Fuzzy Multi-Criteria Decision-Making Applications in Complex Systems
Summary
Fuzzy multi-criteria decision-making (MCDM) provides a flexible framework for addressing problems characterised by uncertainty, imprecision and conflicting goals within complex systems. By extending classical MCDM with fuzzy logic, analysts can represent qualitative judgements as graded membership degrees rather than binary choices. This approach has been applied across domains such as energy planning, healthcare resource allocation, supply-chain management and urban infrastructure design. Central to these applications are fuzzy set generalisations—intuitionistic, Pythagorean and q-rung orthopair fuzzy sets—which allow richer parameterisation of membership, non-membership and hesitation. Aggregation operators then synthesise multiple criteria into composite indices, while ranking functions or entropy measures guide the selection of optimal alternatives. Advances in fuzzy soft set theory further incorporate parameterised uncertainty, enabling decision support systems to adapt dynamically to stakeholder preferences and evolving data streams. Integration with machine learning and network modelling has enhanced scalability for large-scale systems, such as smart grids and pandemic response planning, reinforcing the global impact of fuzzy MCDM in guiding robust and transparent policy decisions.
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Recent work on complex polytopic fuzzy information systems has introduced decision support models for vaccine allocation under evolving epidemiological data, demonstrating how high-dimensional parameter spaces can be partitioned into polytopes to capture nonlinear interactions among clinical, logistical and demographic criteria. Another line of research has proposed a novel generalisation of fuzzy soft sets—so-called (a,b)-fuzzy soft sets—that decouple the calibration of membership and non-membership importance, leading to flexible aggregation operators and a robust MCDM strategy validated on supplier selection and environmental impact assessment cases. A complementary contribution has developed an (m,n)-fuzzy set framework, defining score and accuracy functions alongside tailored aggregation operators to resolve multi-criteria prioritisation problems in manufacturing process optimisation and sustainable resource management. These studies illustrate the continuous evolution of fuzzy MCDM tools to accommodate higher-order uncertainty and parameter heterogeneity in large-scale, real-world decision environments.
Fuzzy Multi-Criteria Decision-Making Applications in Complex Systems publication trend
The graph below shows the total number of articles in fuzzy multi-criteria decision-making applications in complex systems across all publications each year (not limited to Nature Index journals).
Technical terms
Fuzzy set: A collection in which each element has a membership degree between 0 and 1.
Intuitionistic fuzzy set: Extends a fuzzy set by specifying both membership and non-membership degrees, with a residual hesitation margin.
Pythagorean fuzzy set: Generalises intuitionistic fuzzy sets by enforcing the sum of squared membership and non-membership degrees ≤ 1.
q-Rung orthopair fuzzy set: Further generalises Pythagorean fuzzy sets by raising membership and non-membership values to the qth power before summation.
Fuzzy soft set: A parameterised family of fuzzy sets enabling context-dependent representation of uncertainty.
Aggregation operator: A mathematical function that combines multiple criteria values into a single overall evaluation.
Multi-criteria decision-making (MCDM): A systematic process for evaluating and ranking alternatives based on several, often conflicting, criteria.
References
- Application of Complex Polytopic Fuzzy Information Systems in Knowledge Engineering: Decision Support for COVID-19 Vaccine Selection. International Journal of Knowledge and Innovation Studies (2023).
- A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management. Energies (2020).
- New generalization of fuzzy soft sets: $ (a, b) $-Fuzzy soft sets. AIMS Mathematics (2023).
- Generalized Frame for Orthopair Fuzzy Sets: (m,n)-Fuzzy Sets and Their Applications to Multi-Criteria Decision-Making Methods. Information (2023).
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