Spherical Fuzzy FUCA Framework Transforms College Physical Fitness Evaluation: A Robust MCDM Decision‑Support Model

Table of Contents

  1. Key Highlights
  2. Introduction
  3. Why multi-criteria decision making is essential for campus fitness assessment
  4. What spherical fuzzy sets bring to the table
  5. FUCA aggregation: Faire Un Choix Adequat explained
  6. The SF-FUCA model applied: structure of the case study
  7. Results: interpreting the rankings
  8. Why SF-FUCA offers better discrimination and uncertainty management
  9. Sensitivity analysis: probing robustness to weight variation
  10. Practical steps for implementing SF-FUCA on campus
  11. Case interpretation: turning rankings into interventions
  12. Comparative performance: SF-FUCA versus classical SF-MCDM and crisp methods
  13. Data collection and expert elicitation: best practices
  14. Limitations, caveats, and areas for improvement
  15. Real-world examples: how institutions might use SF-FUCA
  16. Governance, transparency, and ethical considerations
  17. From scores to continuous improvement: feedback loops
  18. Recommendations for practitioners
  19. Research directions and potential extensions
  20. FAQ

Key Highlights

  • Introduces the SF-FUCA framework that combines spherical fuzzy sets with the Faire Un Choix Adequat (FUCA) aggregation to evaluate college student physical fitness under uncertainty.
  • Demonstrates through a 15-alternative, 7-criterion, 4-expert case study that SF-FUCA produces clear, stable rankings (top: Improving Physical Condition, score 10.38) and better discrimination between closely performing options than classical MCDM methods.
  • Sensitivity analysis confirms robustness to changes in decision-maker and criterion weights; practical recommendations guide campus interventions, resource allocation, and monitoring.

Introduction

Assessing student physical fitness on university campuses requires more than raw test scores. Evaluators confront multiple criteria — aerobic capacity, muscular strength, flexibility, body composition, injury risk, participation rates, and psychological well-being — each varying in scale, direction, and importance. Decision-makers must reconcile these heterogeneous measures with expert judgments that are often uncertain, hesitant, or partially conflicting.

The spherical fuzzy Faire Un Choix Adequat (SF-FUCA) framework addresses this complexity by blending a refined fuzzy-set representation with an aggregation procedure designed to respect expert hesitation and ambiguous inputs while handling both benefit and cost criteria. The result is a decision-support model tailored to the messy realities of campus health evaluation: it ranks alternatives (student fitness states, program options, or intervention portfolios) in a way that is interpretable, discriminative, and resilient to changes in weighting assumptions.

This article explains the SF-FUCA approach, examines the illustrative case study reported by Xie, Bai, and Li (2026), and translates the findings into concrete guidance for physical education faculty and campus administrators. It explores the mathematical intuition without sacrificing clarity, highlights comparative advantages over classical MCDM approaches, and outlines practical steps for implementation and future work.

Why multi-criteria decision making is essential for campus fitness assessment

College physical fitness evaluation rarely reduces to a single metric. A student with excellent cardiovascular endurance may have poor flexibility or a high injury risk. A fitness program might raise participation but be expensive or contraindicated for students with certain conditions. These tensions produce trade-offs that single-criterion analysis cannot resolve.

Multi-criteria decision-making (MCDM) provides a structured way to weigh and combine disparate criteria. MCDM enables administrators to:

  • Incorporate both quantitative measures (e.g., timed runs, lift weights) and qualitative judgments (e.g., adherence likelihood, motivational factors).
  • Distinguish between benefit criteria (higher values preferred) and cost criteria (lower values preferred).
  • Explicitly assign importance (weights) to reflect institutional priorities, accreditation requirements, or health guidelines.

However, traditional MCDM assumes that criterion values and weights are precise and that experts can express judgments without ambiguity. That assumption fails in practical settings where experts hesitate, disagree, or express partial confidence. The SF-FUCA framework brings an uncertainty-aware approach suited to these realities.

What spherical fuzzy sets bring to the table

Fuzzy sets were introduced to model imprecision: instead of classifying a student as simply "fit" or "unfit," fuzzy membership allows degrees of belonging. Extensions such as intuitionistic fuzzy sets added a separate degree of non-membership to capture explicit doubt. Spherical fuzzy sets (SFS) extend those ideas further by allowing three independent parameters — membership, non-membership, and hesitation — that must satisfy a spherical constraint instead of summing to at most one.

