Notes on the approximation rate of fuzzy KH interpolators

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

This paper investigates the approximation behaviour of the Kóczy-Hirota (KH) interpolative fuzzy controllers. First, in accordance with the remarks in (Fuzzy Sets and Systems 125(1) (2002) 105), it is pointed out that it is a fuzzy generalization of the Shepard operator. Shepard operator has thoroughly studied by approximation theorist since the mid-1970s. Exploiting the aforementioned relationship, we establish analog results on the approximation rate of KH controllers. The optimal order and class of approximation (saturation problem) are determined for certain values of the exponent λ. Corresponding results on the modified alpha-cut based interpolation method, being an improvement of the KH interpolator, are also provided. The results offer trade-off facilities between approximation accuracy and the number of rules. As a consequence, the necessary and sufficient number of rules can be determined for a prescribed accuracy.

Original languageEnglish
Pages (from-to)441-453
Number of pages13
JournalFuzzy Sets and Systems
Volume138
Issue number2
DOIs
Publication statusPublished - Sep 1 2003

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Rate of Approximation
Controllers
Fuzzy systems
Approximation
Fuzzy sets
Interpolation
α-cut
Interpolation Method
Fuzzy Controller
Operator
Fuzzy Systems
Fuzzy Sets
Saturation
Trade-offs
Exponent
Sufficient
Analogue
Controller
Necessary

Keywords

  • Analysis
  • Approximation error estimates
  • Fuzzy inference systems
  • KH interpolator
  • Saturation problem
  • Shepard operator
  • Trade-off between accuracy and number of rules
  • Universal approximation

ASJC Scopus subject areas

  • Statistics and Probability
  • Electrical and Electronic Engineering
  • Statistics, Probability and Uncertainty
  • Information Systems and Management
  • Computer Vision and Pattern Recognition
  • Computer Science Applications
  • Artificial Intelligence

Cite this

Notes on the approximation rate of fuzzy KH interpolators. / Tikk, D.

In: Fuzzy Sets and Systems, Vol. 138, No. 2, 01.09.2003, p. 441-453.

Research output: Contribution to journalArticle

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