Multi-Attribute Decision Making Using Spherical Fuzzy Sets

Multi-attribute decision making (MADM) frameworks enable decision makers to evaluate and rank alternatives when multiple, often conflicting criteria are present. Spherical fuzzy sets extend classical fuzzy logic by representing uncertainty through three independent membership functions—truth, indeterminacy and falsity—subject to the constraint that the sum of their squares does not exceed unity. This geometry imparts a higher degree of expressiveness in capturing expert hesitation and partial belief. In MADM contexts, spherical fuzzy values are aggregated via tailored operators to synthesise criterion evaluations, derive overall scores for alternatives and support transparent, robust choices. Recent developments have introduced enriched operational laws, interval extensions and complex-valued generalisations, all of which preserve the geometric intuition of the spherical model while accommodating more intricate interrelationships among criteria. Applications span environmental management, energy system selection, financial system assessment and pattern recognition, demonstrating both practical relevance and theoretical depth.

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Novel prioritised aggregation techniques have been proposed to handle T-spherical fuzzy information in environmental applications. By integrating a parameterised Schweizer–Sklar t-norm, researchers constructed new weighted and geometric operators that emphasise key criteria in recycled water planning. A case study on water-recycling strategies illustrated superior discrimination of alternatives compared with existing methods.

A T-spherical fuzzy TOP-DEMATEL framework has been developed for social banking evaluation, capturing both causal relationships and weightings of factors such as risk analysis, personnel quality and technological infrastructure. The model identifies critical drivers of performance in interest-free banking systems and offers a systematic route to policy optimisation under uncertainty.

Similarity measures for spherical and T-spherical fuzzy sets have been refined to improve pattern recognition tasks. New cosine, grey and set-theoretic distance functions overcome limitations of earlier metrics by guaranteeing compliance with distance axioms and enhancing separability of classes in a building-material recognition problem. Comparative experiments demonstrate clearer clustering and higher classification accuracy.

Multi-Attribute Decision Making Using Spherical Fuzzy Sets publication trend

The graph below shows the total number of articles in multi-attribute decision making using spherical fuzzy sets across all publications each year (not limited to Nature Index journals).

Technical terms

Spherical Fuzzy Set: A fuzzy set characterised by three membership degrees—truth, indeterminacy and falsity—whose squared-sum constraint ensures a spherical geometry of uncertainty.

Multi-Attribute Decision Making (MADM): A methodological framework for ranking or selecting alternatives evaluated against multiple quantitative or qualitative criteria.

Aggregation Operator: A mathematical function that combines individual criterion values or fuzzy numbers into a single composite score for each alternative.

T-Spherical Fuzzy Set: An extension of spherical fuzzy sets incorporating a parameterised triangular norm to modulate conjunction operations in aggregation.

References

1. Multi-Attribute Decision-Making for T-Spherical Fuzzy Information Utilizing Schweizer-Sklar Prioritized Aggregation Operators for Recycled Water. Decision Making Advances (2024).
2. An assessment of alternative social banking systems using T-Spherical fuzzy TOP-DEMATEL approach. Decision Analytics Journal (2023).
3. Similarity Measures for T-Spherical Fuzzy Sets with Applications in Pattern Recognition. Symmetry (2018).