This paper proposes a hybrid approach to the design of a compact fuzzy rule-based classification system with a small number of linguistic rules. The proposed approach consists of two procedures: rule extraction from a trained neural network and rule selection by a genetic algorithm. We first describe how linguistic rules can be extracted from a multilayer feedforward neural network that has been already trained for a classification problem with many continuous attributes. In our rule extraction procedure, a linguistic input vector corresponding to the antecedent part of a linguistic rule is presented to the trained neural network, and the fuzzy output vector front the trained neural network is examined for determining the consequent part and the grade of certainty of that linguistic rule. Next we explain how a genetic algorithm can be utilized for selecting a small number of significant linguistic rules from a large number of extracted rules. Our rule selection problem has two objectives: to minimize the number of selected linguistic rules and to maximize the number of correctly classified patterns by the selected linguistic rules. A multi-objective genetic algorithm is employed for finding a set of non-dominated solutions with respect to these two objectives. Finally we illustrate our hybrid approach by computer simulations on real-world test problems.