### 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 language | English |
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Pages (from-to) | 159-219 |

Number of pages | 61 |

Journal | International Journal of Approximate Reasoning |

Volume | 12 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - Jan 1 1995 |

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### Keywords

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

### ASJC Scopus subject areas

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