The article is devoted to the development of an innovative neural network decision support system for firefighting in conditions of limited visibility. A comprehensive approach based on the integration of data from multispectral sensors (lidar, ultrasonic phased array, temperature and hygrometric sensors) is presented. The architecture includes a hybrid network that combines three-dimensional convolutional and bidirectional LSTM neurons. To improve the quality of processing, a cross-modal attention mechanism is used to evaluate the physical nature and reliability of incoming signals. A Bayesian approach is used to account for the uncertainty of forecasts using the Monte Carlo dropout method. Adaptive routing algorithms allow for quick response to changing situations. This solution significantly improves the efficiency of firefighting operations and reduces the risk to personnel.

Keywords: mathematical model, intelligence, organizational model, gas and smoke protection service, neural networks, limited visibility, fire department, management, intelligent systems, decision support

The article discusses methods for automated determination of threshold values of parameters when assessing the critical state of technical systems. It explores the theoretical foundations and practical aspects of setting thresholds, including statistical, expert, and combined approaches. Particular attention is paid to mathematical models and algorithms for processing monitoring data. Various methods for determining threshold values are presented: computational, experimental, statistical, and expert. The features of applying adaptive thresholds, dynamic control, and machine learning systems are described. An analysis of existing approaches to determining critical conditions of equipment is conducted. Recommendations are developed for selecting optimal methods for determining thresholds, taking into account the specifics of technical systems. Comprehensive solutions are proposed that combine analytical and machine methods to improve the reliability and safety of computing complexes.

Keywords: automated control, threshold values, technical diagnostics, critical state, computing systems, machine learning, statistical analysis, expert systems, equipment monitoring, technical safety

The article discusses the conceptual foundations of the transformation of the fire extinguishing management system based on the theory of complex organizational systems. The author substantiates the need to move from linear-hierarchical models to adaptive and networked structures capable of providing high stability and efficiency of response in conditions of uncertainty and dynamics of emergency situations. The analysis of the compliance of the fire extinguishing system with the characteristics of a complex organizational system has been carried out, contradictions between its complex nature and primitive control mechanisms have been identified, the causes and consequences of this paradox have been identified. Multi-agent digital platforms, the use of digital twins, situation centers, as well as the use of game theory methods to optimize resource allocation and decision support are proposed as ways to solve the identified problems.

Keywords: system approach, organizational system, firefighting, network structures, management, digitalization, transformation, game theory, optimization, criteria

The article presents a basic model for information support of decision-making designed to enhance the efficiency and resilience of organizational systems within the information security units of the Russian Ministry of Emergency Situations (EMERCOM). The model constitutes an integrated, multi-level system based on the interaction of five interrelated mathematical models: data collection and preprocessing, automated classification, situation forecasting and analysis, decision option generation, and knowledge management. To enhance the model’s functionality and adaptability under conditions of uncertainty, the following formulas have been introduced: assessment of data processing system workload; automatic calibration of weighting coefficients based on forecast error minimization; calculation of information source credibility index; weighted event evaluation accounting for source credibility; decision explainability using the SHAP method; and knowledge utility metrics together with criteria for knowledge archiving. These formulas ensure objectivity, transparency, and robustness of management processes, enabling rapid response to cyber threats, minimizing the impact of human factors, and maintaining high-quality managerial decision-making.

Keywords: information support, decision-making, organizational system, basic model, explainability of decisions, knowledge management

This article examines the impact of artificial intelligence (AI) on the speed and quality of decision-making in management processes. The key factors determining the effectiveness of using AI are analyzed, including the volume and quality of data, the complexity of models, computing resources, and the level of technology integration. Statistical data on the introduction of AI in global practice are presented: only 38% of companies are fully prepared for the effective use of AI, whereas in Russia this figure is 22%. The main obstacles are data quality (60% of global companies face problems, 75% in Russia) and lack of computing resources (35% of organizations in the world have the necessary infrastructure, 19% in Russia). The conclusions of the article emphasize the need to invest in digital infrastructure and increase the transparency of algorithms to increase confidence in AI solutions.

