Computer systems and information technologies
ISSN 2710-0766 ISSN 2710-0774 (online) Published from the year 2020. Publisher: Khmelhytskyi National University (Ukraine), Frequency: 4 times a year Manuscript languages: English Editors: T. Hovorushchenko (Ukraine, Khmelnitskiy), Certificate of state registration of print media: Series КВ № 24512-14452Р (20.07.2020). Registration in Higher Attestation Commission of Ukraine: in processing License terms: authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License International CC-BY that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal. Open-access Statement: journal Problems of Тribology provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. Full-text access to scientific articles of the journal is presented on the official website in the Archives section. Address: International scientific journal “Computer Systems and Information Technologies Journal”, Khmelnytsky National University, Institutskaia str. 11, Khmelnytsky, 29016, Ukraine. Tel.: +380951122544. E-mail: csit.khnu@gmail.com. Website: http://csitjournal.khmnu.edu.ua.
METHOD FOR ENHANCING FMECA (XMECA) SAFETY ASSESSMENT PROCEDURES CONSIDERING THE CRITICALITY OF ASSUMPTIONS AND ANALYSIS ERRORS
In existing studies that discuss the Failure Modes, Effects, and Criticality Analysis (FMECA, XMECA) method, two principal limiting factors are commonly identified: the significant influence of engineers’ and auditors’ experience on the resulting safety assessments, and the presence of restrictive assumptions embedded in assessment procedures and supporting tools. To address these limitations, this paper proposes a method for enhancing FMECA (XMECA) safety assessment procedures that explicitly accounts for the criticality of underlying assumptions and analysis errors. Case study of applying the proposed method demonstrate that it can serve as an effective instrument for researchers and developers working on reliability and safety assessment problems in critical systems. Further research is devoted to application of the method in different contexts and industrial sectors.
Copyright (c) 2026 Євген БАБЕШКО, Вячеслав ХАРЧЕНКО, Костянтин ЛЕОНТІЄВ https://creativecommons.org/licenses/by/4.0
DECISION SUPPORT SYSTEM FOR PROJECT RESOURCE PLANNING BASED ON THE RANDOM FOREST METHOD
The study develops and justifies the structure of a decision support system (DSS) designed to automate project resource planning processes using the Random Forest method. The relevance of the research is driven by the necessity to transition from subjective estimates to analytical tools for forecasting project costs and duration. The proposed system architecture covers the full data processing cycle: from automated input data collection from corporate databases (such as Jira or MS Project) to the generation of visual reports for management. Implementing the Random Forest algorithm within the DSS framework enables the identification of critical project parameters, specifically technical complexity and external risks, directly at the initiation and planning stages. Special emphasis is placed on the development and implementation of a feature importance visualization mechanism, which transforms the forecasting model into a transparent analytical tool. This allows managers to not only obtain predicted values but also understand the underlying structure of the factors influencing them. It was established that the feature hierarchy, where technical complexity plays a leading role (0.793), enables the project manager to focus on the most critical planning nodes. Such an approach significantly enhances the transparency of decision-making and fosters increased stakeholder trust in the system's recommendations. The practical significance of the results lies in the possibility of implementing predictive management methods. The system identifies potential project bottlenecks before actual difficulties arise, providing the manager with a basis for timely reviews of team composition, budget limit adjustments, or schedule modifications. Thus, the proposed DSS serves as an effective tool for active management, providing decision support to prevent cost overruns and project schedule delays in dynamic environments.
Copyright (c) 2026 Єлизавета ГНАТЧУК, Марія ЛЕБЕДОВСЬКА https://creativecommons.org/licenses/by/4.0
METHODS OF HIDING DATA IN COMPUTER NETWORKS: FROM CLASSICS TO IoT AND Ai
The article presents an overview of key methods in network steganography, including the classification of data hiding techniques in network protocols and discussion of promising directions for further research. Special attention is paid to the use of steganography in modern network environments such as IoT, as well as the application of artificial intelligence to traffic masking. The paper also outlines current approaches to hidden channel detection and threat modeling in digital communication systems.
