In this paper, we propose a multiobjective genetic method to learn fuzzy rules and optimize fuzzy sets in Fuzzy Rule Based Classification Systems (FRBCSs) aiming at finding a balance between the accuracy and interpretability objectives. The proposed method comprises three sequential stages: Data Base definition, Rule Base Learning and Data Base Optimization. The two objectives considered are related to the accuracy and interpretability. In the rule generation phase, which adopts the iterative rule learning approach, the accuracy objective is measured by the error rate in classification and the interpretability objective is defined as the number of conditions in the rules. In the second phase, the accuracy objective is defined as the error rate and the interpretability objective is evaluated by a concept of semantic interpretability of fuzzy sets. The second and third stages have been implemented in two versions, inspired on the two well-known techniques of multiobjective optimization: Non-dominated Sorting Genetic Algorithm (NSGA-II) and Strength Pareto Evolutionary Algorithm (SPEA2). The proposed method was compared with other genetic methods that learn the rule base and optimize fuzzy sets found in the literature, and the results showed that our method performs better than the other ones, concerning the accuracy objective while maintaining similar number of rules and conditions.