The paper proposes a method for improving the accuracy of early detection of cyber attacks with a small impact, in which the mathematical expectation is a fraction of the total, and the pulse repetition period is quite long. Early detection of attacks against telecommunication networks is based on traffic analysis using extreme filtering. The algorithm of fuzzy logic for deciding on the results of extreme filtering is suggested. The results of an experimental evaluation of the proposed method are presented. They demonstrate that the method is sensitive even with minor effects. In order to eliminate the redundancy of the analyzed parameters, it is enough to use the standard deviation and the correlation interval for decision making. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.