Copyright (c) 2026 Mariia Kapustian https://creativecommons.org/licenses/by/4.0
LLM-DRIVEN QUERY GENERATION FOR GRAPH-BASED BUSINESS INTELLIGENCE: TOWARDS A COLLABORATIVE KNOWLEDGE RETRIEVAL TOOL
This paper explores the use of large language models (LLMs) to support collaborative business intelligence in the tourism domain through two key tasks: extracting travel-related tags from user queries and generating Cypher queries for accessing knowledge graphs. We focus on evaluating the performance of compact and efficient LLMs, aiming to balance accuracy with computational feasibility. To assess tag extraction, we evaluated Phi-3 Mini, LLaMA 3.2, and Gemma 3 using the DeepEval framework with G-Eval scoring. Phi-3 Mini showed the best balance between accuracy and efficiency, while Gemma 3 achieved the highest scores at the cost of increased resource usage. For Cypher query generation, we tested more powerful models: Mistral Small 3.1, Phi-4, Gemma 3, and ChatGPT-4o. ChatGPT-4o achieved the highest correctness, while Mistral Small demonstrated the best trade-off among smaller models. Our results suggest that lightweight LLMs are suitable for basic natural language processing tasks, but structured query generation remains challenging and requires stronger models. Further research is needed to improve the reliability of generated queries and to develop robust validation mechanisms. This study introduces a comparative evaluation of lightweight and standard LLMs specifically applied to collaborative business intelligence in the tourism domain. It highlights the feasibility of using compact LLMs for natural language processing tasks while demonstrating the challenges of structured query generation, which requires more powerful models.
Copyright (c) 2026 Олександр СУТЯГІН, Ольга ЧЕРЕДНІЧЕНКО https://creativecommons.org/licenses/by/4.0
AI-BASED AUTOMATION OF DECISION LOGIC REPRESENTATION: BRIDGING GAP IN AUTOMATED DECISION MODELING VALIDATION
The study aims to resolve the "modeling bottleneck" in Business Process Management by developing an automated method for ensuring the correctness of Decision Model and Notation (DMN) tables generated by Large Language Models (LLMs). The primary goal is to determine whether shifting the AI's role from a pure generator to a validator within a closed-loop system can overcome the structural limitations inherent in stochastic models. The research employs a comparative experimental design using a "Mutation Testing" approach. We analyze two distinct workflows: (1) Static Generation, where test cases are fixed, and (2) Dynamic Paired Generation, where the LLM regenerates both the decision logic (DMN XML) and the validation criteria (Test Cases JSON) simultaneously upon failure. The methodology integrates concepts from "Struc-Bench" for structural analysis and utilizes a deterministic DMN engine (Camunda) for execution-based verification. The experiments demonstrate that "out-of-the-box" LLM generation fails in approximately 4.5% of cases due to semantic drift and structural hallucinations when validated against static benchmarks. However, the proposed "Dynamic Paired Generation" workflow achieved a 100% convergence rate across 200 cycles. The system successfully identified and corrected both syntactic errors (XML schema violations) and logical errors (Hit Policy violations) without human intervention. The study introduces the concept of "Dynamic Paired Generation" for neuro-symbolic systems. Unlike traditional "Chain-of-Thought" prompting, this approach leverages the mutual consistency between two independent structural representations (Logic and Examples) to filter out hallucinations, proving that dynamic validation is superior to static prompting for structured data tasks. The proposed framework provides a blueprint for "Self-Healing" decision management systems. It allows non-technical business analysts to convert natural language policies into executable, error-free DMN models, significantly reducing the time and cost of regulatory compliance and process automation.
