FUZZY-SYSTEMS AND APPROXIMATION

The basic motivation of using fuzzy rule-based systems especially for control purposes is to deduce simple and fast approximations of the un known or too complicated models. Fuzzy rule-based systems have become very popuar because of their transparency and easiness of tuning and m odification. Recently, some results concerning the explicit functions implemented by realistic fuzzy controllers presented the class of func tions that could be implemented in this way. Some parallel results, on the other hand, attempted to prove that the main advantage of using f uzzy systems was the suitability for approximation with arbitrary accu racy 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 gener ate only very rough approximations of given transference functions. In connection with approximation the question can be asked, whether ther e is an optimal fineness/roughness of a fuzzy rule-base that controls a certain action with roughness gives minimal time complexity. As an e xample, a target tracking problem was chosen (''Cat and Mouse'', or '' Hawk and Sparrow'' problem) where the antagonistic criteria of minimiz ing inference time by the given rule-base and minimizing action time ( search for the target, with given uncertainty provided by the rule mod el) were examined, Under certain assumptions the solution of this opti mization problem leads to nontrivial rule-base sizes. These results ha ve also practical applicability since if a fine enough model of the sy stem is known it is always possible to generate a rougher version of t he same, by applying the model transformation technique offered by rul e interpolation with alpha-levels.