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The method of the generalized interval estimations (GIE) developed by authors earlier is offered for using in scenario analysis of the theory of decision-making. GIE procedures to study problems with dependent parameters in the framework of the scenario approach are developed in addition to previous mathematical tools. An example of similar problems is the task of forecasting volumes of commercial developed reserves of ill-studied objects in dependence on prices for hydrocarbons.

The task of interrelated features selection is considered. A lot of approaches assume that feature vector is unordered set of numerical coefficients. However in some tasks features are serial measurement along some axes, for example, counts of some kind of signal. The technique of feature selection using a priori information about one-dimensional order is suggested.

In article the intellectual system of recognition of prints of fingers is offered on the basis of the combined method. The hierarchical structure of the description of algorithm guarantees very high efficiency of the offered system.

In the paper the complex-organized data structural analysis methods and the results expert correction procedures in connection with of large-scale control systems efficiency problems are described. Algorithms of such structuring were developed on the base of range data analysis methods.

Building integral (complex) indexes is considered as a problem of hierarchical ordinal classification of multiple criteria alternatives. Various ways for constructing integral (complex) indexes are compared. A new approach to ordinal classification of alternatives estimated upon many criteria with verbal scales, that uses an interactive procedure of attribute space dimension reduction, is suggested.

The paper describes the embedded method of informative feature selection, based on two-stage training scheme of neural-fuzzy classifier. The method provides the possibility of separate feature set selection for every class of data, retaining the maximal classification accuracy, which is attained by applying modified technique of classifier parameter tuning.

Partial boolean functions taking their values 0, 1 and -- with a probability equal to 1/3 are considered. The lower and upper bounds on the length of minimum DNF representation of such functions are obtained in the paper.

The paper considers analysis methods of texts in natural language. It proposes 1) the model cause-and-effect relation in Russian text; 2) application of derived relations as expert statements in the algorythm of extremal situations forecasting.

We know a lot of cases, when topological entropy of continious map determine by structure of periodic orbits. The classical result in this field is the Sharkovskiy ordering. Sharkovskiy $\left [ 6 \right ]$ enter mapping, that turn manifold of natural numbers in to ordered set as follows:
$$3 \prec 5 \prec 7 \prec 9 \prec 11 \cdots \prec 2 \cdot 3 \prec 2 \cdot 5 \prec \cdots \prec 2^{2} \cdot 3 \prec 2^{2}\cdot 5 \prec \cdots \prec 2^{3} \prec 2^{2} \prec 2 \prec 1$$

A three-stage scheme for synthesis of semimetric adjustment algorithms in data-mining problems is proposed. Within its framework algorithms designed to modify the distance between a single pair of objects at the given value are studied. These ajustment algorithms guarantee preservation of the simetric properties. The proposed adjustment procedures constructed within the three-stage scheme framework are completed within the first two stages, and in the specials case - within the first stage.

In work the spatial problem of a comuter tomography with use of tomograms which lay on system of mutually perpendicular planes with use blending approximations is solved. The offered method allows to smooth experimental data (tomograms) and has rather high accuracy. In article computing experiment for restoration of internal structure of a brain of the person with the help of operators blending approximations by Bernstein's polynoms is shown.

The materials represented in this article carry, mainly, surveying character. The aim of the paper is complete enough presentation of possibilities of mathematical apparatus of algorithmic complexity and probability for application in machine learning. Nevertheless, some new results are presented: theorems about exact compressors and decompressors, approach to determination of the moment of stopping of learning procedure on the basis of complexity analogue of the Bayes rule et al.

In this paper we propose a new approach to constructing the Delaunay Triangulationfor the case of multidimensional spaces $(d > 2)$. Analysing the modern state, it is possible to draw a conclusion, that the ideas for the existing effective algorithms developed for the case of $d ≤ 2$ are not simple to generalize on a multidimensional case, without the loss of efficiency. We offer for the solving this problem an effective algorithm that satisfies all the given requirements.