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Related Experiment Video

Updated: Jul 7, 2026

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
08:18

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

Sufficient conditions on fuzzy logic controllers as universal approximators.

W Chen1

  • 1Inst. of Autom., Qufu Normal Univ.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|February 5, 2008
PubMed
Summary

This study establishes conditions for fuzzy logic controllers (FLCs) to accurately approximate polynomials. It offers methods to determine the number of fuzzy rules needed, improving upon previous research.

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Last Updated: Jul 7, 2026

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
08:18

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Published on: August 15, 2020

Area of Science:

  • Control Theory
  • Fuzzy Systems
  • Artificial Intelligence

Background:

  • Fuzzy logic controllers (FLCs) are widely used in control systems.
  • Previous research (Ying, 1994) established conditions for FLC universal approximation.
  • Castro (1995) proposed specific FLC structures requiring further analysis.

Purpose of the Study:

  • To establish sufficient conditions for Castro's FLCs to approximate real polynomials with high accuracy.
  • To determine conditions under which these FLCs act as universal approximators.
  • To provide explicit formulas for calculating the number of fuzzy rules required for approximation.

Main Methods:

  • Utilizing novel techniques distinct from Ying (1994).
  • Developing analytical methods to derive sufficient conditions for polynomial approximation.
  • Deriving explicit formulas for rule computation in both single and multivariable polynomial approximation.

Main Results:

  • Identified less conservative sufficient conditions for polynomial approximation compared to Ying (1994).
  • Demonstrated that Castro's FLCs can be universal approximators under specific conditions.
  • Provided direct formulas for determining the number of fuzzy rules for multivariable polynomials.
  • Established conditions and formulas for approximating inexact functions.

Conclusions:

  • The proposed conditions for fuzzy logic controllers offer a less conservative approach to polynomial approximation.
  • The derived formulas provide a direct method for rule estimation, enhancing practical applicability.
  • This work advances the theoretical understanding and practical design of fuzzy logic controllers for approximation tasks.