Copyright (c) 2026 Владислав МАЛЯРЕНКО https://creativecommons.org/licenses/by/4.0
ANALYTICAL WEB SERVICE FOR IDENTIFYING SUSPICIOUS HIGH-RISK DIGITAL ASSET TRANSACTIONS
The rapid growth of digital asset transactions significantly complicates their analysis and monitoring. Although blockchain provides transparency of operations, the high level of pseudonymity among participants creates substantial challenges in identifying the nature of interactions and detecting potentially undesirable activity. This increases the demand for modern tools capable of automatically processing large volumes of data, grouping addresses into clusters, and evaluating their behavior based on aggregated transactional characteristics. The development of a web service for digital asset transaction analytics that automatically forms address clusters and classifies them using machine learning models is proposed. The system provides an informative and interpretable data presentation, enabling users to assess the nature of activity associated with a given address. The methodology is based on heuristics for clustering blockchain addresses in networks utilizing the UTXO model, as well as on the calculation of structural and behavioral characteristics of the formed clusters. Random Forest, Extra Trees, and XGBoost models were used for classification, which were trained on a labeled subset of the scientific dataset. The technical implementation of the web service is based on the Symfony framework for the server side, the React library for the client side, MySQL and PostgreSQL DBMS for data storage, the Python programming language for machine learning, as well as Docker and Nginx tools for deployment and stability. The results of the study demonstrate that machine learning models can effectively classify clusters of digital asset addresses according to their behavioral characteristics, and the integration of algorithms into the web service provides automatic generation of analytical reports. The scientific novelty lies in combining heuristics for address clustering with machine learning models, which allows evaluating the behavior of clusters and identifying potential risk. The practical significance of the developed web service is defined by the possibility of its application for rapid preliminary checks of cryptocurrency addresses, detecting relationships between them, and assessing potential interaction risks, making it valuable for organizations and individual users alike.
Copyright (c) 2026 Віталій КОЧУРА, Тамара ЛОКТІКОВА, Надія КУШНІР https://creativecommons.org/licenses/by/4.0
METHOD FOR SYNTHESIS OF A SCALABLE ARCHITECTURE OF A DISTRIBUTED CS, RESISTANT TO SOCIAL ENGINEERING ATTACKS
Social engineering continues to be one of the most dangerous classes of threats for modern distributed IT systems, where event processing, resource access, and protection mechanisms are performed on a large number of heterogeneous nodes. The growth of the scale of architectures, the emergence of multi-channel interaction scenarios, remote users, and a high level of dynamism create challenges for the synthesis of systems that are able to maintain resistance to social engineering attacks. The study proposes methods and tools for the synthesis of distributed systems focused on ensuring structural, behavioral, and functional resistance to such attacks. The basis of the approach is the use of a population multi-agent mean-field model, which allows considering a large number of nodes as a coordinated system of local detectors interacting through an aggregated state space. This makes it possible to describe the impact of attacks not on individual components, but on the entire distributed system as a whole, and to evaluate its response through integrated risk and resilience indicators. The study forms a generalized model of a distributed system, defines the roles of different types of nodes, protections and interaction channels, and also describes the methodology for architecture synthesis, which includes the classification of local actions, coordination mechanisms and evaluation criteria. Special attention is paid to the integration of protective measures - deception components, multifactor authentication, filtering and segmentation mechanisms - into the structure of a distributed system. Methods for optimizing the distribution of these measures at different levels of the architecture are proposed in accordance with the dynamics of the mean field and target requirements for stability. An iterative approach to architecture synthesis is developed, which combines the adaptation of local node strategies with the tuning of global system parameters. The results demonstrate that the use of the mean field concept allows to ensure scalability of solutions, consistency of node behavior, and also to increase the ability of a distributed system to counteract social engineering attacks in conditions of uncertainty and high variability of scenarios. The methodology can be used for the design, improvement and engineering synthesis of real distributed IT architectures operating in critical environments.
Copyright (c) 2026 Олександр БОХОНЬКО, Ольга АТАМАНЮК https://creativecommons.org/licenses/by/4.0
APPROACH TO A DECENTRALIZED PHYSICIAN-ORIENTED EHR ARCHITECTURE WITH CRYPTOGRAPHIC PROTECTION
Modern electronic health record (EHR) systems face challenges related to security, privacy, and accessibility, especially in centralized architectures where there are risks of database compromise, data leakage, and limited interoperability between institutions and/or data storage nodes. Distributed systems in which servers operate autonomously without requiring constant connectivity demand decentralized solutions with cryptographic protection and minimal user-side requirements. A physician-centric approach enables medical institutions to optimize workflow within a trusted environment while preserving transparency for patients regarding data access. The proposed architecture combines local physician nodes with a shared archival registry node used for long-term data storage and patient access. Protection is achieved through envelope encryption with combined DEKs, daily rotation of server keys, and internal hash chains for detecting unauthorized modifications. The system supports profile migration between nodes, exchange of signed data within a local network, and offloading of completed records to the registry to optimize resource usage. A key principle is transparency: any data decryption is accompanied by a patient notification, and if the notification subsystem is unavailable, the operation is not performed. Access is logged with identification of the entity performing the decryption. Profile creation begins on the physician’s node: data are encrypted with a combined DEK, and hash chains ensure integrity. Two independently encrypted copies of the user key enable administrators to restore access without exposing key material. Data exchange between physicians occurs within the local network with signature verification, making the system resilient to failures.
