Algorithmic aspects of fuzzy control

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Fuzzy control is at present still the most important application of fuzzy theory. It is a generalized form of expert control using fuzzy sets in the definition of vague/linguistic predicates, modeling a system by If... then rules. In the classical approaches (Zadeh, Mamdani) the essential idea is that a fact (observation) known concerning the actual state of the system will match with one or several rules in the model to some positive degree, the conclusion will be calculated by the evaluation of the degree of these matches, and the matched rules themselves. In these approaches, the rules contain linguistic terms, i.e., fuzzy sets in the consequent parts, and these terms, weighted with their respective degrees of matching, will be combined in order to obtain a fuzzy conclusion-from which the crisp action is obtained by defuzzification, as e.g. the center of gravity method. This paper summarizes these classical methods and turns attention to their weak point: the computational complexity aspect. As a partial solution, the use of sparse rule bases is proposed and rule interpolation as a fitting inference engine is presented. The problem of preserving or not preserving linearity is discussed when terms in the rules are restricted to piecewise linear.

Original languageEnglish
Pages (from-to)159-219
Number of pages61
JournalInternational Journal of Approximate Reasoning
Volume12
Issue number3-4
DOIs
Publication statusPublished - 1995

Fingerprint

Fuzzy sets
Fuzzy control
Fuzzy Control
Linguistics
Inference engines
Computational complexity
Interpolation
Gravitation
Fuzzy Sets
Term
Control Sets
Defuzzification
Inference Engine
Centre of gravity
Fuzzy Theory
Rule Base
Linearity
Piecewise Linear
Predicate
Computational Complexity

Keywords

  • fuzzy control
  • hierarchical rule base
  • preservation of normality
  • preservation of piecewise linearity
  • rule interpolation

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Applied Mathematics
  • Theoretical Computer Science

Cite this

Algorithmic aspects of fuzzy control. / Kóczy, L.

In: International Journal of Approximate Reasoning, Vol. 12, No. 3-4, 1995, p. 159-219.

Research output: Contribution to journalArticle

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