Set Theory Method Research Articles

Assessment of digital culture in sustainable university development systems

The object of this study is the processes of assessing digital culture, the purpose is to devise methodological foundations for assessing digital culture in the systems of sustainable development of universities. The problem of insufficient methodological support for assessing digital culture makes it impossible to effectively manage the sustainable development of the university. The study is based on the example of projects carried out by students at the Lviv Polytechnic National University's course ‘Fundamentals of Entrepreneurship and Business Planning Using IT’, which applies digital technologies based on sustainable development. For the expert evaluation of the digital culture of student projects, a system of indicators has been formed that comprehensively covers it (‘digital security’, ‘digital literacy’, ‘creativity in the digital environment’, ‘use of social networks and communications’, ‘innovation’, ‘digital rights and ethics’). The diversity of the indicators was agreed upon by establishing their significance and using the Saati pairwise comparison method. The substantiation of the digital culture indicators was implemented with the help of a mathematical model based on the matrix approach, using the methods of fuzzy set theory. The calculation of the significance of the digital culture indicators showed that the largest share is accounted for by the indicators ‘digital literacy’ (36 %), ‘digital rights and ethics’ (28 %), ‘digital security’ (16 %), ‘creativity in the digital environment’ (12 %). The lowest is ‘use of social networks and communications’ (4 per cent) and ‘innovation’ (4 per cent). In order to measure the level of digital culture, a pairwise comparison of the projects for each indicator was performed. On the basis of resulting estimates, the corresponding matrices of pairwise comparisons of projects were constructed, for each of which the measures of belonging of elements to a fuzzy set were established. The fuzzy sets were defined, which indicate the degree of certainty in the compliance of student projects with the indicators of digital culture. Based on the results of testing, the student project ‘MyNature’ satisfies the group of indicators of the level of digital culture by 71.2 %, ‘HealthyWay’ – by 53.5 %, ‘!!!Boooya’ – by 48.8 %. The other projects – FizMat:), Medix, and ‘Їііііisty!’ – 36.3 %, 36.4 %, and 42.1 %, respectively

Optimization Problem for Probabilistic Time Intervals of Quasi-Deterministic Output and Self-Similar Input Data Packet Flow in Telecommunication Networks

Introduction. When managing traffic at the packet level in modern telecommunication networks, it is proposed to use methods that transform a self-similar stochastic packet flow into a quasi-deterministic one. To do this, it is required to apply complex probabilistic laws of distribution of self-similar flows. From the literature, methods of balancing the network load are known, which, with the problem indicated above, contribute to increasing the efficiency of telecommunication systems. However, there is no strictly mathematical solution to find out the optimal probabilistic characteristics of the output flow, based on the input flow. The presented research is intended to fill this gap. Its objective is to create a method for determining the optimal probabilistic characteristics of the packet flow, using the minimum value of the proximity measure of the self-similar input and quasi-deterministic output flows.Materials and Methods. To solve the research problem, the parameters of the output flow distribution were selected so that the approximation function was close to 𝛿𝛿-function. The Kullback-Leibler divergence was used as a proximity measure of the input and output distributions of time intervals. Methods of set theory, metric spaces, multidimensional optimization, and teletraffic were used. The solution algorithm included minimization of the Kullback-Leibler divergence and the limit passage to 𝛿𝛿-function.Results. A probability distribution is shown — an approximation of 𝛿𝛿-function, which maintains the equality of time intervals of a quasi-deterministic output packet flow. A method for transforming a self-similar input flow into a quasideterministic output flow is presented. The Kullback–Leibler divergence was used as a measure of their proximity. The minimum of the Kullback-Leibler divergence between the input and output flows with a normal distribution was achieved in the case of equality of the mathematical expectations of these flows. Using the passage to the limit, it has been established that time interval T between packets of the quasi-deterministic output flow must be equal to the mathematical expectation of the time intervals between packets of the input self-similar flow. To obtain a quasi-deterministic flow, the passage to the limit is performed for the found value of the mathematical expectation at σ → 0.Discussion and Conclusion. The application of this method will reduce the negative impact of self-similarity of network traffic on the efficiency of the telecommunication network. The use of quasi-deterministic flows makes it possible to predict the load of network resources, which can be the basis for improving the quality of user service. Two difficulties associated with calculations and practical implementation of the solution are eliminated. Firstly, it is difficult to use the delta function as a function of the output flow distribution density. Secondly, there are no ideal deterministic flows in the operation of telecommunication networks. The proposed method has great potential in the design and optimization of communication networks.