Keywords: artificial intelligence, decision-making, automation, digital transformation, data, interpretability, computing resources

The article considers the application of the Stackelberg equilibrium model with a feedback mechanism for control under incentives. The relevance of the study is due to the need to improve the efficiency of interaction between construction participants - customers, contractors and investors - in the conditions of high competition, uncertainty and limited resources. It is proposed to formalize the dynamic interaction of the parties through a model that takes into account their interests and reactions to the current project parameters. The developed mathematical apparatus includes a two-level management structure, where the upper level is represented by the Customer, and the lower one is the General Contractor, and implements an approach with a feedback mechanism that allows adjusting strategies in real time. The conducted analytical and numerical modeling demonstrates the advantages of implementing such a model: increased stability of strategies, reduced implementation times, minimized risks of cost overruns and delays, as well as increased profits of participants. The obtained results confirm the efficiency of using the Stackelberg equilibrium model with feedback under incentives in the management of complex investment and construction projects, which contributes to the development of modern methods of strategic planning and system management in the construction industry. The results of numerical experiments are presented. A number of conclusions are made.

Keywords: two-level hierarchical model, Stackelberg equilibrium with feedback control under incentive, customer, general contractor, leader, follower

The article focuses on developing and testing a methodology for quantitatively assessing the robustness of time series models (SARIMA, Prophet, LSTM) used in inventory management under unstable external conditions. The proposed approach involves modeling input data distortion scenarios, including holiday demand surges, logistical disruptions, inflationary trends, and structural shifts. Robustness metrics—Robustness Index (RI) and Degradation Ratio (D)—are introduced to evaluate forecast degradation. Experiments on synthetic data show that high accuracy on clean data does not guarantee robustness: SARIMA is sensitive to inflationary trends, Prophet is robust to seasonality, and LSTM is vulnerable to structural shifts. The findings are applicable in logistics and retail for optimizing supply planning.

Keywords: inventory management, time series, model robustness, demand forecasting, SARIMA, Prophet, LSTM, Robustness Index, Degradation Ratio, logistical disruptions, seasonal fluctuations

The paper presents a methodology that includes stages of task performance control, data collection and analysis, determination of reliability and efficiency criteria, reasonable selection, communication, implementation and control of the results of management decisions. A cyclic algorithm for comprehensive verification of compliance with the reliability and efficiency criteria of the system has been developed, allowing for prompt response to changes, increased system stability and adaptation to adverse environmental impacts. Improved mathematical formulas for assessing the state of organizational systems are proposed, including calculation of the readiness factor, level of planned task performance and compliance with established requirements. The application of the methodology is aimed at increasing the validity of decisions made while reducing the time for decision-making, as well as ensuring the relevance, completeness and reliability of information in information resources in the interests of sustainable development of organizational systems.

Keywords: algorithms, time, control, reliability and efficiency criteria, indicators, resources, management decisions, cyclicity

A two-level hierarchically organized model of managing the interaction of the director with the personnel in a company related to the development of projects in the construction sector is presented. The director acts as the leader, and the company's employees act as followers. Both management entities strive to maximize their target functions, reflecting their income and expenses. The study of the model was conducted taking into account its hierarchical structure.  An algorithm for constructing a Stackelberg solution under inducement has been developed. A numerical study of the model has been conducted using the scenario method by partially enumerating the areas of admissible controls of subjects with a certain step. When conducting simulation experiments, all input parameters of the model varied in a fairly wide range. The results of the simulation experiments have been analyzed, and some patterns of system development have been identified.

Keywords: hierarchy, incentive, control system, solution algorithm, Stackelberg equilibrium, leader, follower, imitation, experiment, investment project