Key advantages of spherical fuzzy sets in the context of fitness evaluation:

  • They separate explicit non-membership (e.g., "this student is not aerobically fit") from hesitation (e.g., "the expert is unsure whether the VO2 measurement truly reflects fitness because of recent illness"), preserving both kinds of uncertainty.
  • The spherical constraint permits a more flexible allocation of belief, disbelief, and uncertainty than earlier fuzzy frameworks, enabling richer representation of nuanced expert judgments.
  • SFS support arithmetic and comparison operations suited for aggregation in MCDM workflows, allowing direct incorporation into ranking algorithms.

Consider an expert evaluating whether a student requires a targeted strength program. They might assign a high membership (strong indicator of need), a low non-membership (few reasons against), but still a moderate hesitation reflecting incomplete longitudinal data. Spherical fuzzy values capture this triple and keep hesitation explicitly available during aggregation — crucial when multiple experts express different hesitation patterns across criteria.

FUCA aggregation: Faire Un Choix Adequat explained

FUCA stands for Faire Un Choix Adequat, a French phrase meaning making an adequate choice. As an aggregation method within MCDM, FUCA systematically fuses evaluations across criteria and experts into scalar scores that can be compared and ranked.

What distinguishes FUCA when combined with spherical fuzzy sets:

  • FUCA respects the spherical fuzzy parameters during aggregation, rather than forcing a premature crisping or collapsing of hesitation.
  • It accounts for both benefit and cost criteria, converting cost scores appropriately so higher aggregated scores still indicate better alternatives.
  • FUCA can incorporate decision-maker weights, allowing institutions to privilege certain stakeholders (e.g., athletic trainers vs. public health officers) in the final ranking.

In practical terms, FUCA applies aggregation operators that preserve the uncertainty structure offered by spherical fuzzy representations and produce interpretable numeric scores. These scores enable ranking while reflecting the underlying expert hesitation and inter-criterion trade-offs.

The SF-FUCA model applied: structure of the case study

Xie, Bai, and Li demonstrated the SF-FUCA framework through a hypothetical illustrative case. The structure clarifies the workflow and shows how the method handles real decision-making complexity:

  • Alternatives: 15 student-related options. These represent distinct fitness states or programmatic choices such as "Improving Physical Condition," "Reduced Fitness Level," "Critical Fitness Condition," "Low Fitness Stage," and others. The alternatives span desirable and undesirable states, making the ranking informative for triage and intervention prioritization.
  • Criteria: 7 evaluation criteria. While the source abstract does not list each criterion by name, typical choices in fitness assessment include aerobic capacity, muscular strength, flexibility, body composition, injury risk, psychosocial readiness, and participation/engagement. The model handles both benefit and cost criteria.
  • Decision-makers: 4 experts. These experts provide spherical fuzzy evaluations for each alternative-criterion pair. Their inputs are aggregated with weights that can reflect differing influence (e.g., head of physical education may carry more weight than a part-time coach).
  • Aggregation and ranking: SF-FUCA integrates the spherical fuzzy inputs via the FUCA operator to compute scores for each alternative. The top-ranked alternative attains the highest SF-FUCA score.

This setup mirrors real campus assessment committees: a modest number of experts, several relevant criteria, and a set of practical alternatives or fitness states to rank.

Results: interpreting the rankings

The SF-FUCA model produced clear numerical scores in the case study. The highest-scoring alternative was "Improving Physical Condition" with a score of 10.38. Close behind were "Reduced Fitness Level" (9.90) and "Critical Fitness Condition" (9.70). The lowest-ranked option was "Low Fitness Stage" (4.49).

Two immediate interpretations emerge:

  • The model discriminates tightly among closely performing alternatives. The narrow gaps between the top three indicate they are near the decision boundary, which flags a need for careful resource allocation or further data collection for those groups.
  • A low score for "Low Fitness Stage" suggests either consistently poor evaluations across multiple criteria or substantial uncertainty that depresses the aggregated value. That distinction matters: if uncertainty drives the low score, targeted assessment could remediate; if stable poor values drive it, the institution needs direct intervention.

Real-world analogy: Suppose a university fitness taskforce must decide which of four programmatic options to fund for the coming semester — a general wellness campaign, targeted strength clinics, cardiovascular training modules, or injury prevention workshops. The SF-FUCA rankings would show which option aligns best with expert judgments across multiple dimensions (effectiveness, cost, reach, risk), flagging close calls for deliberation and obvious winners for immediate deployment.

