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Enhancing Interval Type-2 Fuzzy Logic Systems: Learning for Precision and Prediction Intervals

Ata Koklu, Yusuf Guven, Tufan Kumbasar

TL;DR

The paper tackles reliable prediction-interval generation in high-risk contexts using interval Type-2 fuzzy logic systems (IT2-FLS), addressing learning challenges such as parameter abundance, center-of-sets selection, and high dimensionality. It introduces flexible center-of-sets CS-CMs (WKM and WNT) for KM and NT, respectively, and employs DL-based unconstrained learning alongside an HTSK2 extension to mitigate the curse of dimensionality. A dual-focused learning framework is proposed to optimize both accuracy and HQ-PI generation, with a composite loss balancing prediction error and calibrated uncertainty. Experiments on multiple datasets show reduced training failures and improved PI quality, demonstrating enhanced uncertainty quantification and safer decision support in high-stakes applications.

Abstract

In this paper, we tackle the task of generating Prediction Intervals (PIs) in high-risk scenarios by proposing enhancements for learning Interval Type-2 (IT2) Fuzzy Logic Systems (FLSs) to address their learning challenges. In this context, we first provide extra design flexibility to the Karnik-Mendel (KM) and Nie-Tan (NT) center of sets calculation methods to increase their flexibility for generating PIs. These enhancements increase the flexibility of KM in the defuzzification stage while the NT in the fuzzification stage. 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. 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. Additionally, we introduce a framework to learn the enhanced IT2-FLS with a dual focus, aiming for high precision and PI generation. Through exhaustive statistical results, we reveal that HTSK2 effectively addresses the dimensionality challenge, while the enhanced KM and NT methods improved learning and enhanced uncertainty quantification performances of IT2-FLSs.

Enhancing Interval Type-2 Fuzzy Logic Systems: Learning for Precision and Prediction Intervals

TL;DR

The paper tackles reliable prediction-interval generation in high-risk contexts using interval Type-2 fuzzy logic systems (IT2-FLS), addressing learning challenges such as parameter abundance, center-of-sets selection, and high dimensionality. It introduces flexible center-of-sets CS-CMs (WKM and WNT) for KM and NT, respectively, and employs DL-based unconstrained learning alongside an HTSK2 extension to mitigate the curse of dimensionality. A dual-focused learning framework is proposed to optimize both accuracy and HQ-PI generation, with a composite loss balancing prediction error and calibrated uncertainty. Experiments on multiple datasets show reduced training failures and improved PI quality, demonstrating enhanced uncertainty quantification and safer decision support in high-stakes applications.

Abstract

In this paper, we tackle the task of generating Prediction Intervals (PIs) in high-risk scenarios by proposing enhancements for learning Interval Type-2 (IT2) Fuzzy Logic Systems (FLSs) to address their learning challenges. In this context, we first provide extra design flexibility to the Karnik-Mendel (KM) and Nie-Tan (NT) center of sets calculation methods to increase their flexibility for generating PIs. These enhancements increase the flexibility of KM in the defuzzification stage while the NT in the fuzzification stage. 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. 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. Additionally, we introduce a framework to learn the enhanced IT2-FLS with a dual focus, aiming for high precision and PI generation. Through exhaustive statistical results, we reveal that HTSK2 effectively addresses the dimensionality challenge, while the enhanced KM and NT methods improved learning and enhanced uncertainty quantification performances of IT2-FLSs.
Paper Structure (17 sections, 27 equations, 4 figures, 1 table, 1 algorithm)

This paper contains 17 sections, 27 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background on IT2-FLS
  3. Enhancements for Learning IT2-FLSs
  4. Increasing the Flexibility of CSCMs
  5. KM and WKM CSCMs
  6. NT and WNT CSCMs
  7. Learning IT2-FLS via DL Optimizers
  8. Learnable Parameter Sets
  9. Parameterization Tricks for DL Optimizers
  10. Curse of Dimensionality: the HTSK2 Method
  11. Dual-Focused IT2-FLS: Accuracy and HQ-PI
  12. Comparative Performance Analysis
  13. Design of Experiments
  14. Performance Evaluation
  15. Curse of Dimensionality
  16. ...and 2 more sections

Figures (4)

  • Figure 1: Illustration of an antecedent MF: IT2-FS
  • Figure 2: White Wine dataset: Notched box-and-whisker plots
  • Figure 3: Parkinson's Motor UPDRS dataset: Notched box-and-whisker plots
  • Figure 4: AIDS dataset: Notched box-and-whisker plots

Theorems & Definitions (2)

  • Remark 1
  • Remark 2