This paper presents a novel neuro-fuzzy inference system, called RBFuzzy, capable of knowledge extraction and generation of highly interpretable Mamdani-type fuzzy rules. RBFuzzy is a four layer neuro-fuzzy inference system that takes advantage of the functional behavior of Radial Basis Function (RBF) neurons and their relationship with fuzzy inference systems. Inputs are combined in the RBF neurons to compound the antecedents of fuzzy rules. The fuzzy rules consequents are determined by the third layer neurons where each neuron represents a Mamdani-type fuzzy output variable in the form of a linguistic term. The last layer weights each fuzzy rule and generates the crisp output. An extension of the ant-colony optimization (ACO) algorithm is used to adjust the weights of each rule in order to generate an accurate and interpretable fuzzy rule set. For benchmarking purposes some experiments with classic datasets were carried out to compare our proposal with the EFuNN neuro-fuzzy model. The RBFuzzy was also applied in a real world oil well-log database to model and forecast the Rate of Penetration (ROP) of a drill bit for a given offshore well drilling section. The obtained results show that our model can reach the same level of accuracy with fewer rules when compared to the EFuNN, which facilitates understanding the operation of the system by a human expert.