Why SF-FUCA offers better discrimination and uncertainty management

Classical MCDM techniques typically transform fuzzy or imprecise inputs into crisp scores via defuzzification or simplified averaging. Doing so risks losing the nuanced hesitation information that affects confidence in a ranking. SF-FUCA avoids premature loss of uncertainty by preserving spherical fuzzy parameters until aggregation.

Consequence of this design:

  • Alternatives that perform similarly on crisp measures can be distinguished by their hesitation patterns. For example, two fitness programs might have similar projected effectiveness, but one may have high expert hesitation due to limited pilot data. SF-FUCA will reflect that difference in the aggregated score.
  • The model better manages contradictory inputs. If experts disagree — some assigning high membership, others high non-membership — the spherical fuzzy representation and FUCA aggregation integrate these conflicting signals while keeping hesitation visible.
  • Sensitivity to weight changes becomes explicit. When institutions test alternative weighting schemes, SF-FUCA shows how confidence in rankings shifts, enabling more informed governance decisions.

These properties matter in practice. Funding committees, health services, and athletics departments need not just a ranking — they need to understand where the judgment is robust and where it depends heavily on contested or uncertain inputs.

Sensitivity analysis: probing robustness to weight variation

Any MCDM model depends on weights assigned to criteria and decision-makers. SF-FUCA researchers conducted sensitivity analysis for both decision-maker weight variation and criteria weight variation. The analysis aimed to answer: Do small changes in weights produce large ranking shifts?

Findings reported:

  • The SF-FUCA rankings remained largely stable across reasonable deviations in both decision-maker and criterion weights. Top alternatives retained their positions, and relative separations were preserved.
  • Where rankings did change, the alternatives involved were those with very close baseline scores, indicating the model correctly signals marginal cases rather than over-reacting to weight perturbations.

Why this matters operationally:

  • Administrators can have confidence that the ranked priorities will not flip dramatically in response to modest changes in stakeholder influence or shifting institutional emphasis.
  • Where the model does show sensitivity, decision-makers receive a valuable cue to investigate further: collect more data, run pilot programs, or convene additional expert review for the marginal alternatives.

Practical example: A college considers raising the weight on "injury risk" after a spate of campus injuries. Sensitivity analysis with SF-FUCA would show whether that policy shift meaningfully reorders program priorities — if it does, administrators may need to prepare for reallocation; if not, the current portfolio likely already accounts for risk.

Practical steps for implementing SF-FUCA on campus

Deploying SF-FUCA requires a sequence of institutional actions. The framework is methodological but depends on careful data and governance practices to produce useful outputs.

  1. Define alternatives clearly
    • Alternatives can be individual student fitness states, program options, class formats, or resource allocations. Clarity prevents ambiguous comparisons.
    • Example: Alternatives might be "Expand morning cardio classes," "Introduce on-campus strength program," "Subsidize off-campus gym memberships," and "Invest in physiotherapy services."
  2. Select and operationalize criteria
    • Choose criteria that are measurable and aligned with institutional objectives. Label each as benefit or cost.
    • Example criteria: aerobic performance (benefit), injury incidence (cost), cost per student (cost), participation potential (benefit), long-term retention (benefit), required staff hours (cost), and psychosocial well-being impact (benefit).
  3. Assemble and weight expert panel
    • Include diverse stakeholders: PE faculty, athletic trainers, student health clinicians, student representatives, and finance officers.
    • Assign decision-maker weights transparently. Weighting can be equal or reflect expertise and responsibility.
  4. Collect spherical fuzzy evaluations
    • Experts express membership, non-membership, and hesitation for each alternative-criterion pair. Provide training and exemplars to help experts translate intuition into spherical fuzzy values.
    • Use surveys or structured interviews with prebuilt scales to make entry consistent.
  5. Apply FUCA aggregation
    • Convert cost criteria as needed, apply FUCA operators to aggregate across experts and criteria, and compute SF-FUCA scores.
    • Produce rankings and visualize scores with confidence bands representing hesitation.
  6. Conduct sensitivity analysis
    • Systematically vary decision-maker and criterion weights to test ranking stability.
    • Report scenarios where rankings flip and quantify the minimal weight change required to cause a change.
  7. Translate rankings into action
    • Use top-ranked alternatives for immediate pilots or resource allocation.
    • For closely ranked or sensitive alternatives, plan additional data collection, small-scale experiments, or monitoring.
  8. Monitor and iterate
    • After implementation, collect outcome data to validate the model’s predictions and update expert evaluations accordingly.