The aim of the study is to analyze modern models and algorithms for managing fire and rescue units during rescue of people in different types of public buildings. Research methods: general scientific methods (analysis and synthesis of information, comparison). The article provides a literature review of current methods and algorithms for managing fire and rescue units during rescue of people. Based on previous studies, three main approaches are identified: approaches based on technical superiority; approaches based on mathematical modeling; approaches based on taking into account the individual characteristics of the places where fire and rescue operations are carried out. The advantages and disadvantages of each approach are highlighted in terms of the effectiveness of their use in rescuing people in public buildings. When analyzing previous approaches, it is concluded that at the moment there is no methodology for substantiating the tactical capabilities of gas and smoke protection service units during fire and rescue operations depending on the technical characteristics of the premises and the number of people. The combination of mathematical modeling and consideration of individual characteristics of public buildings seems to be the most effective method of managing fire and rescue units. The study concludes that it is necessary to create an algorithm for the movement of gas and smoke protection service units that will take into account the characteristics of buildings, combustion products and the time of rescuing people. The scientific novelty of the study is due to the following elements: a systematization is proposed, and an assessment of the advantages and disadvantages of models and algorithms for managing fire and rescue services is performed; a scheme of measures for managing fire and rescue units is proposed, which takes into account the functional tasks of the fire and rescue garrison, guard service and work with the population. The scheme for managing fire and rescue units assumes both work with the entire fire and rescue garrison and with individual guard services of the fire protection service, with the population and the administration of public buildings. The proposed scheme complements the existing theoretical knowledge about the organization of the work of fire and rescue units and the management of their work when rescuing people in different types of public buildings. 

Keywords: Key words: fire and rescue unit, public building, gas and smoke protection service, fire safety, method, model, algorithm

This article proposes a new concept of production management of a chemical industry holding as the basis for mathematical support of an automated control system. The concept is based on the use of both traditional methods of proactive management (preventive and predictive) and new generation proactive management, which not only prevents the occurrence of undesirable events, but also ensures a decrease in the frequency of occurrence of such events in the future. A system of basic concepts and principles of proactive production management has been developed. The proposed concept will allow developing the existing mathematical support of an automated production control system and increasing its efficiency.

Keywords: production, automated production control system, mathematical support, concept, proactivity, strategies, proactive management

The article presents a mathematical model that formalizes the process of managing the scientific activities of an organization. The model based on the theory of queuing. The principle of death - reproduction used in the construction. For a special case, a graph of states and a system of Kolmogorov differential equations are given. The intensity of the input and output streams are time-dependent non-stationary streams. The model allows us to consider various structures and schemes of interaction between scientific departments and various sce-narios for setting scientific tasks and the intensity of their solution by employees of the organization. A software package for decision-making has developed for the model for optimal management of the scientific activities of the department. The article presents one of the results of an experimental and model study of the influence of the motivational component and the level of competence of employees. Graphs of the system states given for the resulting solution. The research can used for comprehensive evaluation of results, planning, resource allocation and management of scientific activities.

Keywords: scientific activity, mathematical model, queuing system, death-reproduction principle, graph of states, system of differential equations

This article evaluates various methods for determining the technical condition of structures, buildings and structures. To date, probabilistic (statistical) methods are considered to be one of the possible options for determining the degree of destruction of building structures. The advantage of these methods is the ability to comprehensively take into account the parameters present in a variety of material nature. This is due to the possibility of describing them in dimensionless quantities. The purpose of the method under consideration is to formulate a certain number of technical conditions (events) through which it is planned to determine the degree of destruction and find a set of technical conditions of building structures. Diagnostic matrices are created by combining diagnostic features and their conditional probabilities, acquired by analyzing a large amount of accumulated statistical data.

Keywords: construction and technical expertise, defects, reliability, diagnostic methods, efficiency

Effective communication between project managers and engineering teams is critical for the success of construction projects. This article develops a hierarchical (Stackelberg) game-theoretic model, where the manager acts as the leader and engineering teams act as followers. The model quantifies how both the leader and followers balance the benefits and costs associated with increasing communication efforts. We propose a two‐level (Stackelberg) model of strategic interaction between a project manager (leader) and engineering teams (followers) in construction projects.  An efficient numerical algorithm is implemented in MATLAB to compute optimal strategies and analyze different project scenarios. Scenario analysis demonstrates how changes in project parameters affect the balance of efforts and profits, thereby guiding managerial recommendations for improving communication and reducing project risks. By considering aspects like risk, time delay, cost overruns, and resistance to change, we provide supervisors and agents communication efficiency functions. Using scenario analysis and numerical optimization, we determine the most efficient communication tactics to match the hierarchical structure of building projects.