Copyright (c) 2026 Володимир КИСІЛЬ, Тетяна КИСІЛЬ https://creativecommons.org/licenses/by/4.0
ENTROPY-CRYPTOGRAPHIC APPROACH FOR TRANSMISSION OF SATELLITE DATA IN TELECOMMUNICATION NETWORKS
Amid rapid advances in satellite observations and increasing risks associated with high-resolution multispectral data downloads, stronger satellite image encryption techniques are becoming increasingly important. To address these challenges, the paper proposes a new cryptographic methodology based on entropy and nonlinear methods. This approach offers high resistance against brute-force attacks, generates a high-entropy key, and employs a dynamic non–linear transformation in multi-layered encryption, which is AES-256-bit encrypted. This comprehensive approach is designed to safeguard the security of satellite data in transit from modern cryptanalysis as it traverses communication networks. The approach begins with entropy-based initializations, iteratively expands the key space, and applies adaptive transformations to render the encrypted data highly unpredictable. Experiments with satellite images of various resolutions demonstrate that this approach is resistant to cryptanalysis. The evaluation included measuring entropy, analysing the correlation between neighbouring pixels, and testing resistance to statistical and frequency-based attacks. The encrypted images achieved entropy values close to the theoretical maximum and showed almost no correlation between adjacent pixels, demonstrating the strength and uniformity of the encryption process. Performance tests on systems with multiple threads and processors revealed clear links between execution time, data size, and the level of parallelization. Moderate parallelism provided the best speed improvements, and the method remained scalable for large datasets, making it suitable for high-throughput environments. This approach ensures strong satellite-image robustness in image size, content, or spectral characteristics. The flexible structure and good performance make it a promising candidate for future telecom networks and secure satellite data distribution systems.
Copyright (c) 2026 Віта КАШТАН, Володимир ГНАТУШЕНКО https://creativecommons.org/licenses/by/4.0
USE OF GRADATION CORRECTION METHOD FOR IMPROVING THE VISUALIZATION OF COMPUTED TOMOGRAPHY RESULTS
The aim of this work is to enhance the quality of visualization of computed tomography (CT) results by improving digital image processing methods, particularly through the use of the gradation correction (GC). The research methodology involves the application of algorithms for the automatic determination of the optimal pixel brightness range in CT images, which reduces the influence of extreme brightness values and increases the contrast of diagnostically significant structures. The proposed gradation correction is applied not within the standard 0–255 range but based on the statistical distribution of brightness, with the exclusion of non-informative tail regions of the histogram. The research results indicate that the proposed approach improves the visual clarity of organ boundaries and pathological formations without loss of diagnostic information and can be integrated into automated medical image analysis systems. The scientific novelty of the work lies in the enhancement of the gradation correction method for CT image processing through the automation of brightness range selection. The practical significance of the study is in improving the efficiency of visual analysis and computer-aided diagnostics at the stages of preliminary medical image processing, contributing to higher accuracy in pathology detection and reduced evaluation time.