These steps transform the SF-FUCA output from a theoretical ranking into a practical governance tool.

Case interpretation: turning rankings into interventions

A university facing diverse fitness needs can use SF-FUCA rankings to triage students and programs.

Example scenarios:

  • Triage for individualized interventions: Suppose the model ranks "Critical Fitness Condition" high among students flagged by screening. Administrators should prioritize immediate medical evaluation, personalized training plans, and physiotherapy referrals. The SF-FUCA score will help establish urgency and resource needs.
  • Program selection: If SF-FUCA scores favor "Improving Physical Condition" as the top programmatic alternative, the institution might scale that program while reallocating funds from lower-ranked options. Sensitivity analysis identifies whether this decision is robust.
  • Resource allocation: Low scores for "Low Fitness Stage" that are driven by definitive low criterion values suggest investment in targeted remediation—perhaps linking students to structured exercise prescriptions and nutrition counseling.
  • Pilot testing: For alternatives close in score (e.g., second and third-ranked options with narrow differences), run randomized or quasi-experimental pilots. Use outcome data to refine spherical fuzzy inputs for subsequent rounds.

By translating numerical scores into a graded set of actions (immediate, plan/pilot, monitor), administrators can allocate finite staff and facilities where they will have the greatest expected benefit.

Comparative performance: SF-FUCA versus classical SF-MCDM and crisp methods

The SF-FUCA framework was compared to existing spherical fuzzy MCDM procedures and classical crisp MCDM. Reported comparative benefits include:

  • More consistent derivation of priorities. SF-FUCA produces rankings that reflect the interplay among membership, non-membership, and hesitation without collapsing uncertainty too early.
  • Better differentiation of closely performing alternatives. Traditional defuzzification methods can mask subtle differences; SF-FUCA preserves them through the aggregation process.
  • Enhanced management of spherical fuzzy uncertainty. By embedding hesitation directly in aggregation, SF-FUCA prevents overconfident conclusions and provides richer diagnostic outputs.

Operational implications:

  • Institutions using classical methods may observe sudden, unexplained ranking changes when criteria or weights are adjusted because those methods lack explicit hesitation tracking.
  • SF-FUCA reduces the risk of allocating resources based on spurious certainty. That is valuable when interventions have health and safety consequences.

Illustrative comparison: A classical weighted-sum approach might rank two programs identically if their defuzzified scores coincide. SF-FUCA could reveal that one program's score is underpinned by high hesitation across experts, while the other is supported by consistent membership — a distinction that should inform decision-making.

Data collection and expert elicitation: best practices

The quality of SF-FUCA outputs depends on careful input elicitation. The following practices reduce noise and bias:

  • Provide clear guidelines and examples for translating judgments into spherical fuzzy parameters. Use anchored scales (e.g., 0–1 with descriptors) and training sessions.
  • Encourage experts to separate disbelief from hesitation. Frame questions that tease apart "I think this is not suitable" from "I lack information to decide."
  • Use anonymized aggregation to reduce conformity bias; let experts express candid uncertainty without social pressure.
  • Validate expert judgments against objective measures where possible. Where experts express high hesitation, prioritize collecting objective data (e.g., re-testing physical performance, injury records).
  • Review inter-expert variance. High variance across experts on a key criterion signals the need for further review or for giving more weight to objective data.

Good elicitation improves both the interpretability and reliability of the final ranking.

Limitations, caveats, and areas for improvement

No model eliminates all uncertainty. SF-FUCA addresses many practical issues but has limitations:

  • Dependence on expert quality: Poorly informed or biased experts produce unreliable spherical fuzzy inputs. Governance around expert selection and training is essential.
  • Complexity of elicitation: Asking experts to provide three-parameter spherical fuzzy values requires training and may increase cognitive load compared with simpler scales.
  • Computational and interpretive demands: Administrators unfamiliar with fuzzy-set logic need tools and dashboards that translate SF-FUCA outputs into actionable visualizations.
  • Hypothetical demonstration: The reported study used a hypothetical case study. While illustrative, real-world deployment should include pilot implementations and empirical validation.

