Abstract: The object of studies involves intellectual algorithm for solving optimization problems. It is known that for the same type of project procedures some cases require exact solutions, while others allow for approximate solutions. For this reason the issue of managing the exactness of the approximate solutions is so topical. An approximate solution may be regarded as some sphere of dots, each of them being a possible problem solution.  It is supposed that at the early stages of solving optimization problems, it is possible to operate fuzzy ranges, while gradually narrowing the search area. The authors offer an approach, which complements the well-known algorithm of particle swarm optimization with the possibility to process fuzzy numbers with the triangular expression. The current multi-agent methods for the adaptive search for the optimization solutions are developed towards improvement of the interaction among the agents.  For example, the well-known particle swarm optimization methods (PSO) is based upon the idea of population and it models the behavior of the birds in a flock or fish in a shoal. At the same time classic bio-inspired methods for finding solutions usually operate with clear solutions. The authors have developed the  modification of the PSO algorithm thanks to performance of a number of known operations with the fuzzy numbers involving triangular expressions. The special feature of this approach is organization of the intellectual searching process  in a fuzzy solution space. Its  originality is due to the development of the method for the movement of an agent (group of agents) within the area formed with the triangular expression of fuzzy numbers. This approach allows for searching for solutions in fuzzy spaces, operating with the variables of the "close to X" type, avoiding the linguistic analysis.

Keywords: optimization, vague estimates, swarm optimization method, search area, fuzzy operations, evolutionary method, swarm optimization methods, fuzzy multitudes, adaptation, evolution method

Abstract: The study is devoted to the influence (centrality) model of a social network participant.  The object of studies involves calculations for the centrality metrics, which are based upon the shortest path lengths between the graph vertices for the social graph based upon the iterative performance of the Flajolet-Martin algorithm. The author evaluates the possibility of approximateе evaluation of closeness-centrality based on a simple example. Then, having the calculation results, teh author compares the computed values with the real closeness values, as computed by breadth-first search algorithm (BFS-Algorithm). The methodology of the study involves graph theory elements, as well as the social network analysis apparatus, which allows to compute different centrality metrics of a graph vertex. The key conclusion provides that the Flajolet-Martin algorithm is an easily adaptable tool for the approximate social graph vertex centrality evaluation related with the shortest paths, such as closeness or centrality of the disintegration, as provided for in the work so M. Jackson. In turn, it provides for the new possibilities for the process modeling for the spread of information in the social networks.

Keywords: approximation, code sequence, Flajolet-Martin algorithm, shortest path, closeness, centrality, social graph, social network, computational complexity, social network analysis

Abstract: The article is devoted to working out the constructive method of approximation the sum of independent random variables with the same distribution by Pearson curves. The summation theory was and still is one of the key parts of the theory of probability. The limiting theorems are proven within this theory, and they allow one to understand which frequencies may be used for the approximation for the sum so random values with large m. At the same time the approximation error is evaluated by the admissible error. However, in most practical cases the number of the summed values is not large, so the admissible error evaluation may not be sufficiently precise. The purpose of the study is to develop a constructive method for the approximation of the frequency function for the spread of the final sum of  the independent random values with the same frequency. The Pearson curves are then used as approximative frequencies. Such an approximation lacks the defects related to the application of limiting theorems. It is applicable for any number of summed accidental frequencies m>1. The calculated ratios for the initial moments of the final sum of independent random variables are obtained. It is shown that the parameters of the Pearson curves for the sum m of random variables are related by simple ratios with the corresponding parameters of the summed value. The solution used in order to achieve the goal is based upon the moments method. Thе author offers a recursion formula for calculating the starting moments of for the sum of independent random values, allowing to find the central moments of the sum, as well as the parameters for the Pearson curves.  It is proven that there's a dependency between the distance from the point of  The exact expression for the distance from  the point, corresponding to the distribution of the sum of the random variables in the coordinate system of Pearson parameters to the point (0, 3), corresponding to the normal distribution is found. By the distance value, one can indirectly assess the possibility of applying normal approximation. The author studies the possibility for the approximation of Pearson curves with normal distribution. An approximate formula for estimating the error in approximating the sum  of random variables by normal distribution is given. The author provides examples of approximations for the distribution of the sum of random variables are found, which are often met in statistical radio engineering tasks. The reference materials include complete formulae for the key types of Pearson curves. All the obtained results are applicable for any random variables having finite first four initial moments. The correctness of the conclusions is confirmed by numerical calculations performed in the MathCad program.

Keywords: probability measure, recursive algorithm, sum of random variables, normal distribution, moments of a random variable, density function, Pearson curve, random variable, approximation error, method of the moments

Abstract: There is currently a functional expansion within the ADS systems (automatic design systgems), allowing for the implementation of new capabilities. One of such solutions allows for the forecasting in the sphere of engineering networks, including thermal ones. The object of study is the Automatic Design System for the Engineering Networks ( ADS EN), which is based upon the intellectual components for the automatised systems. Intellectual components within the ADS are implemented via programming modules involving fuzzy logic, and they are orientated towards the use of the frame architecture databases. Functional capabilities are aimed at modeling the processes within the engineering networks, achievement of efficient energy consumption, detecting trouble zones, showing irrational arrangement of the heating units. These goals are key goals and they require primary attention, however while studying ADS EN, there turned out the need for inclusion of the screen forms achieving a number of secondary goals. These secondary features of the ADS EN include provision of the entire range of advise on the protective contour, forecasting based on situation modeling of the contour condition considering the external influences and passage of time, etc.

