Core Concepts
This study proposes enhancements to Interval Type-2 Fuzzy Logic Systems (IT2-FLSs) to improve their learning performance in generating high-quality prediction intervals alongside high accuracy when dealing with high-dimensional data.
Abstract
This paper presents several enhancements to improve the learning performance of Interval Type-2 Fuzzy Logic Systems (IT2-FLSs) for generating high-quality prediction intervals (PIs) alongside high accuracy.
The key highlights are:
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Increased flexibility of Center of Sets Calculation Methods (CSCMs):
- Proposed Weighted Karnik-Mendel (WKM) and Weighted Nie-Tan (WNT) methods to provide extra design flexibility in the defuzzification and fuzzification stages, respectively.
- The enhancements aim to generate high-quality PIs with tight bands and high uncertainty coverage.
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Addressing the curse of dimensionality:
- Expanded the High-Dimensional Takagi-Sugeno-Kang (HTSK) method proposed for Type-1 FLSs to IT2-FLSs, resulting in the HTSK2 approach.
- HTSK2 effectively mitigates the dimensionality challenge by scaling the membership functions based on the input dimension.
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Integration of deep learning:
- Transformed the constrained learning problem of IT2-FLSs into an unconstrained form via parameterization tricks.
- This enables the direct application of deep learning optimizers for learning IT2-FLSs.
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Dual-focused learning framework:
- Introduced a deep learning-based framework to learn IT2-FLSs with a dual focus: high precision and high-quality PIs.
- The framework utilizes a composite loss function to optimize for both accuracy and uncertainty quantification.
The extensive statistical results demonstrate that the proposed HTSK2 effectively addresses the curse of dimensionality, while the enhanced WKM and WNT methods improve the learning performance and uncertainty quantification capabilities of IT2-FLSs.
Stats
The study used the following datasets:
White Wine dataset (11 features, 4898 samples)
Parkinson's Motor UPDRS dataset (19 features, 5875 samples)
AIDS dataset (23 features, 2139 samples)
Quotes
"To address the curse of dimensionality issue, we expand the High-Dimensional Takagi-Sugeno-Kang (HTSK) method proposed for type-1 FLS to IT2-FLSs, resulting in the HTSK2 approach."
"To address the large-scale learning challenge, we transform the IT2-FLS's constraint learning problem into an unconstrained form via parameterization tricks, enabling the direct application of deep learning optimizers."