INTELLECTUAL SUPPORT OF THE PROCESSES OF SEARCHING AND EXTRACTION OF PRECEDENTS IN CASE-BASED REASONING APPROACH

Context. The situational approach is based on the real-time decision-making methods for solving current problem situation. An effective tool for implementing the concept of a situational approach is an experience-based technique that widely known as сasebased reasoning approach. Reasoning by precedents allows solving new (latest) problems using knowledge and accumulated experience of previously solved problems. Since cases (precedents) describing a scenario for solving a certain problem situation are stored in the case library, their search and retrieval directly determine the system response time. In these conditions, there is a need to find ways of solving an actual scientific and practical problem aimed at optimizing case searching and extracting processes. The object of the paper is the processes of searching and extracting of cases from the case library. Objective. The purpose of the article is to improve the process of cases searching in CBR approach by narrowing down the set of cases permissible for solving the current target situation, and excluding from further analysis such cases that do not correspond to the given set of parameters of the target situation. Method. The research methodology is based on the application of rough set theory methods to improve the decision-making procedure based on reasoning by precedents. The proposed two-stage procedure for narrowing the initial set of cases involves preliminary filtering of precedents whose parameter values belong to the given neighborhoods of the corresponding parameters of the target situation at the first stage, and additional narrowing of the obtained subset of cases by the methods of rough set theory at the second stage. The determination of the R-lower and R-upper approximations of a given target set of cases within the notation of rough set theory allows dividing (segmenting) the original set of cases available for solving the current problem stored in case library into three subgroups (segments). The search for prototype solutions can be performed among a selected subset of cases that can be accurately classified as belonging to a given target set; which with some degree of probability can be attributed to the given target set, or within the framework of the union of these two subsets. The third subset contains cases that definitely do not belong to the given target set and can be excluded from further consideration. Results. The problem of presentation and derivation of knowledge based on precedents has been considered. The procedure for searching for precedents in case library has been improved in order to reduce the system response time required to find the solution closest to the current problem situation by narrowing the initial set of cases. Conclusions. The case-based reasoning approach is received the further development by segmenting cases in terms of their belonging to a given target set of precedents uses methods of the rough set theory, then the search for cases is carried out within a given segment. The proposed approach, in contrast to the classic CBR framework, uses additional knowledge derived from obtained case segment; allows modeling the uncertainty regarding the belonging / non-belonging of a case to a given target set; removing from further consideration cases that do not correspond to a given target set.

Web search results processing in an information support system for decision-making processes

Objectives. The problem of the web search results processing in an information support system for decision[1]making is solved in order to create and correct a meaningful description of a problem situation. An approach to solving this problem is proposed based on the use of thematic text corpora (collections of texts on a specific topic) as knowledge about the subject area, as well as a knowledge representation model based on verbal associations. When solving problems of the web search results processing in a decision-making information support system, five main goals are pursued: the formation of an extended description of a problem situation, the synthesis of a search prescription, an Internet search for information about decisions made, the synthesis of a retelling of the information found, and an assessment of the quality of the found analogues of the decisions made.Methods. Methods of set theory, graph theory and mathematical linguistics are used.Results. A mathematical model has been developed for the web search results processing in an information support system for decision making. The concepts of verbal association of words and texts, as well as pragmatically complete lexical structure, are formalized. The proven properties of such structures provide algorithmization of information processes in the model under consideration.Conclusion. The approach to modeling is based on the formalization of the concepts of the informativeness of words, sentences, texts and the informativeness of verbal associations between them. As an implementation of the model proposed in the article, algorithms have been developed for creating a dictionary of pragmatically complete lexical structures, creating structural-lexical templates for sentences, texts and subject areas, synthesizing a brief retelling of the information found, and assessing the quality of the found analogues of the decisions made.