Keywords: inference rules, frames, intellectual components, protective contour, heat exchange, forecasting, modeling, database, engineering networks, ADS EN

Abstract: This article is devoted to the methodological aspects of the development of the digital textbook on information security. The authors analyze types of textbooks and the key requirements for their development. Special attention is paid to the study of the modern approaches to the electronic textbooks design. The practical orientation of the study imposes higher requirements for digital textbooks and laboratory materials. The article  describes the key stages of the textbook development process, as well as the tools for textbook creation.The authors used the following methods in their studies: analysis of the basic principles of the digital textbook design and synthesis for obtaining practice-oriented results.The most important effect of the study  may be found in the sphere of development and implementation of a software prototype for a digital textbook which is an efficient tool for mastering the material and obtaining practical skills on information security

Keywords: Learning Management System, distance education technology, information protection, data protection, methodological aspects, information security, eLearning, digital textbook, electronic textbook development, electronic textbook

Abstract:  The object of study involves fuzzy logical multi-criterion methods and algorithms within the support systems for the decision making. The immediate object of study involves support systems for decision making in the sphere of dependability of technical equipment systems in the situation of fuzzy information input. The purpose of the study is to provide methodological basis for the development of applied fuzzy systems for the traditional priority studies for the multiple objects in the multi-dimensional set of quantity and quality markers based upon the linguistic statements by the experts. The article provides for the methodology of development for the support system for the decision-making  in the conditions of non-precise information with the use of fuzzy theory of sets and fuzzy methods for the hierarchy analysis. The author provides detailed analysis for several aspects of the topic in question, such as application of decision-making methods for multi-criteria alternative analysis, such as the fuzzy inference and the hierarchy analysis method for fuzzy proximities. The author offers the method for ranging alternatives based upon the multi-dimensional sets of facts and criteria in the situation of fuzzy data input. The methodology of studies is based upon the formation of a model for the decision-making support system, method formalization for processing fuzzy data, algorithm development and providing for the simulation experiment for various values of managing parameters within a model. The provided methodology was implemented based upon an example of the support system for the decision-making  for the expert procedure for the evaluation of general dependability of chemical technological systems.  Implementation of fuzzy logic procedures when managing a complex of dependability markers is based upon the results of expert evaluation of four separate industrial objects within a single complicated technical system of oil and gas chemical production based upon five dependability criteria. Taking an example of the hierarchical structure for dependability of oil and gas equipment, the author offers a model and an algorithm for the evaluation for deriving weights with the use of a fuzzy pairwise comparison matrix based upon the judgment matrix. The experimental calculation results show that the fuzzy pairwise comparison method  is efficient with greater degrees of priority fuzziness 50 to 75 percent. Efficiency of the judgment matrix depends upon the evaluation closeness or incoming linguistic values, however, it is completely dependent upon the correct formalization of data input via formation of the membership functions as well as on the formation of fuzzy rule bases. Fuzzy logical algorithms for decision making support in the sphere of managing the complex of dependability markers for the oil and gas equipment form a non-formalized part of the complex management and support systems for ensuring industrial equipment dependability. Such sub-systems allow for the preliminary evaluation of the general situation in the sphere of equipment dependability based upon the expert information.

Keywords: judgment matrix, triangular fuzzy numbers, fuzzy inference, deriving weights, ranking alternatives, decision making, judgment matrix FAHP, computer simulations, equipment dependability, fuzzy analytic hierarchy

Abstract: The article contains the studies, which are aimed at improving the precision of steganalysis in the sphere of digital image DWT. The authors analyze the causes of inaccuracy of the modern stegoanalysis methods based upon the support vectors, then they offer the directions for improving the teaching quality. In order to improve the quality of teaching support vectors machine the authors study the interrelation between the spheres of one-dimensional and two-dimensional DWT and the influence of the changes in the coefficients of the high frequency spheres of the two-dimensional DWT upon the coefficient spheres of the one-dimensional DWT.  The steganographic influence involves the change in the value of the lower meaning bit coefficients of the DWT. Considering the study results the authors develop an original method, guaranteeing greater precision in the sphere of finding incorporated information in the high frequency areas of the two-dimensional DWT image.  In order to prove the precision of the original method, the authors compare it with some modern steganalysis methods. Experimental results of a comparative study prove that the original method provides for greater precision (generally 10-15% higher than other evaluated methods) when detecting the fact of steganographic influence in high frequency areas of HL and LH of the two-dimensional DWT. The original method also provides for the same precision in the high frequency HH area, as do other modern methods evaluated in this article.

Keywords: DVT, steganalysis, support vector machine , data hiding, steganogram, efficiency of steganalysis, machine learning , passive attack, binary classification, steganography