This work presents a new process for building comprehensible fuzzy systems for classification problems. Firstly, a feature selection procedure based on crisp decision trees is carried out. Secondly, strong fuzzy partitions are generated for all the selected inputs. Thirdly, a set of linguistic rules are defined combining the previously generated linguistic variables. Then, a linguistic simplification procedure guided by a novel interpretability index is applied to get a more compact and general set of rules without losing accuracy. Finally, an efficient and simple local search strategy increases the system accuracy while preserving the high interpretability. Results obtained in several benchmark classification problems are encouraging because they show the ability of the new methodology for generating highly interpretable fuzzy rule-based classifiers while yielding accuracy comparable to that achieved by other methods like neural networks and C4.5.