A fuzzy multi-criteria decision model for assessing effectiveness in table tennis training systems

Evaluating sports training systems involves multiple interrelated factors and human judgment, which together introduce uncertainty that limits the effectiveness of conventional assessment approaches. This study develops a fuzzy multi-criteria decision model to assess the effectiveness of table tennis training programs. The proposed framework combines the fuzzy analytic hierarchy process for criterion weighting with conventional TOPSIS to rank the training programs based on crisp, aggregated participant scores. Data were collected from athletes participating in structured table tennis training programs, while expert judgments were used to determine the relative importance of the evaluation criteria. The FAHP analysis identified Skill Acquisition (0.458) as the most influential criterion, followed by Physical Fitness (0.256), Resource Utilization (0.125), Cognitive Engagement (0.109), and Student Satisfaction (0.052). Based on the FAHP–TOPSIS analysis, the training programs were ranked as A 1 > A 2 > A 3 > A 4 > A 5 , with corresponding closeness coefficients of 0.920, 0.828, 0.607, 0.173, and 0.072, respectively. The robustness analysis showed that the ranking order remained unchanged under ± 30% variations in criterion weights, while the closeness coefficients changed only slightly, indicating that the proposed framework is robust to moderate variations in criterion importance. Comparative validation further confirmed the consistency of the obtained ranking results with alternative multi-criteria decision-making methods, supporting the methodological reliability of the proposed approach. The findings demonstrate that the proposed FAHP–TOPSIS framework provides a systematic, transparent, and reproducible approach for evaluating the effectiveness of table tennis training programs. The model supports evidence-based decision-making in sports training evaluation and may be adapted for performance assessment in other sports and educational contexts.