Critical Analysis of External and Internal Structure-Forming Factors Affecting the Quality Indicators of Asphalt Concrete Based on The Industrial Wastes

The article is devoted to the issue of increasing the life cycle of automobile roads as transport infrastructure facilities through designing of asphalt concrete mixtures, taking into account the structure-forming factors that determine the effectiveness of road transport construction. The purpose of the study is to analyze the structure-forming factors affecting the quality indicators of road asphalt concrete based on the industrial wastes. To achieve this purpose, the methods of literary-patent review and set theory were used. The conducted literature review showed possible options for using blast furnace slag and microsilica in road transport construction. Based on its results, subsets of internal and external factors affecting the physical and mechanical characteristics of asphalt concrete were identified. The authors established a set of structure-forming factors that make it possible to select and describe with the help of set theory those factors that need to be taken into account and optimized for a given variant of design of asphalt concrete mixture, for example, when using industrial wastes in its composition. The most important factors determining the quality indicators of asphalt concrete for automobile roads when using blast furnace slag and microsilica in its composition were determined.

IMPROVING THE INTERACTION OF THE TYPES OF TRUCK TRANSPORTATION AT THE "NIBULON" TERMINAL IN KREMENCHUTS WHEN TRANSPORTING GRAIN LOADS

Purpose. Russia's full-scale military aggression against Ukraine significantly disrupted logistics chains, including those that ensured the export of grain. The classic transportation system at “Niboulon” terminals is focused on transshipment of grain from road to river transport with subsequent transportation to foreign countries by “river-sea” vessels. To ensure the full operation of grain terminals after disruption of water transport in the water area of the Dnipro River, it is advisable to conduct a study on the shipment of grain products to alternative modes of transport (road, rail). Accordingly, the purpose of the research is to improve the interaction of types of freight transport at the Kremenchug terminal “Nibullon” in today's conditions when the work of water transport is blocked. The classic operation scheme of the "Nibulon" grain terminal was analyzed. Scientific methods and a method of improving the interaction of different types of transport in the terminal during grain transshipment are substantiated, the determination of the optimal mass of products transferred from the terminal to the main transport is proposed. Methods. An analysis of literary sources was carried out, which made it possible to establish the peculiarities of grain transportation. Methods of set theory, theory of algorithms, theory of transport processes and systems, theory of systems are used. It was established that the optimal mass of products transferred from the terminal to the main transport depends on the average daily number of cars, the gross weight of the car, the traction characteristics of the shunting locomotive and the distance between the terminal and the sorting station of the main transport. Scientific novelty. The scientific novelty obtained as a result of the research to which the article is devoted is the method of determining the average daily number of vehicles (cars, wagons, ships) arriving at the Kremenchug terminal "Nibulon", which depends on the average annual cargo turnover for each mode of transport, the weight of the cargo in the vehicle and the number of working days per year of each type. Practical significance. The mathematical expectation of the optimal mass of grain products transferred from the terminal to the main railway transport is established. In further research, the obtained results will be used as initial data for modeling the operation of grain terminals located along the Dnipro riverbed, and in the future - in the direction of the Black Sea ports of Ukraine.

