SIZE-REDUCTION BY INTERPOLATION IN FUZZY RULE BASES

Fuzzy control is at present still the most important area of real appl ications for fuzzy theory. It is a generalized form of expert control using fuzzy sets in the definition of vague/linguistic predicates, mod elling a system by If... then rules. In the classical approaches it is necessary that observations on the actual state of the system partly match (fire) one or several rules in the model (fired rules), and the conclusion is calculated by the evaluation of the degrees of matching and the fired rules. Interpolation helps reducing the complexity as it allows rule bases with gaps, Various interpolation approaches are sho wn. It is proposed that dense rule bases should be reduced so that onl y the minimal necessary number of rules remain still containing the es sential information in the original base, and all other rules are repl aced by the interpolation algorithm that however can recover them with a certain accuracy prescribed before reduction. The interpolation met hod used for demonstration is the Lagrange-method supplying the best f itting minimal degree polynomial, The paper concentrates on the reduct ion technique that is rather independent from the style of the interpo lation model, but cannot be given in the form of a tractable algorithm . An example is shown to illustrate possible results and difficulties with the method.