Copyright (c) 2026 Євген ВАКУЛІК, Кирило СМЕЛЯКОВ https://creativecommons.org/licenses/by/4.0
LASER INFORMATION SYSTEM FOR MONITORING GLUE EVAPORATION DURING DRYING
In the context of advancing technologies in printing, materials processing, and chemical production, there is a growing demand for precision in monitoring volatile emissions generated during drying processes. Conventional control methods often lack the speed, sensitivity, or selectivity required for real-time analysis of adhesive evaporation products, particularly in dynamic industrial environments such as book block drying chambers. This study substantiates the development of laser-based resonance photometric systems for evaluating the concentration of evaporated chemical components from adhesive mixtures. A methodological framework is proposed for implementing dual-channel laser photometry, enabling non-contact, rapid, and spatially resolved assessment of volatile content. The structure and operating principles of a laboratory-grade concentration meter are presented, incorporating semiconductor lasers, photodetectors, signal processing units, and intelligent control agents. Special attention is given to the physical and quantum-chemical interactions of laser beams with aqueous media, as well as to the solubility dynamics of adhesive components under thermal influence. A two-stage selective photoionization approach is introduced to enhance signal amplification through resonance effects, enabling more precise quantification of emissions. The proposed methods can be applied not only to printing production environments but also to broader ecological monitoring tasks involving laser-based diagnostics of airborne and liquid-phase contaminants. These technologies contribute to the development of next-generation intelligent sensing systems capable of supporting environmental safety and process optimization.
Copyright (c) 2025 Ольга ФЕДЕВИЧ https://creativecommons.org/licenses/by/4.0
IMPROVEMENT OF THE AUTOMATED NLP SYSTEM AS A FACTOR IN IMPROVING THE QUALITY OF MARKETING STRATEGY FORMATION
Along with the rapid growth of the Internet of Things and edge computing, collaborative training of machine learning models on resource-constrained edge devices, while ensuring user data privacy, has become a key and challenging research challenge. The presented paper aims to fill this research gap by designing, implementing, and evaluating a synergistic and optimized federated learning infrastructure with differential privacy called PriFed-IoT, specifically designed for Internet of Things edge computing scenarios. The novelty of this work lies in the creation of a system of several modules working together, rather than a simple combination of techniques. The main idea is to use adaptive differential privacy to create an environment with a higher signal-to-noise ratio for the clustering algorithm in the late stages of training, allowing for more accurate separation of clients. In order to test the efficiency of the PriFed-IoT infrastructure, a series of complex simulation experiments were developed and conducted on a standard CIFAR-10 dataset, simulating different degrees of data heterogeneity. The study successfully offers a comprehensive solution, the experimental results convincingly prove the advantages of PriFed-IoT infrastructure in balancing privacy protection, model utility, and system efficiency, providing a valuable theoretical framework and technical implementation for building secure, efficient, and reliable intelligent applications at the edge of the Internet of Things.
Copyright (c) 2026 Юрій СКОРІН https://creativecommons.org/licenses/by/4.0
CROP YIELD MODEL BASED ON MAXIMUM VALUES OF CUMULATIVE VEGETATION INDICES
This research develops a precision modeling approach for cereal crop yield estimation utilizing remote sensing data within a secure information architecture framework. A two-tier model is proposed wherein the first tier conducts vegetation index dynamics modeling (NDVI, MTCI) through an adaptive modified Monod model based on contemporary differential equation systems, while the second tier performs yield prediction via linear regression and machine learning methodologies to accommodate nonlinear interdependencies. An efficient parametric identification algorithm for models is developed, accounting for their nonlinearity characteristics and employing the Levenberg-Marquardt gradient method for refined parameter optimization. A multi-tier information architecture incorporating blockchain technologies is proposed as a decentralized layer for ensuring data integrity and authenticity to mitigate cyber threats including data poisoning attacks and industrial espionage. An adaptive prediction algorithm based on observation window methodology is implemented, leveraging an ensemble of previously observed trajectories to maximize forecasting precision. Practical applicability is validated through numerical experiments on empirical vegetation index data from rice cultivation. The synthesized findings demonstrate the potential of the proposed methodology for addressing contemporary precision agriculture challenges, systematic food security monitoring, and strategic decision-making processes in the agricultural sector.
