This paper proposes the use of a multiobjective genetic algorithm to tune fuzzy partitions and t-norm parameters in Fuzzy Rule Based Classifications Systems (FRBCSs). We consider a rule base and a data base already defined and apply a multiobjective genetic algorithm to tune the database, and simultaneously search for the most appropriate t-norm to be used in the inference engine. The optimization process is designed to handle the trade-off between interpretability and accuracy. We present a comparative study which examines a number of t-norms and their influence in the quality of the non-dominated solutions found in the optimization process. The experiments showed that significant improvements can be made in the Pareto front when the most appropriate t-norm is optimized for a specific domain. The proposed algorithm is based on the well-known technique Strength Pareto Evolutionary Algorithm (SPEA2).