In this paper, a GA-based framework for finding membership functions suitable for fuzzy mining problems is proposed. Each individual represents a possible set of membership functions for the items and is divided into two parts, control genes and parametric genes. Control genes are encoded into binary strings and used to determine whether membership functions are active or not. Each set of membership functions for an item is encoded as parametric genes with real-number schema. Seven fitness functions are proposed, each of which is used to evaluate the goodness of the obtained membership functions and used as the evolutionary criteria in GA. Experiments are also made to show the effectiveness of the framework and to compare the seven fitness functions.