A novel approach for the development of linguistically interpretable fuzzy models from data is proposed. Based on this approach a methodology for inverse and indirect adaptive fuzzy control is presented. The proposed methodology includes clustering techniques to determine rules, the minimum squares method to adjust consequents and, for a sharp tuning, the descendant gradient to adjust the modal values of sets that confirm the antecedent. The antecedent partition uses triangular sets with 0.5 interpolations. The most promissory aspect in our proposal consists in achieving a great precision without sacrificing the fuzzy system interpretability. The real-world applicability of the proposed approach is demonstrated by application to a classic benchmark in system modeling and identification (Box-Jenkins gas furnace) and to a temperature control of a food process.