Knowledge extraction from data in the form of rules is a widespread direction in data mining area, which allows to obtain interesting relationships in data from large databases in for a human easily understandable form. This paper deals with one of the methods for extraction of rules from data which extract rules in form of a formula in considered fuzzy logic by means of artificial neural networks with special architecture. Using artificial neural networks in extraction process, above mentioned methods gain good approximation of analyzed data and thanks to special architecture allows to extract human-understandable knowledge. The method described in this paper was, however, missing any module, that is a standard part of the most of methods used for rules extraction from data, that would allow to the user subjective selection of the best ratio between accuracy and comprehensibility of the model. This is especially important feature for solving data mining tasks called searching of concepts descriptions, which allow to the user to get a good insight and understanding of the analyzed data. Thus, the main contribution of this paper is a design of such a module inspired by a similar module in methods for extraction of the so-called decision trees. Performance of this new module is illustrated on a standard dataset in two experiments.