It is well known that beyond the fact that fuzzy systems have favorable modeling capabilities from the viewpoint of accuracy, they also have outstanding inherent interpretability possibilities, which is a rather unique property among modeling architectures and which is a strong motivation for their research and application. This paper focuses on both mentioned property types and proposes a new technique for adjusting between accuracy and interpretability in modeling systems where fuzzy rule based architectures together with evolutionary algorithms are used for knowledge extraction.First, an inconsistency problem of conventional interpretable fuzzy systems is resolved. Then, a new search space narrowing technique for evolutionary algorithms is proposed, which can be applied for constructing interpretable fuzzy rule bases. Finally, the favorable properties of this new approach will be verified experimentally by carrying out simulation runs.