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In the last few years a number of studies have focused on the design of fuzzy rule-based systems which are interpretable (i.e. simple and easy to read), while maintaining quite a high level of accuracy. Therefore, a new tendency in the fuzzy modeling that looks for a good balance between interpretability and accuracy is increasing in importance. In fact, recently multi-objective evolutionary algorithms have been applied to improve the difficult trade-off between interpretability and accuracy. In this paper, we focus both on rule learning and fuzzy memberships tuning proposing a technique based on a multi-objective genetic algorithm (MOGA) to design deep-tuned Fuzzy Rule Based Classifier Systems (FRBCSs) from examples. Our technique generates a FRBCS which includes certain operators (known as linguistic hedges or modifiers) able to improve accuracy without losses in interpretability. In our proposal the MOGA is used to learn the FRBCS and to set the operators in order to optimize both model accuracy and metrics of interpretability, compactness and transparency in a single algorithm. The resulting Multi-Objective Genetic Fuzzy System (MOGFS) is evaluated through comparative examples based on well-known data sets in the pattern classification field.