Copyright (c) 2025 Роман ПАСІЧНИК, Михайло МАЧУЛЯК https://creativecommons.org/licenses/by/4.0
ANALYSIS OF ELECTRICITY CONSUMPTION USING THE COMPONENT METHOD OF PERIODICALLY CORRELATED RANDOM PROCESSES
Contemporary energy systems, considering the diverse challenges emerging within energy infrastructure, require advanced analytical methodologies for electricity consumption forecasting. Traditional statistical approaches prove insufficient for modeling dynamic multi-scale temporal structures of electricity consumption signals aimed at predicting electrical loads in residential households. This research presents a comprehensive approach to electricity consumption analysis utilizing the mathematical framework of periodically correlated random processes (PCRP), specifically employing the component method. The mathematical foundation of the methodology consists in representing electricity consumption signals as PCRP models with decomposition into constituent elements: deterministic trend components, periodic components of cyclical variations, and stochastic components of random deviations. Component analysis enables the identification of latent consumption patterns through decomposition of periodic characteristics. Therefore, the proposed method allows for the elimination of limitations inherent in traditional stationary models. Empirical validation was conducted using a comprehensive dataset of residential electricity consumption spanning the period from July to August 2025. Experimental data demonstrated pronounced repetitive characteristics with systematic daily periodicity, confirming the theoretical premise regarding daily component dominance. Three-dimensional visualization of results revealed complex interaction dynamics between different frequency components of electrical load signals. Spectral analysis exhibited characteristic distribution with maxima for low-frequency components corresponding to daily harmonics. The obtained results can be utilized for residential electrical load forecasting and enable both short-term and medium-term energy consumption predictions. This is significant not only for forecasting residential electrical loads, but also for optimizing electrical energy resources and managing intelligent networks.
periodically correlated random processes
Copyright (c) 2025 Андрій ВОЛОЩУК, Галина ОСУХІВСЬКА, Микола ХВОСТІВСЬКИЙ, Андрій СВЕРСТЮК https://creativecommons.org/licenses/by/4.0
IMPLEMENTATION OF INFORMATION TECHNOLOGY FOR THE MODEL OF PREDICTION POTENTIAL CARS COLISION
This research focuses on developing an information technology solution capable of delivering real-time notifications about potential car accidents to Internet of Things (IoT) devices installed in vehicles. Since vehicles are mobile and frequently change location, there is a need to have stable and timely notifications. To address this, the proposed solution leverages cloud technologies, which offer scalability, low latency, and high availability for real-time data transmission. The main objective is to design and implement architecture that enables effective real-time messaging between cloud services and moving IoT devices. The system is tested across various simulated driving scenarios to evaluate its performance and reliability. A key aspect of the methodology involves measuring the time interval between when a message is sent and when it is received by the IoT device, followed by assessing whether the driver has adequate time to respond appropriately. The experimental setup is based on test cases created using Python, the BeamNG.tech simulation environment, and AWS IoT Core as the cloud service provider. The results demonstrate that the proposed technology can reliably handle real-time messaging in dynamic conditions. As a conclusion, the research confirms the potential of the developed solution for real-life applications in connected vehicle safety systems.
Copyright (c) 2025 Олександр БИЗКРОВНИЙ, Кирило СМЕЛЯКОВ https://creativecommons.org/licenses/by/4.0
LEGAL AND ETHICAL BASES FOR CREATING REPRESENTATIVE DATASETS TO DETECTING MANIFESTATIONS OF CYBERBULLYING IN TEXT CONTENT
The article is devoted to developing the method for creating of representative text data datasets for detecting manifestations of cyberbullying in text content, considering ethical and legal principles. The primary focus is ensuring fair and equal representation of different demographic groups in text samples, which is critical for creating non-discriminatory and socially responsible artificial intelligence models. Emphasis is placed on compliance with key ethical principles – preventing harm, avoiding bias, and ensuring representativeness – and provisions of international law, particularly the General Data Protection Regulation. Proposed method for creating of representative text data datasets for detecting manifestations of cyberbullying in text content, taking into account ethical principles, which includes the following stages: preliminary processing of text data, analysis of distributions according to ethical aspects (age, gender, religion etc.), and representative adjustment through multi-criteria optimization. Machine learning models are trained on prepared balanced samples using appropriate reference datasets to classify text samples according to ethical criteria. The comparison is based on official demographic data for Ukraine, which ensures the reliability of the assessment of deviations. As a result of applying the developed method, a representative sample was created with a deviation of the proportions of ethical groups from the target values within 0.00-0.04%. The statistical metrics obtained confirmed the effectiveness of the selected models and demonstrated a high degree of compliance with the ethical responsibility requirements of the results. The analysis showed that the initial datasets contained imbalances, which were successfully eliminated through multi-criteria optimization and data augmentation. The developed approach can be integrated into preparing training samples for ethically oriented artificial intelligence systems that perform automated detection of cyberbullying manifestations in text content, reducing the risks of reproducing social biases and increasing trust in algorithmic decisions.