Keywords: project efficiency, leader-follower dynamics, profit maximation, project management, communication efforts, time delay, cost overrun, risk, resistance to change

The purpose of this article is to analyze algorithms and models for conducting search and rescue operations in crowded areas during fires, as well as other man-made or natural emergencies. The chance of saving people's lives directly depends on the effectiveness of search and rescue operations. The article describes the brief essence of the Graph Model as a method of finding optimal solutions when building a route for conducting search operations in emergency situations, including fires at facilities with a mass presence of people.

Keywords: search and rescue operations, facilities with a mass presence of people, emergencies, rescue of people, fires, search for victims

The article addresses the challenges and proposes mathematical models for optimizing container freight transportation within complex logistics systems, emphasizing the growing importance of digital technologies and artificial intelligence in logistics by 2025. It highlights key industry issues such as decentralized global supply chains, environmental risks, infrastructure deficiencies, safety concerns, and notably, the costly problem of transporting empty containers, which accounts for a significant portion of operational expenses worldwide and in Russia.
The core contribution is a modified three-dimensional transport optimization model that incorporates container types, cargo volumes, and transportation costs, including the cost variations due to partially filled or empty containers. The model extends classical transportation problem formulations by introducing a potentials method that accounts for the contributions of suppliers, recipients, and container costs to determine an optimal transport plan minimizing total costs.
Constraints ensure that supply and demand conditions, container capacities, and route feasibility are respected. The model uniquely integrates the degree of container filling into cost calculations using a coefficient to adjust transportation costs accordingly. This approach enables more accurate and cost-effective freight planning.
Additionally, the article discusses the development of a simulation model and a client-server application to automate the search for optimal transport plans, facilitating practical implementation. The proposed framework can be expanded to include various container types, cargo characteristics, and transport modes, offering a comprehensive tool for improving logistics efficiency in container freight transportation.

Keywords: diversification of management, production diversification, financial and economic purposes of a diversification, technological purposes of ensuring flexibility of production

The article examines the network model of district management within the subsidized region from the point of view of the upper level, taking into account the optimal response of the districts – the Stackelberg equilibrium is found. The results obtained are compared with the corresponding results in the creation of horizontal and integrated coalitions of districts and the region. The author examines the preference for creating coalitions for all participants in the system. It has been proven that cooperation is more profitable for weak and medium-sized districts, hierarchy is more profitable for a strong district, and independence is more profitable for the region as for the upper level. It is not profitable for the strong elements of the system to join a coalition, while it is more profitable for the weak elements to join a coalition.

Keywords: network model, Nash equilibrium, Stackelberg equilibrium, resource allocation, Lagrange multiplier method, cooperation, horizontal coalition, maximal coalition, complex coalition, independent behavior

A set of techniques for obtaining retrospective, statistical, expert information, data integration, competence deficit assessment and knowledge management to compensate for competence deficit in organisational systems is presented. For the purpose of practical implementation of an integrated approach to improving the management of organisational systems, a model and an algorithm for obtaining data by applying a set of techniques have been developed. In the future, the proposed methodological solutions will significantly improve the efficiency of organisational systems management through the rational application of automated management systems with components of trusted artificial intelligence.

Keywords: algorithm, critical events, integration, information resources, recommendations, systematisation, efficiency

The article focuses on the integration of digital educational technologies (EdTech) into the management of organizational systems in the context of digital transformation in education. Special attention is given to the analysis of the interconnection between technological, organizational, and market components of EdTech, as well as their impact on optimizing business processes and management strategies in educational institutions. The aim of the study is to develop a comprehensive definition of EdTech that reflects its evolution and role as a tool for management transformation. The research methodology includes a systematic analysis of the EdTech concept, modeling the interaction between technologies and educational organizations, and a critical evaluation of case studies on digital platform implementation. As a result, the paper proposes defining EdTech as a dynamic ecosystem that integrates digital management, personalized learning, and organizational culture adaptation. The conclusions emphasize the necessity of an ecosystem approach to EdTech management, considering infrastructure limitations, staff training, and regulatory aspects. The findings can be applied to the development of digital transformation strategies for educational institutions, resource planning optimization, and the formation of sustainable business models in the EdTech sector.

