Distance-Based Similarity Measures in T-Spherical Fuzzy Hypersoft Environment for Cluster Analysis

The notion of T-spherical fuzzy hypersoft set (TSFHSS) provides a powerful generalization of the picture fuzzy hypersoft set, offering additional amount of flexibility in modeling uncertain and unreliable information where the sum of membership, non-membership, and neutrality degrees can exceed one. The concept of similarity/distance measures plays a crucial role in various pattern recognition, decision-making, and classification tasks. In the present study, we introduce a novel distance measure for T-spherical fuzzy hypersoft sets to effectively quantify the dissimilar aspects of two objects. The necessary basic axioms are satisfied by the proposed measures along with some key properties. Based on this, we define corresponding similarity measures that are particularly effective in distinguishing highly similar elements. Some important theorems demonstrating the mathematical properties of these measures have also been proved. For the sake of validation of the proposed measures, we provide a numerical illustration demonstrating their accuracy and discriminating behavior. Furthermore, we develop a clustering algorithm that well utilizes the introduced similarity measures under the TSFHSS framework, enabling robust classification of objects in uncertain environments.