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

Psychological safety and mental well-being independently predicted lower risk across all mental health outcomes in elite athletes.

• Sample consisted of 247 elite athletes completing validated measures including SMS-6 Intrinsic Motivation, Psychological Safety, SWEMWBS, GAD-7, PHQ-9, APSQ, and BMS.
• Multiple regression analyses confirmed PS and MWB as significant negative predictors of anxiety, depression, athlete-specific strain, and burnout.
• Results held across all four outcome measures assessed.

Intrinsic motivation emerged as a significant positive predictor of depression and anxiety, identified as a suppression effect.

• IM was a statistically significant positive predictor of depression and anxiety (p < 0.05).
• Further diagnostics confirmed this as a suppression effect rather than a direct causal relationship.
• All variance inflation factor (VIF) values were < 1.5, ruling out multicollinearity as an explanation.
• This finding was unexpected given typical assumptions about intrinsic motivation as a protective factor.

The Mamdani-type Fuzzy Inference System offered superior predictive accuracy and interpretability compared to standard linear regression approaches.

• Comparative metrics including MAE and RMSE were used to evaluate model performance.
• The FIS model used trapezoidal membership functions for boundary linguistic variables and triangular membership functions for intermediate categories.
• The system utilized min-max aggregation and centroid defuzzification.
• Rule weights and breakpoints were calibrated against observed score distributions to minimize mean absolute error (MAE).

The fuzzy logic model identified three consistent regularities in the relationship between motivational-psychological inputs and mental health risk.

• Regularity (i): a primary risk gradient when intrinsic motivation, psychological safety, and mental well-being are all low.
• Regularity (ii): a buffering effect as psychological safety or mental well-being increase.
• Regularity (iii): a low-risk 'basin' when psychological safety and mental well-being are jointly high.
• These regularities were confirmed through both visual and quantitative analyses.

The fuzzy inference system was constructed with a transparent rule base capturing primary risk and protective mechanisms among elite athletes.

• The rule base specified primary risk arising from low intrinsic motivation.
• Protection was modeled from psychological safety and mental well-being individually.
• Synergistic protection was modeled when both psychological safety and mental well-being are high simultaneously.
• The Mamdani-type FIS was chosen to accurately represent non-linear transitions between psychological states.