Description: The description of TOPSIS-kernel method and results of its analysis is given. It is shown that it belongs to a group of methods designed to form the kernel of alternatives. In this case, the best alternative is that which is as close as possible to the best point and as far removed from the worst. However, its imperfection is the incompleteness of the comparison of alternatives, as well as the possible effect of the compensation effect on the kernel composition. In order to eliminate the influence of these imperfections on the results of the comparison of alternatives, a new method of a three-criterion Euclidean kernel is proposed which, during the formation of the nucleus, additionally takes into account the third criterion - minimizing the value of the indicator, which characterizes the distance of the alternative from the best point in the indicator with the greatest distances. For the new method, the calculated dependencies, as well as the rules for comparing alternatives, are given. The practical use of the proposed method is shown in the examples. Comparison of the results of calculations by known and new methods shows that the use of the three-criterion Euclidean method in combination with other methods can increase the validity of the developed recommendations or identify promising alternatives that were left out of the attention of other methods. This allows us to conclude that the use of the proposed method can be promising during multicriteria optimization of complex objects.
Keywords: multicriteria optimization; TOPSIS-kernel method; the method of a three-criterion Euclidean kernel; method for kernel forming