Suggested improvements for practice and research:

  • Develop intuitive elicitation tools (mobile apps or web forms) that guide experts and perform consistency checks.
  • Combine SF-FUCA with longitudinal outcome tracking to calibrate the relationship between initial spherical fuzzy evaluations and realized student outcomes.
  • Explore automated hybrid approaches that blend objective metrics (device-measured activity, wearable sensors) with expert spherical fuzzy inputs to reduce reliance on subjective judgment.

Acknowledging these limitations clarifies where institutional processes, training, and empirical validation must supplement the method.

Real-world examples: how institutions might use SF-FUCA

Example 1 — Regional State University: targeted intervention roll-out A regional state university screens first-year students and identifies large subgroups with varying fitness profiles. Using SF-FUCA with a panel of PE instructors, student health clinicians, and student reps, the university ranks program options. SF-FUCA indicates a robust preference for a combined cardiovascular-strength hybrid program. Sensitivity analysis shows the ranking persists across plausible weight shifts, so the university pilots the hybrid program across two dorms, measures outcomes over a semester, and scales if results meet predefined benchmarks.

Example 2 — Athletic department: pre-season risk management An athletic department must decide whether to invest in expanded preseason conditioning or additional sports medicine staff. Experts provide spherical fuzzy evaluations incorporating past injury records and projected team loads. SF-FUCA suggests prioritizing additional sports medicine staffing for high-contact teams while recommending conditioning investments for non-contact squads. The granular hesitation signals that data collection on off-season workload is needed before committing to conditioning infrastructure.

Example 3 — Campus wellness office: resource allocation under budget constraints The campus wellness office considers four interventions but has limited funds. SF-FUCA ranks "online guided fitness modules" high because of low cost and moderate expected impact, while "facility upgrades" rank lower due to high cost and moderate uncertainty about increased student uptake. Decision-makers use these results to allocate funds to online modules immediately and schedule facility upgrades for the next fiscal year, contingent on improved participation metrics.

These examples show how SF-FUCA integrates complex trade-offs into actionable priorities.

Governance, transparency, and ethical considerations

Applying SF-FUCA should comply with institutional governance and ethical standards. Key considerations:

  • Transparency about weights and expert roles: Publish the weight schema and expert composition so stakeholders understand how priorities align with values.
  • Privacy: When SF-FUCA evaluates individual students or small groups, ensure data are anonymized and health information appropriately protected.
  • Equity: Check that criteria and weights do not systematically disadvantage particular student populations. For example, weighting participation potential without considering access barriers could bias against lower-income students.
  • Validation: Use pilot outcomes to validate and recalibrate the model. Avoid making permanent policy changes on the basis of a single SF-FUCA run.

The original research reported no involvement of human participants; expert opinions were anonymized and aggregated for illustration. Real deployments must adhere to relevant human subjects protections when individual-level health data are used.

From scores to continuous improvement: feedback loops

SF-FUCA functions best as part of an iterative assessment cycle:

  1. Use SF-FUCA to prioritize interventions.
  2. Implement top-ranked actions on a pilot scale.
  3. Collect outcome metrics (fitness improvements, injury rates, participation).
  4. Feed results back into expert panels and update spherical fuzzy evaluations.
  5. Re-run SF-FUCA with updated inputs and adjusted weights.

This loop drives evidence-based refinement. Over successive cycles, hesitation terms should decline as data accumulate, and the model’s predictive validity should improve.

Recommendations for practitioners

  • Start small: Pilot SF-FUCA on a single program or cohort to build experience with elicitation and interpretation.
  • Invest in training: Provide brief workshops for expert panels to understand spherical fuzzy parameters and practice scoring with examples.
  • Build user-friendly tools: Develop interfaces that convert membership/non-membership/hesitation triples into visual aids and automatically compute FUCA aggregates.
  • Pair with objective data: Use wearables, test-retest measures, and health records to complement expert judgments and reduce unnecessary hesitation.
  • Institutionalize sensitivity checks: Make sensitivity analysis a standard deliverable to inform governance deliberations.
  • Document decisions: Archive SF-FUCA inputs and outputs for auditability and future research.

Following these steps increases the practicality and integrity of SF-FUCA-based decision-making.

Research directions and potential extensions

SF-FUCA opens several avenues for further work:

  • Empirical validation: Deploy SF-FUCA across multiple campuses with diverse student bodies to compare predicted rankings with longitudinal outcomes.
  • Hybrid models: Blend SF-FUCA with machine learning approaches that can infer expert-like hesitation patterns from historical data.
  • Group dynamics: Study how panel composition affects spherical fuzzy inputs and whether structured deliberation reduces harmful bias.
  • Automation: Create open-source libraries implementing spherical fuzzy arithmetic and FUCA aggregation to lower implementation barriers.
  • Policy integration: Explore how SF-FUCA outputs can feed into accreditation reporting, campus health dashboards, and funding decisions.