Copyright (c) 2025 Олена СОБКО, Арчіл ЧОЧІА https://creativecommons.org/licenses/by/4.0
MARKETING DECISION SUPPORT SYSTEM BASED ON FUZZY TRAINED ASSOCIATIVE RULES EXPERT SYSTEM
The fuzzy-associative metaheuristic approach addresses the urgent task of developing a marketing decision support system based on a fuzzy trained associative rules expert system, aimed at improving the accuracy and efficiency of consumer preference analysis. The proposed system combines the interpretability of fuzzy logic with data-driven learning via associative rules and parameter identification using an adaptive multi-agent optimization method. To achieve this goal, associative rule learning techniques (Apriori and FP-Growth) were used to extract frequent consumer behavior patterns. A fuzzy expert system was developed, in which the parameters of membership functions are optimized by the Adaptive Vibrating Particle System (AVPS) metaheuristic. Unlike traditional vibrating particle systems, AVPS integrates iteration-dependent control of particle positions, enabling global search in early iterations and local refinement at later stages, thus improving convergence speed and solution precision. The architecture was implemented using Python-based tools (TensorFlow, Keras, Pandas, mlxtend, Scikit-Fuzzy), and validated on the “Consumer Behavior and Shopping Habits” dataset. The fuzzy expert system achieved an accuracy of 0.98, outperforming human experts (0.80), traditional VPS optimization (0.93), and backpropagation-based training (0.90). The system also reduces reliance on manually tuned parameters and increases robustness to data incompleteness and noise. Scientific novelty lies in combining a fuzzy associative rule-learning framework with AVPS-based optimization, offering a scalable and interpretable decision-making mechanism. The developed system contributes to the advancement of intelligent recommendation engines, personalized marketing tools, and decision support systems in consumer-oriented analytics.
Copyright (c) 2025 Євген ФЕДОРОВ, Марина ЛЕЩЕНКО, Тетяна САХНО, Владислав ПАСЕНКО, Олена КРАВЧЕНКО https://creativecommons.org/licenses/by/4.0
ADVANCED METHODS OF APPLYING CODING SYSTEMS IN THE DESIGN OF DIGITAL COMPONENTS FOR CYBER-PHYSICAL SYSTEMS
This study aims to develop highly efficient digital components for cyber-physical systems capable of self-recovery, high-speed data processing, and reliable operation in real-time environments. The paper proposes new approaches to information encoding, particularly for RGB color image representation, and the modeling of neuro-like structures using the code systems of Krestenson, Rademacher, and Haar. The methodology is based on the mathematical foundations of the residue number system (RNS), modular arithmetic, and structural analysis of digital components. Hybrid models of formal neurons, perceptrons with delay lines, and wavelet neurons are employed to solve signal classification tasks. A model of signal self-recovery in a neural bundle is developed, taking into account failures of individual elements and inhibitory effects. As a result, a fault-tolerant mechanism for information transmission in bioneural structures is implemented, along with algorithms for encoding RGB pixels in the R-C and H-C code systems. These methods ensure unambiguous decoding and allow adaptive encoding in the presence of data loss or corruption. The scientific novelty lies in the integration of biological fault-tolerance principles with digital encoding methods based on RNS, providing adaptive signal recovery without the need for complete decoding. The practical significance of the research is in the potential application of the results to digital vision devices, sensor platforms, embedded systems, and high-performance processors for intelligent computing in cyber-physical environments.
