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Updated: May 24, 2025

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On Ordered Weighted Averaging Operator and Monotone Takagi-Sugeno-Kang Fuzzy Inference Systems.
IEEE Transactions on Cybernetics
|March 3, 2025
Summary
This study establishes conditions for monotone Takagi-Sugeno-Kang Fuzzy Inference Systems (TSK-FIS) using product T-norm. It introduces necessary and sufficient conditions to ensure reliable fuzzy inference, applicable to FMEA and image processing.
Area of Science:
- Fuzzy Logic Systems
- Computational Intelligence
- Mathematical Modeling
Background:
- Monotonicity is crucial for Takagi-Sugeno-Kang Fuzzy Inference Systems (TSK-FIS), with research focusing on its conditions for two decades.
- Existing research has not fully addressed the necessary and sufficient conditions for TSK-FIS monotonicity, particularly with product T-norm.
Purpose of the Study:
- To define necessary and sufficient conditions for a Takagi-Sugeno-Kang Fuzzy Inference System with product T-norm (TSK-FIS-product) to be monotone.
- To develop a general joint sufficient condition for TSK-FIS-product monotonicity.
Main Methods:
- Defined fuzzy membership functions (FMFs) with single and continuous support.
- Utilized a grid partition strategy for TSK-FIS-product firing strength computation.
- Derived a general joint sufficient condition based on ordered weighted averaging (OWA) principles and hyperboxes.
Main Results:
- Established two necessary conditions for TSK-FIS-product monotonicity: non-indeterminate normalized firing strength and defined restricted consequents.
- Derived a general joint sufficient condition for monotonicity.
- Demonstrated the applicability of the developed methods through three case studies in Failure Mode and Effect Analysis (FMEA) and image processing.
Conclusions:
- The derived conditions provide a robust framework for ensuring monotonicity in TSK-FIS-product models.
- The methods are effective for practical applications like FMEA and image processing, as shown by case study results.
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