Mathematical Modelling of Context-Dependent Fuzzy Decision Support Systems for Doctoral Researchers

Abstract

Doctoral researchers must constantly make multiple trade-offs related to data collection, writing, and supervisor requests. Choices that seem clear today may change in urgency and context based on fatigue, deadlines, and supervisor requests. This research proposes a context-dependent Pythagorean fuzzy decision support system (CD-PF-DSS) to address these challenges. The proposed decision support system employs a context-dependent softmax function that facilitates a reliability transformation and preserves Pythagorean fuzzy feasibility. Four theorems provide sufficient conditions under which feasibility is preserved, the model is bounded, dominance is consistent, and the model is stable. A sufficient condition for rank preservation is also provided. The model is demonstrated through examples and indicates that the revision of thesis chapters is the preferred action compared to the revision of thesis chapters when deadlines are relaxed, and contextual constraints are in place. The model also demonstrates that the revision of thesis chapters is less preferred compared to the revision of manuscripts when deadlines are high. It is expected that the system will provide operational support to researchers based on context and trade-off decisions.

Introduction

This research proposes a Context-Dependent Pythagorean Fuzzy Decision Support System (CD-PF-DSS) to help PhD researchers decide which research task to prioritize when circumstances are uncertain and constantly changing.

Traditional priority systems often use fixed criterion weights, but doctoral research is highly dynamic. Factors such as deadlines, supervisor expectations, resource limitations, workload/fatigue, publication pressure, feasibility, and sustainability can change from week to week. Therefore, the “best” task today may not be the best task next week.

Main idea

The proposed CD-PF-DSS combines:

• Fuzzy modeling to represent uncertain or incomplete judgments.
• Pythagorean fuzzy numbers (PFNs) to represent support, opposition, and hesitation.
• Context-dependent criterion weights that change according to the researcher's current situation.
• Contextual reliability so that weak, outdated, or uncertain information does not produce excessive confidence.
• Uncertainty penalties to discourage selecting options based on highly uncertain evidence.
• Ranking and confidence scores to identify the most appropriate research task while showing how reliable the recommendation is.

Research gap

Existing fuzzy multi-criteria decision-making models generally assume that criterion weights remain constant. This is unsuitable for doctoral research because priorities can change substantially when:

• A publication deadline is approaching.
• Laboratory or other resources become unavailable.
• A supervisor requests an urgent chapter.
• The researcher experiences excessive workload or fatigue.
• Career or publication pressure increases.

The proposed model therefore makes criterion weights responsive to context rather than fixed.

Design principles

The model is based on five principles:

1. Context responsiveness – criterion importance changes smoothly as circumstances change.
2. Feasibility preservation – mathematical transformations remain within the valid Pythagorean fuzzy domain.
3. Uncertainty honesty – limited or unreliable evidence increases hesitation rather than artificially increasing confidence.
4. Decision monotonicity – a clearly better alternative should not become worse simply because of the ranking process.
5. Human governability – recommendations should be explainable, reviewable, and open to supervisor/researcher criticism or override.

Model and algorithm

The researcher first defines possible actions and criteria such as:

• Scientific value
• Urgency
• Feasibility
• Supervisory alignment
• Sustainability/workload

The system then:

1. Assigns fuzzy assessments to each possible task.
2. Records the current research context.
3. Dynamically adjusts criterion weights.
4. Estimates the reliability of the available information.
5. Calculates an uncertainty-adjusted score and confidence level.
6. Ranks the possible tasks.
7. Performs sensitivity analysis to determine how stable the recommendation is.

Numerical example

Four possible doctoral tasks were compared:

• Data collection
• Journal manuscript writing
• Methodology workshop
• Thesis chapter revision

Two different situations were examined.

Context I: High deadline and publication pressure
→ Journal manuscript received the highest score (0.728).

Context II: High resource constraints and fatigue
→ Thesis revision became the highest-ranked option (0.680), while data collection dropped substantially.

This demonstrates the key advantage of the system: the recommended task changes when the researcher's circumstances change, rather than relying on a fixed priority list.

Analytical properties

The proposed mathematical framework claims four important properties:

• Validity: transformed fuzzy values remain mathematically valid.
• Boundedness: scores and weights remain within defined limits.
• Consistency: dominance relationships between alternatives are preserved.
• Stability: small changes in context should not cause unreasonable changes in rankings.

If two alternatives have very similar scores, the system recommends supervisory review rather than automatic selection.

Calibration and governance

The system should be tested over multiple planning cycles by comparing its recommendations with what researchers actually chose and achieved. Researchers and supervisors should help determine the criteria, weights, fuzzy assessments, and reliability values.

Importantly, the system is intended as a decision-support tool, not a surveillance or disciplinary system. Context information should preferably be self-reported, users should be able to explain or override recommendations, and the system should not secretly monitor productivity.

Conclusion

This study developed a context-dependent pythagorean fuzzy decision support system for doctoral researchers. This system converts contexts of deadlines, resources, supervision, workloads, and careers into criterion weights and reliability adjusted fuzzy evaluations. A research priority framework is possible based on the bounded score, a preference measure, formal theorems, the robustness condition, and linear computational complexity. The focus of future studies could be on estimating context functions from longitudinal doctoral planning data; assessing and comparing choices of different fuzzy structures; and evaluating the improved models to attain better completion, with no increase in the same, or less researcher autonomy.

References

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Copyright

Copyright © 2026 Prof.(Dr.) Md. Mushtaque Khan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.