ЭФФЕКТИВНОСТЬ АВТОМАТИЗИРОВАННОГО УПРАВЛЕНИЯ ТРАНСПОРТНЫМИ СРЕДСТВАМИ В ТРАМВАЙНЫХ СИСТЕМАХ

The intellectualization of water transport is accompanied by an expansion of the landscape of threats to transport security, caused by the characteristics and weaknesses of the technologies being introduced, which are the convergence of information and telecommunication technologies, automated and automatic control technologies and artificial intelligence. The peculiarity of these technologies is working with large volumes of information. Violation of the security of information processed in intelligent systems of water transport (illegal access, modification, deletion and similar unauthorized influence) causes a violation of transport security and, as a consequence, the security of critical information infrastructure and the country’s critical infrastructure, national security. Convergent technologies used in intelligent transport systems are characterized by multiple and poorly formalized manifestations of the consequences of threats. The article presents a model for assessing the risks of information security of intelligent water transport systems, based on the methods of the theory of fuzzy sets and fuzzy logic, the use of which makes it possible to take into account the above-mentioned features of the technologies being implemented. The hierarchical structure of the model and the use of fuzzy set theory and fuzzy logic methods make it possible to adapt the model to various risk criteria, types of input data and the level of detail of risk analysis. For the presented model, a methodology for assessing information security risks has been developed and an example of risk calculation is given. The developed model and methodology are intended to build an information security risk management system for autonomous shipping, implementing technologies of hybrid (augmented, extended) intelligence, providing for the use of artificial intelligence controlled by people.

НЕЧЕТКАЯ СИСТЕМА ОЦЕНКИ РИСКОВ ИНФОРМАЦИОННОЙ БЕЗОПАСНОСТИ ИНТЕЛЛЕКТУАЛЬНЫХ СИСТЕМ ВОДНОГО ТРАНСПОРТА

The intellectualization of water transport is accompanied by an expansion of the landscape of threats to transport security, caused by the characteristics and weaknesses of the technologies being introduced, which are the convergence of information and telecommunication technologies, automated and automatic control technologies and artificial intelligence. The peculiarity of these technologies is working with large volumes of information. Violation of the security of information processed in intelligent systems of water transport (illegal access, modification, deletion and similar unauthorized influence) causes a violation of transport security and, as a consequence, the security of critical information infrastructure and the country’s critical infrastructure, national security. Convergent technologies used in intelligent transport systems are characterized by multiple and poorly formalized manifestations of the consequences of threats. The article presents a model for assessing the risks of information security of intelligent water transport systems, based on the methods of the theory of fuzzy sets and fuzzy logic, the use of which makes it possible to take into account the above-mentioned features of the technologies being implemented. The hierarchical structure of the model and the use of fuzzy set theory and fuzzy logic methods make it possible to adapt the model to various risk criteria, types of input data and the level of detail of risk analysis. For the presented model, a methodology for assessing information security risks has been developed and an example of risk calculation is given. The developed model and methodology are intended to build an information security risk management system for autonomous shipping, implementing technologies of hybrid (augmented, extended) intelligence, providing for the use of artificial intelligence controlled by people.

Fuzzy adaptive containment control for fractional‐order heterogeneous nonlinear multi‐agent systems with mixed time‐varying delays

SummaryThis study investigates the issue of containment control (CC) of multi‐agent systems (MASs) that are heterogeneous, nonlinear, and fractional‐order while taking practical scenarios into account, such as uncertainties, unknown nonlinearities, time‐varying state delays, and distributed time‐varying delays. A fully distributed adaptive observer is created for each follower in accordance with the communication topology information among agents. This observer is designed to estimate the convex combination information of the leaders. The approach utilizes interval type‐2 fuzzy set theory and adaptive methods to design a distributed containment control strategy that only uses the self‐information of the followers and neighbor nodes' information. Sufficient conditions for implementing containment control are given. A new Lyapunov‐Krasovskii functional (LKF) is constructed, and the stability of the system with feedback loop is proven using fractional‐order theory and inequality methods. Lastly, a simulation example is presented to illustrate the efficacy of the proposed approach.

