Genetic algorithms (GA's) are powerful stochastic search algorithms for general problem solving. Their effectiveness as a tool for evolving other systems has been early identified and has gained increasing research interest. Fuzzy systems may strongly benefit from GA's since they involve a quite large number of parameters that need to be tuned for the system to achieve the required performance. Such parameters include (but are not limited to) the definition of the fuzzy sets stored in the fuzzy rule base. The parameter tuning process becomes more important for the cases where the fuzzy system is meant to be used for function approximation. The evolution of a fuzzy system via GA's involves stochastic varying of the parameters defining the fuzzy sets. It is, thus, important for the "robustness" of the overall process that these parameters are appropriately defined. The conventional representation of fuzzy sets through their membership function values at discrete points or through the a-level set representation do not possess the required characteristics to be directly exposed to GA search. A more efficient representation scheme based on the latter is proposed and its properties are investigated. The advantages of this scheme are illustrated through the non-toy application of evolving a fuzzy system for inverse robot kinematics by the use of GA's. It is argued that the proposed fuzzy set representation possesses better properties from the stochastic search point of view.
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