A new design scheme of a binary decision tree is proposed. In this scheme a binary decision tree is constructed by using genetic algorithm and FCM algorithm. At each node optimal or near-optimal feature subset is selected which optimizes fitness function in genetic algorithm. The fitness function is inversely proportional to classification error, balance between cluster, number of feature used. The binary strings in genetic algorithm determine the feature subset and classification results - error, balance - form fuzzy partition matrix affect reproduction of next genratin. The proposed design scheme is applied to the tire tread patterns and handwriteen alphabetic characters. Experimental results show the usefulness of the proposed scheme.