Fuzzy systems and approximation

L. Kóczy, Alessandro Zorat

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

The paper covers partly the first author's plenary talk at the Fuzzy Systems '94 Workshop held in Munich, Germany, and was partly written during a visiting appointment at the Dept. of Computer and Management Science, University of Trento, Italy. The basic motivation of using fuzzy rule-based systems especially for control purposes is to deduce simple and fast approximations of the unknown or too complicated models. Fuzzy rule-based systems have become very popuar because of their transparency and easiness of tuning and modification. Recently, some results concerning the explicit functions implemented by realistic fuzzy controllers presented the class of functions that could be implemented in this way. Some parallel results, on the other hand, attempted to prove that the main advantage of using fuzzy systems was the suitability for approximation with arbitrary accuracy in their universality. The explicit formulas and some very recent theoretical results made it clear however that fuzzy systems were not really good approximators, as realistic fuzzy controllers could generate only very rough approximations of given transference functions. In connection with approximation the question can be asked, whether there is an optimal fineness/roughness of a fuzzy rule-base that controls a certain action with roughness gives minimal time complexity. As an example, a target tracking problem was chosen ("Cat and Mouse", or "Hawk and Sparrow" problem) where the antagonistic criteria of minimizing inference time by the given rule-base and minimizing action time (search for the target, with given uncertainty provided by the rule model) were examined. Under certain assumptions the solution of this optimization problem leads to nontrivial rule-base sizes. These results have also practical applicability since if a fine enough model of the system is known it is always possible to generate a rougher version of the same, by applying the model transformation technique offered by rule interpolation with α-levels.

Original languageEnglish
Pages (from-to)203-222
Number of pages20
JournalFuzzy Sets and Systems
Volume85
Issue number2
Publication statusPublished - 1997

Fingerprint

Fuzzy systems
Fuzzy Systems
Fuzzy rules
Fuzzy Rule-based Systems
Rule Base
Knowledge based systems
Approximation
Fuzzy Controller
Roughness
Rough
Surface roughness
Management science
Fuzzy Rule Base
Controllers
Target Tracking
Model Transformation
Transparency
Target tracking
Computer science
Universality

Keywords

  • Approximate reasoning
  • Control theory
  • Model transformation
  • Rule-based models
  • Target tracking
  • Time complexity minimization
  • Universal approximators

ASJC Scopus subject areas

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

Cite this

Kóczy, L., & Zorat, A. (1997). Fuzzy systems and approximation. Fuzzy Sets and Systems, 85(2), 203-222.

Fuzzy systems and approximation. / Kóczy, L.; Zorat, Alessandro.

In: Fuzzy Sets and Systems, Vol. 85, No. 2, 1997, p. 203-222.

Research output: Contribution to journalArticle

Kóczy, L & Zorat, A 1997, 'Fuzzy systems and approximation', Fuzzy Sets and Systems, vol. 85, no. 2, pp. 203-222.
Kóczy, L. ; Zorat, Alessandro. / Fuzzy systems and approximation. In: Fuzzy Sets and Systems. 1997 ; Vol. 85, No. 2. pp. 203-222.
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