Advancing these directions will strengthen both the methodological foundations and the applied value of SF-FUCA.

FAQ

Q: What exactly is a spherical fuzzy value and why use it instead of standard fuzzy membership? A: A spherical fuzzy value specifies three numbers: membership (degree of support), non-membership (degree of rejection), and hesitation (residual uncertainty). Unlike standard fuzzy sets that provide only a single membership degree, spherical fuzzy sets explicitly model hesitation and allow all three parameters to coexist under a spherical constraint. This richer representation captures nuanced expert judgments, particularly when experts are unsure or data are incomplete.

Q: How many experts are needed for reliable SF-FUCA results? A: There is no universal minimum, but the quality of aggregation improves with diverse and competent expert representation. The case study used four experts, reflecting practical committee sizes. For larger-scale institutional decisions, panels of 5–10 experts from complementary domains (clinical, academic, student affairs, finance) can improve robustness. Always complement expert judgment with objective data when possible.

Q: How difficult is it to train experts to provide spherical fuzzy inputs? A: Training is modest but necessary. Experts need to understand the meaning of membership, non-membership, and hesitation and how to map their judgments to numeric scales. Two to three short workshops with practice examples typically suffice. Software interfaces can further simplify entry by offering intuitive sliders or categorical descriptors that translate automatically into spherical fuzzy triples.

Q: Does SF-FUCA require new software? A: Implementing SF-FUCA benefits from software that handles spherical fuzzy arithmetic and FUCA aggregation. Institutions can develop simple spreadsheets with custom functions or adopt specialized open-source libraries when available. Visualization tools that show scores with hesitation bands are particularly helpful for decision-makers.

Q: Can SF-FUCA be applied to individual student decisions (e.g., eligibility for advanced training)? A: Yes, SF-FUCA can be used at an individual level, but privacy and ethical constraints apply. Anonymize data when aggregating across groups, and establish clear criteria and appeals processes if decisions affect student opportunities. For high-stakes individual decisions, combine SF-FUCA outputs with objective clinical assessments.

Q: How should an institution set weights for criteria and decision-makers? A: Weights should reflect institutional priorities and stakeholder roles. For example, a university emphasizing injury prevention might assign higher weight to injury risk criteria; a finance-constrained campus might raise the weight on cost criteria. Decision-maker weights can reflect expertise and accountability. Importantly, present weights transparently and run sensitivity analysis to see how alternative weight schemes affect rankings.

Q: How does SF-FUCA handle conflicting expert opinions? A: SF-FUCA integrates conflicting inputs while preserving hesitation. If experts disagree, the aggregated spherical fuzzy parameters will reflect both membership and non-membership signals and often elevated hesitation. This outcome flags the need for further deliberation or data collection rather than masking disagreement in a single averaged number.

Q: What does a high hesitation value imply operationally? A: High hesitation indicates insufficient information or low confidence among experts. Operationally, this suggests prioritizing data collection (e.g., re-testing, additional surveys) before committing substantial resources. It can also mean piloting an intervention on a small scale to generate evidence.

Q: Are there cost or resource barriers to adopt SF-FUCA? A: Costs include developing or procuring software, time for expert panels, and training. These are comparable to or lower than other structured decision-support processes when considering the value of improved prioritization. Piloting on a contained problem helps manage initial costs.

Q: Where can I find more technical resources on spherical fuzzy sets and FUCA? A: Technical literature on spherical fuzzy sets covers their mathematical foundations and operations; FUCA-specific materials outline aggregation operators and ranking procedures. For practical adoption, seek applied papers that include case studies and implementation notes, and consult methodological appendices in recent MCDM publications.


This article synthesizes and expands upon the SF-FUCA framework and its illustrative case study. The approach gives campus decision-makers a practical, uncertainty-aware tool for prioritizing fitness interventions, allocating resources, and monitoring outcomes. Its capacity to preserve expert hesitation and to discriminate among closely performing alternatives makes SF-FUCA particularly valuable where stakes are high and data are imperfect. With careful elicitation, transparent governance, and iterative validation, SF-FUCA can become a central component of evidence-based campus health strategy.

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