Explicit functions of fuzzy control systems

László T. Kóczy, Michio Sugeno

Research output: Contribution to journalArticle

2 Citations (Scopus)


Fuzzy control systems have proved their applicability in many areas. Their user-friendliness and transparency certainly belong to their main advantages, and these two enable developing and tuning such controllers easily, without knowing their exact mathematical description. Nevertheless, it is of interest to know, what mathematical functions hide behind a set of fuzzy rules and an inference machine. For practical purposes it is necessary to consider real, implementable fuzzy control systems with reasonably low computational complexity. This paper discusses the problem of what types of functions are generated by realistic fuzzy control systems. In the paper the explicit formulae of the transference functions for practically important special cases are determined, controllers having rules with triangular and trapezoidal membership functions, and crisp consequents. Here we restrict our investigations to rules with a single input.

Original languageEnglish
Pages (from-to)515-535
Number of pages21
JournalInternational Journal of Uncertainty, Fuzziness and Knowlege-Based Systems
Issue number6
Publication statusPublished - Dec 1996



  • Explicit functions
  • Fuzzy controllers
  • Rational interpolation

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Information Systems
  • Artificial Intelligence

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