Complex Fuzzy Logic Systems for Decision-Making Applications

Complex fuzzy logic systems represent a significant evolution of classical fuzzy theory by assigning each element a complex-valued membership degree, incorporating both amplitude and phase. This extension enables richer modelling of uncertainty, periodic phenomena and contextual dependencies. In decision-making contexts, such systems offer enhanced discrimination between alternatives, capturing subtle variations and temporal patterns that real-valued sets cannot. At their core, complex fuzzy logic frameworks integrate algebraic structures—such as lattices and interval-valued extensions—with inference engines akin to Mamdani and Takagi–Sugeno architectures. Aggregation operators, including geometric, ordered weighted and hybrid forms, play a pivotal role in synthesising complex-valued assessments across multiple criteria. Applications span traffic management under dynamic conditions, medical diagnosis accommodating periodic symptom patterns, financial forecasting and cybersecurity risk evaluation in industrial control systems. By leveraging the phase component, complex fuzzy approaches can encode directional information—such as time of day or cyclic behaviour—while amplitude conveys confidence. The interplay between structural generality and computational practicality positions complex fuzzy logic systems as versatile decision-support tools for modern, data-intensive environments.

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Recent developments have introduced a complex intuitionistic fuzzy soft lattice of circular and quaternion types to model directional time entities in traffic monitoring during pandemic scenarios. By fusing intuitionistic fuzzy membership and non-membership with soft set parameters, this structure captures both the magnitude and timing of congestion, enabling dynamic control strategies in retail precincts. Another line of inquiry has extended picture fuzzy sets into a complex cubic framework, integrating neutral membership to enrich decision matrices. Complement, score and accuracy functions, together with weighted, ordered weighted and hybrid geometric operators, facilitate multi-criteria analysis in engineering and management settings. A further advance involves a Mamdani Complex Fuzzy Inference System with rule reduction through granular computing and complex fuzzy measures. By employing similarity metrics for rule selection, the system iteratively refines its inference base, enhancing accuracy and reducing computational overhead in classification and prediction tasks. These studies collectively illustrate a progression from theoretical constructs to scalable architectures, underscoring the adaptability of complex fuzzy logic for diverse decision-making challenges.

Complex Fuzzy Logic Systems for Decision-Making Applications publication trend

The graph below shows the total number of articles in complex fuzzy logic systems for decision-making applications across all publications each year (not limited to Nature Index journals).

Technical terms

Complex fuzzy set: A generalisation of fuzzy sets where membership grades are complex numbers, encoding amplitude and phase for richer uncertainty modelling.

Intuitionistic fuzzy set: A fuzzy set characterised by degrees of membership, non-membership and an implicit hesitation margin.

Soft set: A parameterised family of subsets providing flexible modelling of uncertain attributes without over-rigid membership functions.

Aggregation operator: A mathematical function that combines multiple fuzzy or complex fuzzy values into a single representative measure.

Mamdani fuzzy inference system: A rule-based decision framework using fuzzy logic to map input variables through if-then rules to output conclusions, extended here with complex memberships.

References

1. A New Decision Making Model Based on Complex Intuitionistic Fuzzy Soft Lattice for Traffic Monitoring in the Pandemic Scenarios. Advanced Intelligent Systems (2024).
2. Innovative discussion of decision-making model based on complex cubic picture fuzzy information and geometric aggregation operators with applications. Complex & Intelligent Systems (2023).
3. Complex Fuzzy Geometric Aggregation Operators. Symmetry (2018).
4. Medical Diagnosis and Life Span of Sufferer Using Interval Valued Complex Fuzzy Relations. IEEE Access (2021).
5. Cybersecurity against the Loopholes in Industrial Control Systems Using Interval-Valued Complex Intuitionistic Fuzzy Relations. Applied Sciences (2021).
6. M-CFIS-R: Mamdani Complex Fuzzy Inference System with Rule Reduction Using Complex Fuzzy Measures in Granular Computing. Mathematics (2020).