Divergence measures for T-spherical fuzzy sets with applications to multi-criteria decision making and pattern classification

T-spherical fuzzy sets are a powerful extension of fuzzy, intuitionistic, and picture fuzzy frameworks, providing greater flexibility in modeling uncertainty through three independent membership degrees: positive, neutral, and negative. Despite their growing applications in decision-making and pattern classification, research on divergence measures for T-spherical fuzzy environments remains scarce. To date, only a few studies have introduced divergence measures for T-spherical fuzzy sets; however, these measures have theoretical and practical limitations that constrain their applicability to complex real-life problems. To overcome these shortcomings, this paper introduces new divergence measures for T-spherical fuzzy sets and thoroughly investigates their axiomatic and mathematical properties to ensure theoretical soundness. Based on the proposed divergence, a novel divergence-based TOPSIS method is developed, accompanied by a new approach to determining criteria weights for spherical fuzzy data. Furthermore, the proposed divergence measures are applied to extend a pattern classification algorithm. To demonstrate practical applicability, the proposed decision-making framework is further validated through a real-world-inspired case study on selecting an all-rounder cricketer for a test-match competition under uncertain and imprecise evaluation conditions. Sensitivity, comparative, and numerical analyses are conducted to demonstrate the stability, effectiveness, and superiority of the proposed measures over existing approaches. The results confirm that the developed divergence framework enhances the interpretability and reliability of decision-making under T-spherical fuzzy environments.