Searching for complexity. Application of the set-theory to the analysis of urban mobility readiness index

Numerous initiatives have been developed to monitor the sustainability performance of cities, with rankings and indicators emerging as crucial tools for understanding complex urban phenomena. However, these indices require deeper analytical methods to fully interpret their results. This study highlights the application of Set-Theory methods, specifically Qualitative Comparative Analysis with process-tracing in analyzing the Urban Mobility Readiness Index (UMR) across 60 cities for 2021 and 2022. Our primary achievement is the demonstration of Set-Theory´s ability to unravel the causal complexity in urban dynamics. We find that urban mobility readiness and its negation are not determined by singular conditions but by a combination of conditions. Necessary conditions such as infrastructure and socioeconomic factors have been identified, which are critical for achieving a higher level of readiness in the UMR, and its negation. Cities lacking these conditions are less likely to reach the desired level for sustainable development. Additionally, we reveal that certain conditions serve beyond scope definitions, actively triggering causal mechanisms for both readiness and its negation. This insight underscores the multifaceted nature of urban sustainability, guiding cities towards effective strategies for sustainable development. Our study thus contributes a nuanced understanding of urban mobility, essential for policymakers and urban planners.

АНАЛИЗ ОТРАСЛЕВОЙ АНИЗОТРОПИИ В МЕЖДУНАРОДНОЙ ЛЕГКОЙ ПРОМЫШЛЕННОСТИ

In the interests of strategic positioning of enterprises and in order to ensure conditions for their effective competition, it is necessary to clarify the enterprise’s place on the industry map in the “resilience – efficiency” coordinates. Such clarification is possible when studying a new property of sectoral anisotropy. Using the example of international light industry, we show that all enterprises in the industry can be divided into three large classes: “pioneers”, “miners” and “convoys”, with each class dominating each other in the Pareto sense. The current positioning of the enterprise involves clarifying the layer in which it is located, as well as the list of its closest competitors, highlighting the strengths and weaknesses of the company under study. During anisotropy analysis, methods of fuzzy set theory and soft computing are used, including obtaining an industry stability zone in the form of an R-lens.

БАЗОВЫЕ ТЕХНОЛОГИИ, РЕКОМЕНДУЕМЫЕ ДЛЯ ИСПОЛЬЗОВАНИЯ В ХОДЕ СТРАТЕГИЧЕСКОГО ПЛАНИРОВАНИЯ ПРОМЫШЛЕННЫХ ПРЕДПРИЯТИЙ

Strategic planning of industrial enterprises is carried out in conditions of significant infor-mation uncertainty regarding the external conditions of the enterprise's functioning and its positioning in its industry environment, in order to ensure effective competition. Therefore, it is necessary to develop new approaches to strategic planning of enterprises in conditions of uncertainty. The aim of the study is to present a number of new basic technologies that are advisable to use in the course of strategic planning of industrial enterprises based on the application of fuzzy set theory and soft computing. The following basic technologies are analyzed in the article: analysis of industry anisotropy; application of matrix aggregate calculator (MAС) technology to assess economic resilience; fuzzy numerical interpretation of the «scarlet» and «blue» market oceans; strategic positioning of the enterprise in the «resili-ence – efficiency» space; predictive modeling of activity levels based on probability processes; assessment of the risk of non-fulfillment of the plan according to strategic indicators. All the basic technologies described in the work are recommended for implementation in standard processes of strategic planning and forecasting of industrial enterprises. Such an application will ensure that the planning procedure is consistent with the expressed strategic goals of the business owner. The study is original, it uses methods of fuzzy set theory and soft computing. A new technology for analyzing industry anisotropy based on R-lens clustering is proposed, as well as a method for predicting performance levels based on probability processes.

