<p>Mediation analysis is widely employed to explore how an independent variable (X) affects a dependent variable (Y) through a mediating variable. Traditional methods, such as the Baron and Kenny approach or Sobel test, often assume normal distributions and are inadequate when applied to ambiguous or fuzzy data, which are prevalent in behavioral and social sciences. Existing research has not adequately addressed the integration of fuzzy set theory with modern inferential tools like bootstrapping, leaving a gap in accurate analysis of uncertain, imprecise, or linguistically expressed data. This study aims to bridge that gap by introducing a novel methodology for conducting fuzzy mediation and moderated-mediation analysis using bootstrapping techniques. We propose an innovative framework combining fuzzy regression methods—Fuzzy Least Squares Estimation (FLSE) and Fuzzy Least Absolute closed-form solution, while FLAD, being non-differentiable, is optimized via Genetic Algorithm (GA) and Harmony Search (HS). Model performance is evaluated using fuzzy-specific error metrics, such as Fuzzy Root Mean Square Error (FRMSE) and Fuzzy Mean Absolute Error (FMAE). Empirical validation across three datasets—team dynamics, adolescent hate speech, and solar energy output—demonstrates the robustness of our approach. The proposed methods outperform traditional crisp-number models by capturing uncertainties more accurately and producing statistically significant estimates even in small or asymmetric datasets. This study pioneers the integration of bootstrapping into fuzzy mediation and moderated-mediation analysis, offering a statistically rigorous, interpretable, and scalable solution for handling ambiguity in empirical research. Our framework is particularly effective in fields like psychology, renewable energy, and social behavior, where linguistic and imprecise data are common.</p>