Bipolar Fuzzy Set Theory in Decision-Making Systems
Summary
Bipolar fuzzy set theory extends classical fuzzy sets by assigning to each element two independent degrees: a positive membership reflecting support and a negative membership reflecting opposition. This dual grading enables representation of ambivalent or contradictory information, a frequent condition in complex decision-making environments. The framework generalises to intuitionistic, complex and soft settings, providing a rich algebraic structure for union, intersection, complement and aggregation operations. In practice, bipolar fuzzy sets underpin multi-criteria decision analysis methods such as VIKOR, PROMETHEE and TOPSIS, where the interplay of positive and negative evaluations yields more nuanced rankings of alternatives. Recent advances have explored hybrid models—combining bipolar fuzzy sets with soft-set theory to address phase-altering and multidimensional problems—and novel aggregation operators based on Hamacher norms, sine-trigonometric laws and entropy weighting. Applications span supplier selection, energy management, healthcare logistics and clustering tasks, demonstrating global relevance across engineering, management science and environmental planning. By capturing both desirable and undesirable attributes in a unified formalism, bipolar fuzzy set theory has become a vital tool for designers of decision support systems, enabling more flexible, interpretable and robust solutions to uncertainty and vagueness in real-world problems.
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Bipolar Fuzzy Set Theory in Decision-Making Systems publication trend
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Technical terms
Bipolar fuzzy set: A set in which each element has two membership degrees, positive and negative, representing support and opposition respectively.
Positive membership degree: A value in [0,1] indicating the extent to which an element belongs to or supports a concept.
Negative membership degree: A value in [0,1] indicating the extent to which an element does not belong to or opposes a concept.
Soft set: A parameterised family of subsets used to model uncertain or vague information without the need for a membership function.
Aggregation operator: A mathematical function that combines multiple input values (e.g. membership degrees) into a single representative output, preserving specified properties.
Multi-attribute decision-making (MADM): A class of methods for evaluating and ranking alternatives based on multiple criteria, often under uncertainty or imprecision.
References
- Hybrid integrated decision-making algorithm for clustering analysis based on a bipolar complex fuzzy and soft sets. Alexandria Engineering Journal (2023).
- Group Decision-Making Based on the VIKOR Method with Trapezoidal Bipolar Fuzzy Information. Symmetry (2019).
- Bipolar Complex Fuzzy Soft Sets and Their Applications in Decision-Making. Mathematics (2022).
- Multi-Criteria Group Decision-Making for Selection of Green Suppliers under Bipolar Fuzzy PROMETHEE Process. Symmetry (2020).
- Bipolar Complex Fuzzy Hamacher Aggregation Operators and Their Applications in Multi-Attribute Decision Making. Mathematics (2021).
- Identification and Classification of Aggregation Operators Using Bipolar Complex Fuzzy Settings and Their Application in Decision Support Systems. Mathematics (2022).
- Innovative Bipolar Fuzzy Sine Trigonometric Aggregation Operators and SIR Method for Medical Tourism Supply Chain. Mathematical Problems in Engineering (2022).
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