АНАЛИЗ ОТРАСЛЕВОЙ АНИЗОТРОПИИ В МЕЖДУНАРОДНОМ МАШИНОСТРОЕНИИ

Industry anisotropy, including in international mechanical engineering, is a poorly studied property of the industry system. At the same time, it is anisotropy that determines the nature of intra-industry competition. The aim of the study is to propose an approach for the analysis of industry anisotropy in the coordinate space “ resilience – efficiency” where a two–petalled R-lens will be formed, which is then clustered, with the allocation of seven reference clusters. The inclusion of such enterprise image points in one of the six selected clusters allows companies from the industry to assess their location, nearest competitors, risks, and methods of repositioning (if applicable). The study is original, it uses methods of fuzzy set theory and soft computing. A new technology for analyzing industry anisotropy based on clustering of R-lenses is proposed.

THE APPLICATION OF FUZZY SETS THEORY IN THE METHODOLOGICAL APPROACH TO ASSESSING PERSONNEL RISKS OF AN ENTERPRISE

The main idea of this paper is the substantiation of the methodological approach to the assessment of personnel risks of enterprises based on the application of the fuzzy logic apparatus in order to identify the problems of personnel risk management and provide appropriate recommendations for their solution. The methodological basis of the study is the classic provisions and fundamental works of foreign and domestic scientists, statistical data, the results of our research into the problems of assessing personnel risks of enterprises. The methods of fuzzy set theory, comparative analysis, scientific abstraction, generalization of scientific experience of modern theoretical research, systemcomplex approach were used. The study proposed a methodological approach to assessing the level of personnel risks of an enterprise; numerical experiments were conducted on the basis of a group of construction equipment manufacturers. Analysis of the results of assessing the level of personnel risks of enterprises made it possible to identify the problems of managing personnel risks at enterprises Statement of a mathematical problem: the work considers hierarchical fuzzy data, namely: four groups of indicators for assessing the level of personnel risks (quantitative composition – F1, state of qualifications and intellectual potential – F2, staff turnover – F3, motivational system – F4), each of the indicators has a different number of fuzzy coefficients (there are twelve of them in the current work – vi , i=1÷12). Indicators are functions of fuzzy coefficients: F1 = r(v1, v2, v3); F2 = g(v4,v5, v6, v7); F3 = h(v8, v9, v10,); F4=q(v11, v12). As an output variable, there is a functional – an integrated indicator Int = f(F1, F2, F3, F4) of the personnel risk level, which, in turn, is also a fuzzy value. Here, the functions r, g, h, q, f are unknown functions of the given variables. We have expert evaluations of the change in all input data; as a rule, they vary within three terms: Low (I), Medium (G), High (E). Formalized information on each variable can be written as , then for a group of indicators we have: . Using a fuzzy system and performing calculations with its help requires the system to have the following structural elements: membership functions of input and output variables, a rule base, and an output mechanism. These structural elements are the components that will be built when designing a fuzzy system. The built mathematical model and the method of its formalization on the basis of FST make it possible to estimate the level of personnel risk at the enterprise, which enables further substantiation of a set of measures to increase the efficiency of its use. The constructed system of fuzzy logical inference can be considered intelligent as it uses elements of computational intelligence, in particular, the theory of fuzzy sets. The proposed methodological approach to assessing the level of personnel risks of enterprises based on the apparatus of fuzzy logic allows, in contrast to existing ones, to integrate the consideration of both qualitative and quantitative indicators when assessing the level of personnel risks and personnel movement indicators and to significantly increase the efficiency of decision-making under conditions of uncertainty and reduce costs in the event of adverse situations.

