The article discusses current problems of forming metatheoretic foundations of modeling in the implementation of analytic hierarchy process (AHP), namely, issues of mathematical justification of the scale of judgments based on interrelated observations, pairwise comparisons of factors, criteria and alternatives, calculation of priorities and their synthesis in the final estimates. It is shown that the basic AHP rules (axioms) are directly related to the properties of partial derivatives that characterize the marginal rate of factors substitution, and to the Euler differential equation for homogeneous functions of many variables. At the metatheoretic level, these relationships are due to the procedures of fibering spaces and sets over elements of bundle bases with different contents. The AHP methodology is based on bundles of numerical sets, tangent bundles over manifolds, and knowledge bundles on system theories, which provides the universality of its application. Mathematical analysis of AHP procedures highlights the requirement of linearity of the research space and the need to linearize indicators at the beginning of data processing with a further transition from the initial absolute indicators to relative ones in order to form a local coordinate system of the tangent fiber (cluster) as local, linear, metric, and bounded space. The Euler equation relates the values of the coordinates of the local space of the tangent fiber in the form of metric dependencies as linear and nonlinear estimation functions known in AHP. To determine the preference scale at different levels of formalization, natural and integer numbers, rational numbers, real and hyperreal numbers of standard and nonstandard analysis are used. It is determined the restriction in AHP procedures, when having a matrix of paired evaluation and not knowing the type of ranking function, it is possible to calculate priorities and choose the desired solution. The calculated priorities are the relative factors sensitivities of the evaluation functions, and their ratios are the rates of substitution of the considered factors with unit values. Equations are derived for the synthesis of evaluation of the global priority based on local priorities across all criteria. The final evaluation function can be represented as a product of vectors and comparison matrices of different hierarchical levels (polylinear form).

The task of the regional management system is to ensure the improvement of the quality of life of the living population by using man-made systems of various levels of complexity, which are created to meet certain needs determined by interests. The concentration of industrial facilities and the complexity of technological processes in them has created safety problems and increased risk of man-made disasters. In this regard, the problem of safety, quality of life, etc. should be considered in the context of the interests of using man-made systems. Objective: to develop an approach to managing regional development based on the concept of "acceptable" risk, while complying with the mandatory requirement to ensure technological safety and quality of life. A study of the problem of decision-making in active self-organizing systems in which people's motivation generates endogenous goals of functioning is performed. Research methods: General methodology and methods of system analysis, analytical modeling methods of the theory of active systems. Results: an approach is proposed for assessing the quality of life, the level of security in the region and studying emerging trends based on the use of active methods and information technologies. It is shown that the basis of their construction is self-organizing expert environments based on modern network and telecommunication technologies. A mathematical formulation and model for making coordinated decisions in the problem of technogenic safety management is developed. In contrast to the known approaches, it is proposed to use additional channels for obtaining information from network expert environments to form representations of the governing body about the state of the control object. A conceptual model of the mechanism of self-organization of such environments is developed.

A robotic complex should be considered as a cyber-physical object, which is an information-related set of physical components, on-Board measurement systems, on-Board Executive systems, on-Board computer system, where control algorithms are implemented, and a control point with an information-control field. Such an object must have the property of self-sufficient behavior that guarantees the fulfillment of a certain mission. The requirement to intellectualize behavior makes us reconsider the logical and mathematical abstractions that are the basis for building their onboard control systems. The problem of developing such systems based on pattern theory is relevant. It is shown that this ensures the transfer of effective experience and ensures the compatibility of the theological approach and the approach based on cause-and-effect relationships. Problems of identification and construction of pattern models are considered. It is proposed to use four information processing positions for this purpose, and a method of logical inference on patterns is developed.

The development of digital technologies is changing the properties of power supply systems and blurring the line between power producers and consumers. This study presents the method of the cost of electricity formation in the regional power system, which serves as a component of the approach to assessing the impact of intelligent systems development on the demand for electricity in the region. Determining the cost of electricity in the system is essentially a matter of the consistent alignment of the required amount of electricity consumption with the capabilities of producers seeking to achieve their best economic performance. Each producer is described as an optimization model, which is a standalone agent in a multi-agent power system model.

