Abstract: The paper is dedicated to the generalization of Matheron’s theorem about covariogram to the case where possible estimation error occurs, modelled by fuzzification of convex bodies. The classic case of identification of convex bodies does not consider the cases when input information and measurement contain error term. This is general issue when applying line segment distributions to recover covariogram and later the body itself. The authors define a body and ask what result will be for the length distribution for the given fuzzy body‎. Through this procedure the authors generalize Matheron’s theorem for this case‎. The authors extensively use fuzzy statistics and fuzzy random variables to extend convex bodies and length ‎distribution functions to the fuzzy case‎. The authors use several properties of fuzzy numbers and fuzzy calculus techniques (mainly Aumann integration)‎.The authors introduce generalized fuzzy distribution to apply them in a general setting of fuzzy convex bodies. Fuzzy convex bodies are defined by adding to the convex body and subtracting (in Hukuhara sense) from its fuzzy numbers in Rn. Then the generalization of Matheron’s theorem for a fuzzy case is derived, based on fuzzy function calculus techniques. Fuzzy convex bodies can be seen as a collection of convex bodies. The authors introduced fuzzy covariogram based on fuzzy convex bodies. ‎

Keywords: Еstimation error, V-lines, Gaussian field, Aumann integration, Integral geometry, Fuzzy covariogram, Fuzzy distribution, Сonvex body, Matheron’s theorem, Hukuhara Differentiability

Abstract: The subject of research is the software development process of automated control systems. The object of study is the development of user interfaces for control automation software. The generally recognized prospective direction for increasing the efficiency of organizational and technical systems is the automation of their management, which ensures increased efficiency and validity of decisions made. A significant impact on the effectiveness of any automated system is provided by its software. This primarily relates to application software. Application development is fraught with certain difficulties, including those associated with the creation of user interfaces. The analysis of development practice shows the presence of a number of problems in this area, determined by the fact that this problem is at the junction of scientific disciplines: control theory, ergonomics, technical aesthetics and psychology. During the study, general scientific methods of analysis and synthesis were used.The authors analyzes the factors affecting the efficiency of user interface development. Based on this analysis, suggestions for solving the problem are synthesized based on the use of standardization, unification and prototyping tools.The analysis showed that for the development conditions of application software for automated control systems, the last of the listed approaches provides the greatest efficiency, namely, the use of specialized prototyping systems. It is proposed to finalize the normative documentation specifying the development of automated control systems for the mandatory stage of prototyping user interfaces in the structure of the process of creating such systems

Keywords: program life cycle, prototyping, layout creation, standardization and unification, interface development, user interface, control automation, software development, approbation stage, decision support

Abstract: The object of study is the volumetric rendering method based on three-dimensional textures and functionally defined surfaces in an interactive mode using graphic accelerators. A hierarchical approach to the representation of textures in memory and a method for managing large arrays of voxels are proposed. The hierarchical structure has a compact texture description using data homogeneity and the importance of information to reduce the required memory and computation speed. The method is based on effective texture management, in which texture memory is assigned according to the degree of significance of the region and the content of voxel data. The combination of data, interpolation, and data importance determine the selected set of tree nodes. These nodes determine how the volume should be laid out and represented in the texture memory. The research method is based on analytical geometry in space, differential geometry and vector algebra, theory of interpolation and matrix theory, based on mathematical modeling and theory of computing systems. The main conclusions of the study are: the ability to visualize a large number of volumes, functionally defined objects, complex translucent volumes, including volume intersections in constructive solid-state modeling. Rendering different volumes at the same time is a more complex problem than rendering one volume, because it requires intersection and blending operations. Functionally defined surfaces are well suited for embedding external objects in volumes. Models of medical instruments and the combination of surfaces with volumetric data are necessary for virtual computer surgery.

Keywords: texels, tile technology of visualization, voxels, graphics processing units, constructive solid geometry, ray casting, volume rendering, perturbation functions, function-based surfaces, three dimensional textures

Abstract: The subject of the research is data conversion algorithms for eliminating outliers in time series. The author considers data conversion algorithms based on arithmetic mean and median, as well as combined smoothing methods like 4253Н and 3RSSH. The author considers such aspects of the topic as changing the statistical characteristics of the time series when applying transformations, and also pays attention to the issues of visual presentation of data and changing the behavior of the series when introducing outliers into the time series. When writing the work, both theoretical and empirical research methods were used: the work and software systems that affect these issues were studied, and a series of experiments was conducted. Computational experiments on processing the time series have been carried out both without emissions and with emissions for smoothing. A comparison of the results of processing time series. A software tool is proposed that allows the use of various smoothing filters. The software tool has been tested for working with various characteristics of the input data.

Keywords: outliers, smoothing by average, smoothing by median, smoothing, filter, transformation, time series transformation, information processing, 4253H filter, 3RSSH filter

Abstract: The article discusses certain issues of intellectualization of control of technical systems in the framework of a functional approach to the construction of intelligent control systems for various objects and processes based on systems engineering and complex engineering. Intellectualization of management allows you to simultaneously get all the benefits of various paradigms for considering processes of various nature, as well as emergent to show new properties of the general approach to increase the degree of controllability and efficiency of operation of technical control objects (and generally practically arbitrary control objects of a technical nature). The application of the functional approach in combination with complex equipment in the intellectual management of such objects as transport, buildings, energy, allows us to transfer their operation to a higher level of service availability, sustainability, environmental friendliness and comprehensive development of not only the control object itself, but also the hierarchy of its super-systems - municipality, region, state. The scientific novelty of the proposed approach lies in the new application of the mathematical apparatus in terms of the general theory of sets and category theory for organizing a distributed computing system in the field of intelligent buildings and managing their internal environment. An article can become the basis for novelty of a higher order in the transition from a systemic to an integrated approach. Furthermore, a systematic approach is used with the use of a simplified cybernetic "streaming" scheme of functioning of an intelligent building.

Keywords: edge computations, intellectualization, artificial intelligence, decentralization, internet of things, functional approach, smart building, management, control system, system approach