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Automatic Extraction of Linguistic Description from Fuzzy Rule Base

Krzysztof Siminski, Konrad Wnuk

TL;DR

This work tackles the interpretability gap in neuro-fuzzy systems by introducing a modular linguistic-description framework that automatically translates fuzzy rule bases into natural English. It defines a taxonomy of descriptors (two-tailed and one-tailed) implemented via various fuzzy sets (Gaussian, triangular, trapezoidal, singleton, sigmoidal, arctan, tanh) to describe premises and conclusions. The method is demonstrated on the synthetic 4 Gaussians dataset across Mamdani-Assilan, Takagi-Sugeno-Kang, and ANNBFIS systems, with an open-source implementation provided. The results show enhanced interpretability of complex rule bases while preserving core predictive structure, aiding model inspection and deployment in real-world settings.

Abstract

Neuro-fuzzy systems are a technique of explainable artificial intelligence (XAI). They elaborate knowledge models as a set of fuzzy rules. Fuzzy sets are crucial components of fuzzy rules. They are used to model linguistic terms. In this paper, we present an automatic extraction of fuzzy rules in the natural English language. Full implementation is available free from a public repository.

Automatic Extraction of Linguistic Description from Fuzzy Rule Base

TL;DR

This work tackles the interpretability gap in neuro-fuzzy systems by introducing a modular linguistic-description framework that automatically translates fuzzy rule bases into natural English. It defines a taxonomy of descriptors (two-tailed and one-tailed) implemented via various fuzzy sets (Gaussian, triangular, trapezoidal, singleton, sigmoidal, arctan, tanh) to describe premises and conclusions. The method is demonstrated on the synthetic 4 Gaussians dataset across Mamdani-Assilan, Takagi-Sugeno-Kang, and ANNBFIS systems, with an open-source implementation provided. The results show enhanced interpretability of complex rule bases while preserving core predictive structure, aiding model inspection and deployment in real-world settings.

Abstract

Neuro-fuzzy systems are a technique of explainable artificial intelligence (XAI). They elaborate knowledge models as a set of fuzzy rules. Fuzzy sets are crucial components of fuzzy rules. They are used to model linguistic terms. In this paper, we present an automatic extraction of fuzzy rules in the natural English language. Full implementation is available free from a public repository.
Paper Structure (21 sections, 7 equations, 4 figures, 3 tables)

This paper contains 21 sections, 7 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Neuro-fuzzy systems
  3. Linguistic description of fuzzy rules
  4. Two-tailed descriptors
  5. Fuzzy singleton
  6. Gaussian descriptor
  7. Triangular descriptor
  8. Trapezoidal descriptor
  9. One-tailed descriptors
  10. Sigmoidal, semitriangular, and arctangent descriptors
  11. Hyperbolic tangent descriptor
  12. Example
  13. Dataset
  14. Fuzzy systems
  15. Fuzzy system with triangular descriptors in premises
  16. ...and 6 more sections

Figures (4)

  • Figure 1: Examples of membership functions in fuzzy descriptors.
  • Figure 2: The semantics of linguistic labels for location applied to a Gaussian descriptor.
  • Figure 3: The semantics of linguistic labels for fuzziness applied to a (half of a) Gaussian descriptor.
  • Figure 4: The surface of the '4 Gausses' dataset.

Theorems & Definitions (1)

  • Example 2.1