Modelling the effect of motivation on mental health components with fuzzy logic among elite athletes.

Elite athletes operate in high-stress, feedback-rich environments where mental health risk is shaped by motivation and training climate. This study models the joint effects of intrinsic motivation, psychological safety, and mental well-being on anxiety, depression, athlete-specific strain, and burnout using an interpretable fuzzy-logic framework alongside conventional regression. A sample of 247 athletes completed validated measures (SMS-6 Intrinsic Motivation, Psychological Safety, SWEMWBS, GAD-7, PHQ-9, APSQ, and BMS). After pre-processing and standard analyses, we constructed a Mamdani-type Fuzzy Inference System. To accurately represent the non-linear transitions between psychological states, the model specifies trapezoidal membership functions for boundary linguistic variables and triangular membership functions for intermediate categories. The system utilises a transparent rule base (primary risk from low IM; protection from PS/MWB; synergistic protection when both are high), min-max aggregation, and centroid defuzzification. Rule weights and breakpoints were calibrated against observed score distributions to minimise mean absolute error (MAE). Multiple regressions indicated that PS and MWB independently predicted lower risk across all outcomes; however, IM emerged as a significant positive predictor of depression and anxiety (p < 0.05). Further diagnostics confirmed this as a suppression effect, with all VIF values < 1.5. Visual and quantitative analyses confirmed three regularities: (i) a primary risk gradient when IM, PS, and MWB are low; (ii) buffering as PS or MWB increase; and (iii) a low-risk "basin" when PS and MWB are jointly high. Comparative metrics (MAE/RMSE) showed that the FIS model offers superior predictive accuracy and interpretability compared to standard linear approaches.