This paper proposes a GA and Gradient Descent Method-based method for choosing an appropriate set of fuzzy rules for classification problems. The aim of the proposed method is to fond a minimum set of fuzzy rules that can correctly classify all training patterns. The number of inference rules and the shapes of the membership functions in the antecedent part of the fuzzy rules are determined by the genetic algorithms. The real numbers in the consequent parts of the fuzzy rules are obtained through the use of the descent method. A fitness function is used to maximize the number of correctly classified patterns, and to minimize the number of fuzzy rules. A solution obtained by the genetic algorithm is a set of fuzzy rules, and its fitness is determined by the two objectives, in a combinatorial optimization problem. In order to demonstrate the effectiveness of the proposed method, computer simulation results are shown.