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Fuzzy approximation via grid point sampling and singular value decomposition.

Y Yam1

  • 1Dept. of Mech. & Autom. Eng., Chinese Univ. of Hong Kong, Shatin.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|January 1, 1997
PubMed
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This study presents a novel fuzzy approximation method using singular value decomposition (SVD) on function samples. This approach generates accurate fuzzy approximators with controllable accuracy and membership functions.

Area of Science:

  • Numerical Analysis
  • Fuzzy Systems Engineering

Background:

  • Continuous function approximation is crucial in various scientific and engineering fields.
  • Existing fuzzy approximation methods often require complex rule base design.

Purpose of the Study:

  • To introduce a novel, data-driven approach for fuzzy approximation of continuous functions.
  • To develop a method that directly extracts fuzzy rules and membership functions from function samples.

Main Methods:

  • Sampling a continuous function on a compact domain over a rectangular grid.
  • Applying Singular Value Decomposition (SVD) to the resulting sample matrix.
  • Tailoring SVD outputs into fuzzy rule consequences and membership functions using normalization and non-negativeness conditions.

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Main Results:

  • A class of equivalent fuzzy approximators is generated directly from function samples.
  • A technique for creating normal or near-normal membership functions is formulated.
  • The approximation error is dependent on sampling density and discarded singular values.

Conclusions:

  • The proposed SVD-based fuzzy approximation method offers an effective way to approximate continuous functions.
  • The approach allows for a trade-off between the number of fuzzy rules (membership functions) and approximation accuracy.
  • This method provides a direct and efficient way to derive fuzzy systems from data.