ДІАГНОСТИКА РИЗИКУ БАНКРУТСТВА ПІДПРИЄМСТВА: МЕТОДОЛОГІЧНИЙ ТА ПРАКТИЧНИЙ АСПЕКТИ

Domestic enterprises have been working under martial law conditions for the second year, what has led to a sharp weakening of the Ukrainian’s economy. All this has a destructive influence on the work of enterprises and escalations the hazardousness of their activities. Risk management and, consequently, ensuring financial security are key tasks of the risk management system at the enterprise, since financial risks have a destructive effect on both its development and the country's economy as a whole. The purpose of the scientific article is to conduct a comparative analysis of methodological approaches to assessing the risk of bankruptcy of an enterprise, based on discriminant analysis and the theory of fuzzy sets, and to determine their effectiveness. Method or methodology of the research. The methodological base of the study were the works of national researchers who expose the practical aspects of the analysis of the risk of insolvency of the enterprise. Methods of comparative analysis, discriminant analysis and fuzzy set theory were used in the study. Results of the study. In the study, the domestic and foreign discriminant models for assessing the risk of bankruptcy of an enterprise were analyzed. The authors proposed to use the theory of fuzzy sets to analyze the risk of enterprise insolvency. Based on the results of the comparative analysis, the effectiveness of the proposed methodical approach to assessing the risk of bankruptcy of the enterprise was determined. Scope of practical application of the results. The obtained results have important practical value and can be used by enterprise managers to improve the risk management strategy. Conclusions. In the conditions of an unstable environment, the use of models based on fuzzy logic becomes appropriate. This makes it possible to form an adaptive model that takes into account the specifics of the country, industry and individual enterprise. The use of a model based on a fuzzy-multiple approach will contribute to obtaining reasonable data on the level of financial security of the enterprise and increase the effectiveness of the formation of strategies for managing business entities in conditions of uncertainty and risk.

Peculiarities of justification of a representative set of requirements for intelligent vehicles

Introduction (problem statement and relevance). The key task of ensuring confidence in motor vehicles with elements of artificial intelligence (AI vehicles) is forming of a representative set of requirements compliance with which ensures the necessary guarantees of AI vehicle functionality and safety.Absence of generally accepted and statutory approaches to justification of the requirements content constrains application of artificial intelligence technologies in motor vehicles and, respectively, impedes creation and improvement of highly automated vehicles. The purpose of the study is to analyze the principles of forming of a representative set of requirements for AI vehicles. Methodology and research methods. The paper uses the principles of qualimetry adapted for the information systems based on machine learning algorithms, it also uses the methods of system analysis, mathematical statistics, combinatorics, set theory and propositional calculus principles. Scientific novelty and results. The approach is formulated to justify the statistically representative set of requirements for AI vehicles, and that allows adequate and accurate assessment of compliance of these systems with the expectations of the customers, developers, suppliers, regulatory authorities and other stakeholders. The structure of such expectations and priorities has been considered taking into account creation and application of AI systems. It is shown that stakeholder requirements apply to both the AI vehicle life cycle processes and the systems per se taking into account particular (given) conditions of their operation. Different significant factors, which variability sets the intended operating conditions, have been considered and conditions of representativeness of test data sets used for AI vehicle trials have been formulated. It is shown that, in order to reduce the dimensionality of space of the intended operating conditions, AI vehicles can be decomposed into separate functional subsystems and then into individual AI algorithms. The ways to perform such functional decomposition have been suggested. Practical significance.The principles of justification of the requirements content offered in the paper can be used in certification testing of artificial intelligence algorithms that are used in highly automated vehicles.