The reliable operation of the electric power systems (EPSs) depends on the quality of data provided by SCADA and WAMS, which are part of the information and communication infrastructure of cyber-physical EPS. Increasing threats to cyber security of EPS indicate the need to develop data analysis methods capable to take into account the effects of cyberattacks on systems for collecting, transmitting and processing the information. The findings of the studies have shown the impact of cyberattacks on the quality of data. The interdependence between the violation of cybersecurity properties and the low quality of data is revealed. The paper proposes an algorithm for quality assessment of SCADA and WAMS data, taking into account the cybersecurity properties of information and communication infrastructure of EPS

As part of this article, a method for ensuring the reliability of the operation of complex electrical equipment in transport is presented. The method consists in developing an intelligent diagnosis system for industrial frequency converters that are part of frequency-controlled electric drives. The authors proposed a procedure for obtaining the optimal logical algorithm for diagnosis of this equipment and performed a software implementation of this procedure. The desired algorithm is obtained. It determines the structure of the knowledge base of the expert system for diagnosis of industrial frequency converters. The correctness and efficiency of the expert system, implemented in accordance with the specified structure, is confirmed in practice.

The paper proposes the development of a system of interrelated ontologies intended for the formalized description and harmonizing of terminology of different subject areas-energy and ecology when performing research on the harmful impact of energy facilities on the environment. The work is carried out within the framework of the RFBR project "Methods of building an ontological knowledge space for intelligent decision-making support in the energy sector and environment, in terms of the quality of life". Ontological engineering of the subject area of research is performed. The methodological approaches used in the study of the problem of anthropogenic impact of energy facilities and the conduct of relevant quantitative assessments are considered. To systematize environmental assessments and establish relationships between the main indicators describing the impact of energy activity on the elements of the environment, semantic methods are proposed, in particular ontological engineering of the subject area. The ontological approach systematizes the used basic terminology and allows you to visualize the relationships between elements of the natural environment, energy objects and their characteristics, impact factors, and also allows you to build a sequence of research and systematize the methodological support used to assess the impact of energy on the environment.

The article is devoted to issues arising in connection with the problem of measuring the characteristics of languages and programming systems that affect the complexity of software development and the productivity of software applications. Paradigmatic models of languages and programming systems can be useful in systematizing programming languages, assessing their similarities and differences, which allows us to build concise definitions regarding such models. This makes it possible to stratify the presentation of the features of the semantics of programming languages into autonomously developed components in the process of step-by-step development of experimental programming systems and the formation of schemes for studying and teaching system programming.

The role of formalization of requirements in software testing is considered in this article. The authors investigate such terms as “requirement to the software” and “testing of the software” and point out their interrelation. The analysis of the influence of low-quality requirements on software testing process is made and its results obtained show that the quality of requirements is important for all software development process. The requirements formalization is offered as a way of improvement of their quality. Several methods of formalization of requirements are considered, on each of them the conclusion is drawn on influence of the formalization on the manual and automated testing, but the considered methods offer formalization of behavior of system. The formal model has to describe the structure of data from the point of view of testing automation simplification (regarding preparation of data sets for tests). The similar model can be organized in the form of hierarchy.

Data analysis in multivariate calculations of interstate power grids expansion requires software tools with a convenient graphical interface to compare results of the optimization model solutions. This article shows the possibilities of visualization and analysis of the “ORIRES” model solutions in the formation of many different options for the initial conditions - the input parameters of the model; and technologies of the web application “ESAS” for presenting research results to a wide range of Internet users.

As a part of study of impact assessment of energy on the geoecology of the region, a Web-based information-analytical system (WIS) is being developed to support decision-making in the field of ecology and energy. One of its modules is the information subsystem (IS PEF) for calculating the amount of harmful emissions from energy facilities and visualizing calculation results. The article describes the domain ontologies used for designing the IS PEF database, and the developed database structure is described in detail. The architecture of IS PEF is presented, a detailed description of its functionality and agents, and the results of the work of IS PEF are illustrated