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

Why student fitness needs a smarter checkup

College students’ bodies and minds are under pressure from long study hours, screen time, and often poor sleep and diet. Universities try to track fitness with tests for running speed, strength, or flexibility, but turning scattered, uncertain opinions from coaches and health staff into fair, reliable scores is hard. This paper introduces a new way to turn those fuzzy judgments into clear, explainable rankings of student fitness, helping schools decide where to focus training, counseling, and resources.

Many pieces of fitness, many views

Physical fitness at college is more than how fast a student can run. It includes heart and lung endurance, muscle strength, flexibility, body fat and muscle balance, quickness and balance, mental wellness, and everyday habits such as sleep, diet, and movement. Different experts may value these pieces differently: a sports coach may prize speed, a counselor may stress stress management, and a health teacher may focus on body composition. Their judgments often conflict, and even a single expert may feel unsure. Traditional scoring systems and simple statistics struggle to capture this mix of hard numbers and human hesitation.

From vague opinions to structured choices

The authors build on a family of methods known as multi‑criteria decision making, which are designed to weigh several factors at once. A key ingredient in their approach is a modern form of “fuzzy” reasoning that allows experts to say not just how strongly they support or oppose a statement, but also how unsure they are. Their chosen version, called a Fermatean fuzzy set, gives extra room for expressing doubt and mixed feelings, which is especially important for soft areas like mental wellness or lifestyle. Instead of forcing experts to give crisp, confident numbers, the method lets them admit when they both agree and disagree to some degree, and when they simply do not know.

Using cards to capture expert priorities

To turn expert views into weights for each fitness factor, the study uses the “deck of cards” approach. Rather than asking people to fill in complex rating tables, it lets them arrange abstract cards from most to least important and place “blank” gaps between them. A bigger gap means a larger jump in importance. Simple checks ensure that the spacing is consistent. These card positions are then converted into numerical weights in a transparent, step‑by‑step way. Because the process feels more like ordering preferences than doing math, it lowers mental effort and makes it easier for experts to explain why, for example, endurance might count more than flexibility in a given campus context.

Testing the framework with a realistic scenario

To show how the method works, the authors create a hypothetical case study with eight fitness criteria and five student groups, ranging from highly active students following personalized programs to students with mostly sedentary habits. Each group is described by fuzzy judgments on every criterion, including degrees of support, opposition, and hesitation. The deck of cards process produces weights for each fitness aspect, and the Fermatean fuzzy engine then combines all this information into an overall score for every group. The resulting ranking clearly separates the groups: a balanced group with steady exercise and strong mental wellness emerges as the best, while groups with patchy or inconsistent fitness patterns fall behind. Sensitivity checks—small tweaks to the weights—show that the top choices remain stable, suggesting that the method is robust and not overly fragile to minor changes in expert opinion.

Why this matters for campuses

For a non‑specialist, the key message is that this framework offers universities a fairer, more human‑aware way to turn complex, uncertain expert views into clear fitness rankings and priorities. By combining intuitive card‑based preferences with a flexible way of expressing doubt, the model reduces hidden bias, copes better with conflicting opinions, and still delivers simple answers about which student groups or fitness dimensions most need attention. This can guide more targeted exercise programs, mental health initiatives, and resource planning, helping campuses promote student well‑being in a way that respects both data and human judgment.

Citation: Xie, L., Huo, Y. & Wang, X. An advanced fermatean fuzzy DoC MCDM architecture for comprehensive quantitative assessment of physical fitness competency across academic institutions. Sci Rep 16, 14510 (2026). https://doi.org/10.1038/s41598-026-43046-1

Keywords: college physical fitness, fuzzy decision making, multi-criteria assessment, student health evaluation, educational policy