STRATEGIC MANAGEMENT OF THE ECONOMIC SUSTAINABILITY OF A COMPANY IN THE PARADIGM OF FUZZY LOGIC

The theory of economic resilience is actively developing in Russian and foreign scientific studies. Most of them lack a comprehensive approach to the issue of resilience, the ability to assess the behaviour of economic systems under conditions of uncertainty and to offer optimal solutions to ensure the resilience of economic systems (enterprises, industries) in difficult conditions. It is necessary to develop optimal algorithms for managing economic systems under adverse effects (AE) of a natural, technological, or military nature. The article describes the method of managing economic resilience in three-dimensional spaces: ‘stability – efficiency’, ‘risk – efficiency’, and ‘chance – efficiency’. The results of three approaches to resilience management are compared.It can be tentatively assumed that the stability of an individual company is ensured if the economic stability index RI exceeds the level of 0.6 and the return on equity is at least 20% per annum. More generally, in the ‘resilience – efficiency’ space, the domain of stable states of the enterprise is described by a fuzzy parabolic R lens. In the ‘risk – efficiency’ and ‘chance – efficiency’ domains, the space of optimal solutions is represented by a set of non-dominated Pareto alternatives, united by a fuzzy parabolic efficient bound of the solution portfolio set. The organisation can control its level of economic resilience within multiple representations and act according to a predetermined plan in the event of a temporary loss of resilience. The research is original, using the methods of fuzzy set theory and soft computing. A technology has been proposed to ensure the economic resilience of systems operating in difficult conditions (e.g. in new regions of the Russian Federation where large-scale military actions are taking place). This makes the study highly relevant and practical.

Development of the fuzzy sets theory: weak operations and extension principles

The paper considers the problems that arise when using the theory of fuzzy sets to solve applied problems. Unlike stochastic methods, which are based on statistical data, fuzzy set theory methods make sense to apply when statistical data are not available. In these cases, algorithms should be based on membership functions formed by experts who are specialists in this field of knowledge. Ideally, complete information about membership functions is required, but this is an impractical procedure. More often than not, even the most experienced expert can determine only their carriers or separate sets of the α -cuts for unknown fuzzy parameters of the system. Building complete membership functions of unknown fuzzy parameters on this basis is risky and unreliable. Therefore, the paper proposes an extension of the fuzzy sets theory axiomatics in order to introduce non-traditional (less demanding on the completeness of data on membership functions) extension principles and operations on fuzzy sets. The so-called α -weak operations on fuzzy sets are proposed, which are based on the use of separate sets of the α -cuts. It is also shown that all classical theorems of Cantor sets theory apply in the extended axiomatic theory. New extension principles of generalization have been introduced, which allow solving problems in conditions of significant uncertainty of information.

Proposing of suggestive influence detection and classification method based on fuzzy logic and feature driven analysis

This research proposes an approach to identify and classify tools utilized in information operations that aim to exert suggestive influence. The proposed method combines fuzzy sets theory and fuzzy inference methods with a feature-based analysis approach. By employing this approach, the study focuses on identifying and categorizing tools such propaganda, fake, disinformation, manipulation, and artificial narrative. This framework provides a comprehensive and nuanced understanding of the various tactics employed in information operations, allowing for improved analysis and mitigation strategies.

Development of fuzzy classifier for technical condition ranking of power transformer

The work aim is to develop a fuzzy classifier for technical condition ranking of power transformer under condition of vagueness and ambiguity diagnostic information. Methodology. The fuzzy classifier developing for technical condition ranking of power transformer was based on approach of using fuzzy set theory and optimization methods. The proposed approach for power transformer rank assessment by using a classifier was developed on the basis of Takagi-Sugeno fuzzy inference system. The input indicators choice is justified and their efficiency for classifier is evaluated by expert evaluation method. This makes it possible to formalize expert assessments regarding the development of power transformer defects. Results. The formalization of technical condition assessment of power transformer in knowledge base form, which implemented in expert system prototype for technical condition assessment, was carried out. The complex technical condition assessment for each functional unit of power transformer was determined based on expert evaluations with using the test and measurement parameters results. Originality. The considered approach to formalization of uncertainty regarding technical condition of power transformer allows building a deterministic decision-making scheme for further maintenance strategy, in which the ranking and decommissioning procedures for specific objects are implemented on the basis of objective criteria. Practical value. The proposed fuzzy classifier allows determination with a high probability degree of technical condition assessment of power transformer based on the test and measurement parameters results. Thus, an applied aspect of using the obtained scientific result is the possibility to objectively rank of power transformers park based on the identified possible defects and their development degree. This constitutes the prerequisites for determining the failure probability evaluation of power transformer at nearest observation period and emergency risk assessment in integrated electric power systems under power transformer failures.