for developing alternate similarity measures for CFFSs utilizing the proposed similarity measures that adhere to the similarity measures axiom. In addition, the connection between similarity and distance measures is utilized to construct a cosine distance metric for CFFSs. This newly suggested cosine similarity measure can not only provide solutions to decision-making problems from a geometric perspective but also from an algebraic point of view. To conclude, a case study is presented to showcase the practicality and effectiveness of the proposed approach, followed by a comparison of the outcomes of the suggested technique with some existing methodologies. This analysis helps to validate the proposed method and demonstrates its potential for outperforming other available approaches in terms of efficiency and accuracy.