AI-driven Linear Diophantine Fuzzy evaluation for advancing quality and innovation in physical education

Physical education (PE) assessment has historically focused on quantitative performance metrics, systematically neglecting motivational, emotional, and social dimensions of student development. To address this gap, this paper introduces a Multi-Attribute Fuzzy Evaluation Model (MAFEM) grounded in Linear Diophantine Fuzzy Set (LDFS) theory, which incorporates independent reference parameters (α, β) to represent expert uncertainty more faithfully than classical fuzzy frameworks. Within the LDFS environment, we formally define Sugeno-Weber t-norm and t-conorm operations and derive two aggregation operators: the LDFS Sugeno-Weber Weighted Averaging (LDFSWWA) operator and the LDFS Sugeno-Weber Weighted Geometric (LDFSWWG) operator. Both operators are proved to satisfy idempotency, monotonicity, and boundedness. These operators are embedded within the WASPAS (Weighted Aggregated Sum Product Assessment) method to form a structured multi-criteria decision-making (MCDM) framework. Six innovative PE strategies are evaluated against six quality criteria by a panel of ten domain experts. Results consistently identify Interdisciplinary Collaboration (Z₂) as the top-ranked strategy across all parametric scenarios. A sensitivity analysis across nine ξ values confirms ranking stability, and comparison with three numerically applicable existing methods validates the competitiveness of the proposed framework. This work provides a mathematically rigorous, data-driven tool for PE quality evaluation, with potential for extension to broader educational and management contexts.