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Clustering is a task of grouping a set of objects in such a way that objects in the same group (called a cluster) are similar to each other and dissimilar to objects belonging to other groups (clusters). The article presents the idea of the hybrid Fuzzy Logic-Genetic Algorithm (FLGA) system that supports solving clustering problems. The Genetic Algorithm (GA) realizes the process of multi-objective optimization - it aims at optimal distribution of clusters and correctly assigns each object to a cluster. The Fuzzy Logic Controller (FLC) is used for setting the number of clusters. The FLC uses additional fuzzy logic criteria obtained from experts. Experiments show that the proposed algorithm is an efficient tool for the clustering problem. The algorithm can be also used for solving similar optimization problems.