Keywords: EdTech, digital transformation, educational technologies, business processes, system analysis, management

The article formulates the task of developing a fire safety management procedure based on a risk-based approach, taking into account the preferences of the decision maker in the multi–criteria system "result - cost – time". A multi-criteria mathematical model of the procedure under consideration has been developed, as well as an algorithm for its implementation with the development of information technology and a test case.

Keywords: risk-based approach, fire risk, decision support systems, Pareto-optimal solutions

This paper explores the content-based filtering approach in modern recommender systems, focusing on its key principles, implementation methods, and evaluation metrics. The study highlights the advantages of content-based systems in scenarios that require deep object analysis and user preference modeling, especially when there is a lack of data for collaborative filtering.

Keywords: сontent - oriented filtering, recommendation systems, feature extraction, similarity metrics, personalization

The article discusses the task of unifying design parts in the manufacture of metal structures, aimed at reducing excessive nomenclature and increasing the efficiency of the production process. A fuzzy clustering algorithm based on the Fuzzy C-Means method is proposed and implemented, taking into account a set of geometric and technological features of parts. The method allows for flexible assessment of the degree to which elements belong to unified groups and provides resistance to deviations and acceptable errors. An experimental check on a real sample of project data showed a 38.7% reduction in the number of unique positions and a reduction in labor costs for documentation preparation. The results obtained confirm the effectiveness of the proposed approach for the tasks of digital transformation of production engineering.

Keywords: fuzzy clustering, Fuzzy C-Means, unification of parts, digital manufacturing, intelligent data processing, metal structures

Introduction: Mobile Gaming Addiction (MGA) has emerged as a significant public health concern, with the World Health Organization recognizing it as a gaming disorder. Russia, with its growing mobile gaming market, is no exception. Aims and Objectives: This study aims to explore the feasibility of using neural networks for early MGA detection and intervention, with a focus on the Russian context. The primary objective is to develop and evaluate a neural network-based model for identifying behavioral patterns associated with MGA. Methods: A proof of concept study was conducted, employing a simplified neural network architecture and a dataset of 101 observations. The model's performance was evaluated using standard metrics, including accuracy, precision, recall, F1-score, and AUC-ROC score. Results: The study demonstrated the potential of neural networks in detecting MGA, achieving an F1-score of 0.75. However, the relatively low AUC-ROC score (0.58) highlights the need for addressing dataset limitations. Conclusion: This study contributes to the growing body of literature on MGA, emphasizing the importance of considering regional nuances and addressing dataset limitations. The findings suggest promising avenues for future research, including dataset expansion, advanced neural architectures, and region-specific mobile applications.

Keywords: neural networks, neural network architectures, autoencoder, digital addiction, gaming addiction, digital technologies, machine learning, artificial intelligence, mobile game addiction, gaming disorder

The article analyzes the existing programs for training the population in actions and organization of actions in the field of civil defense, as well as in the field of protecting the population from natural and man-made emergencies. Conclusions are drawn about the relevance of existing programs, problems in this area are highlighted, and solutions are proposed to increase the effectiveness of these teaching methods.

Keywords: natural emergencies, civil defense, emergency situations, civil defense, training program, population training, avalanches, life safety, railway

The article explores a model in which it is possible to predict the timing of obsolescence of a construction site. The purpose of the described techniques is to ensure stable operation and reliable operation of facilities. The presented methodological approaches make it possible to improve the accuracy of the assessment of degradation processes, covering both technical elements and structural parts of buildings and infrastructure systems. The article focuses on effective tools and methods used to survey the current state of real estate, as well as to anticipate changes in their performance over time. The paper considers the application of a generalized computational wear scheme that demonstrates changes in the organization and destruction of building elements throughout the service life. This scheme takes into account the continuous influence of external conditions on the structure of the structure. The universal formula proposed for the analysis serves as a research tool and displays the course of changes in the state of technical systems under the influence of prolonged loads.

Keywords: organizational and technological solutions, reliability, quality control, monitoring of compliance with standards, efficiency, production costs