Decision-Making Approaches Based on Fuzzy and Rough Set Theory
Summary
Decision-making frameworks grounded in fuzzy and rough set theory address the pervasive challenge of uncertainty in complex systems. Fuzzy sets introduce graded membership to capture vagueness, while rough sets approximate imprecise concepts via lower and upper bounds defined by indiscernibility relations. Hybrid models leverage the complementary strengths of both theories to construct robust multi-criteria decision-making (MCDM) tools. These approaches have evolved to include enriched numeric representations—such as fuzzy rough numbers and Pythagorean fuzzy sets—and granular computing paradigms that cluster information into manageable granules. Through advanced weighting, ranking and reduction mechanisms, practitioners can derive transparent decision rules, prioritise criteria under ambiguity and extract knowledge from noisy or incomplete data. Applications span supply-chain optimisation, renewable energy siting, intelligent manufacturing, medical diagnosis and beyond, reflecting the global significance of uncertainty-aware decision support.
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Decision-Making Approaches Based on Fuzzy and Rough Set Theory publication trend
The graph below shows the total number of articles in decision-making approaches based on fuzzy and rough set theory across all publications each year (not limited to Nature Index journals).
Technical terms
Fuzzy set: A mathematical construct in which each element has a degree of membership between zero and one to represent vagueness.
Rough set: A method for approximating uncertain or imprecise concepts using lower and upper approximations derived from equivalence relations.
Multi-criteria decision-making (MCDM): A suite of techniques for evaluating, ranking and selecting alternatives according to multiple, often conflicting, criteria under uncertainty.
Fuzzy rough number: A hybrid entity combining fuzzy set graded membership with rough set upper and lower bounds to handle both vagueness and indiscernibility.
Pythagorean fuzzy set: An extension of fuzzy sets allowing independent specification of membership and non-membership degrees subject to a Pythagorean constraint.
Information granulation: The process of grouping data or concepts into granules to reduce complexity and manage uncertainty in decision-making.
Attribute reduction: The elimination of superfluous or redundant attributes from a dataset while preserving its essential decision-making or classification power.
References
- A Comprehensive Evaluation Model for Smart Supply Chain Based on The Hybrid Multi-Criteria Decision-Making Method. Journal of Soft Computing and Decision Analytics (2023).
- Floating photovoltaic site selection using fuzzy rough numbers based LAAW and RAFSI model. Applied Energy (2022).
- Attribute reduction and information granulation in Pythagorean fuzzy formal contexts. Expert Systems with Applications (2023).
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