Neutrosophic Information Gain for Decision Tree Construction: Application to Teaching Performance of Tennis Instructors in Sports Universities

This paper introduces a novel framework for constructing decision trees using neutrosophic logic, where uncertainty is represented across three independent dimensions: truth (T), indeterminacy (I), and falsity (F). Unlike classical or fuzzy decision trees, the proposed model uses neutrosophic entropy and neutrosophic information gain to identify optimal attribute splits under ambiguous, conflicting, or incomplete data conditions. The methodology is applied to tennis teaching performance evaluation in sports universities, where assessments often include subjective judgments, partial records, and conflicting performance indicators. A complete decision tree is constructed using real-world-inspired data with neutrosophic annotations. Comparative analysis with classical models shows that the neutrosophic tree provides superior interpretability and robustness when handling uncertainty in student classification.