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The paper discusses outlier detection algorithms used in data mining systems. Basic approaches currently used for solving this problem are considered, and their advantages and disadvantages are discussed. A new outlier detection algorithm is suggested. It is based on methods of fuzzy set theory and the use of kernel functions and possesses a number of advantages compared to the existing methods. The performance of the algorithm suggested is studied by the example of the applied problem of anomaly detection arising in computer protection systems, the so-called intrusion detection systems.