Abstract

Many researchers have conducted empirical studies with multiple moderators to better understand the complex mechanisms underlying causal relations. In real-world settings, linguistic expressions and ambiguous human experiences cannot be accurately modeled using crisp numbers; thus, fuzzy theory offers a more suitable framework. While existing studies have applied fuzzy methods to simple models, more complex structures remain largely unexplored. This paper proposes Fuzzy Multiple Moderators Analysis (FMMA), integrating fuzzy least squares estimation (FLSE) and fuzzy least absolute deviation (FLAD) based on L2 and L1 metrics. To estimate model coefficients, we provide a closed-form solution in FLSE and apply optimization algorithms such as Genetic Algorithm (GA), Harmony Search (HS), and neural networks. Empirical analysis was conducted using real-world datasets in psychology, solar power generation, and bike rental counts. These datasets encompass both subjective survey-based and sensor-driven variables, offering diverse degrees of ambiguity and nonlinearity. The proposed FLSE method achieved lower fuzzy mean squared errors (FMSE) and higher fuzzy R² values compared to classical models, demonstrating superior fit and explanatory power in contexts involving ambiguous data. Particularly, the fuzzy moderated-mediation model captured nuanced indirect effects and multi-way moderator interactions that were overlooked by crisp models. FLAD further demonstrated robustness in handling asymmetric errors and outlier-prone conditions. This study highlights the potential of fuzzy analytical frameworks in complex social and environmental domains, providing robust estimation and interpretability even in the presence of vague or imprecise information.

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