An advanced fermatean fuzzy DoC MCDM architecture for comprehensive quantitative assessment of physical fitness competency across academic institutions

The fitness of the students in the college is a critical parameter of their health, well-being, and academic output. Nonetheless, the assessment of physical fitness determinants is uncertain and subjective due to differing opinions among experts and the interconnection of the standards with one another. In addressing this complexity, the current research presents a new Fermatean Fuzzy (FF) Deck-of-Cards-Method (DoCM) Multi-Criteria Decision-Making (MCDM) model for the quantitative evaluation of physical fitness in academic settings. The model is based on the fact that FF sets have high expressiveness, enabling them to represent expert hesitation and dual uncertainty more effectively than conventional fuzzy models. The DoC approach is used to obtain the systematic and preference-based weights of the evaluation criteria, thereby achieving rational and flexible prioritization. A hypothetical case study is created to demonstrate the relevance of the framework, encompassing criteria such as endurance, strength, flexibility, body composition, and mental well-being. The findings underscore the model’s ability to produce consistent and explainable rankings of fitness determinants using incomplete or unclear information. When compared to current literature where most models use FS/IFS/PFS as their default uncertainty modeling framework with cognitively demanding weighting functions, the proposed FF-DoC framework bridges the gap of integrating high-expressiveness uncertainty modeling with transparent and human-eliciting weight elicitation to assess institutional fitness competency.