Copyright (c) 2025 Наталія ВОЗНА, Володимир ГРИГА, Леся МИЧУДА , Лідія ШТАЄР https://creativecommons.org/licenses/by/4.0
INFORMATION SYSTEM FOR SERVICE PORTFOLIO FORMATION FOR INFOCOMMUNICATION PROVIDERS
This paper addresses the challenge of service portfolios formation for infocommunication service providers. A comprehensive analysis of existing approaches enabled the formulation of the problem within the framework of contemporary business models and underscored the necessity of developing new effective methods. These methods must reflect the specifics of interaction between IT companies, service providers, and end users, as well as the inherent characteristics of services and their delivery environments. The paper substantiates the choice of methodological foundations underlying the proposed system for service portfolio formation. The formal problem is categorized as a nonlinear, multicriteria Boolean programming task. Growing demands for alignment between service packages and user needs, coupled with the resource constraints of modern IT infrastructures and the complexity of inter-service dependencies, highlight the need to solve large-scale optimization problems. To address this, a hybrid method is proposed, combining problem decomposition into subproblems, the application of metaheuristic techniques for their resolution, and heuristic procedures for integrating partial solutions. The paper presents experimental results demonstrating the effectiveness of the proposed approach. Additionally, it outlines system-level design solutions that support the development and implementation of the information system for service portfolio formation.
Copyright (c) 2025 Максим БУКАСОВ, Олена ЖДАНОВА, Святослав ЦИМБАЛ, Вячеслав ЧИМШИР, Ростислав ОМЕЛЬЧЕНКО https://creativecommons.org/licenses/by/4.0
INFORMATION AND LASER SYSTEM FOR ASSESSING HARMFUL MAN-MADE EMISSIONS
At the current stage of development in the energy, chemical, mechanical engineering, and printing industries, there is extensive use of environmentally hazardous resources such as coal, oil, natural gas, paints and coatings, and polymer materials. The high production intensity driven by market demands leads to increased consumption of energy and raw materials, which in turn causes a rise in concentrations of dust, toxic gases, and harmful liquid emissions into the atmosphere and water systems. This contributes to growing environmental pollution, the real-time assessment of which is often impeded by the limitations of conventional data collection methods. In response, new approaches have been substantiated for the development of sensors capable of measuring levels of air contamination, particularly dust and toxic substances. These innovations are based on novel physical principles, enabling the creation of laser-based pollution concentrators, sensors utilizing the optogalvanic effect, and integrated systems that combine ion-selective sensors (such as OCM 5M) with measurement platforms. Such technologies enhance the overall effectiveness of environmental monitoring and safety systems. A comprehensive solution to this issue involves the establishment of global environmental monitoring networks that rely on information and intelligent technologies, as well as the development of next-generation sensor models. Environmental monitoring has remained a critical issue for over a century, as industrial progress — from railroads and textile production to thermal power and petrochemical complexes — has brought not only prosperity but also significant environmental degradation. The impact has been especially pronounced with the advancement of nuclear energy and jet aviation, and further intensified by the consequences of the First and Second World Wars. More recently, the war in Ukraine has introduced a unique set of ecological threats, including explosions, damage to energy infrastructure, and the destruction of oil terminals.
Copyright (c) 2025 Любомир СІКОРА, Наталія ЛИСА, Ольга ФЕДЕВИЧ https://creativecommons.org/licenses/by/4.0
The METHOD FOR ASSESSING THE QUALITY OF FINGERPRINT COMPARISON BASED ON CONVOLUTION OF BOOLEAN METRICS
The proposed approach is designed to determine the degree of similarity between fingerprints. It is based on the comparison of key features of papillary patterns. This method can be used to compare both a pair of fingerprints and one fingerprint with a group of others. Within the framework of this approach, basic metrics are used that reflect the presence of matches between the compared fingerprints. Based on these metrics, the following characteristics are calculated: the percentage of matching features and the weighted average score, taking into account the significance of each match. These parameters are used to establish the belonging of a fingerprint to a certain group. To control the results, threshold values are used, established on the basis of the Bayesian classifier and the Neyman-Pearson lemma, taking into account the differences in the distribution of scores. Testing conducted using the FVC2000 database showed that the accuracy of comparing individual fingerprints is 93.81%. The method is implemented in Python using the Pandas and NumPy libraries. This allows it to be integrated into automated fingerprint identification systems (AFIS). Resistance to moderate distortions and interpretability of parameters indicate its practical applicability, in particular, in the field of forensics. One of the limitations of the method is its susceptibility to strong fingerprint distortions. Further development plans include the introduction of adaptive thresholds and integration with deep learning methods to improve the process of feature extraction on fingerprints. This development is aimed at increasing the accuracy and reliability of biometric identification, which is extremely important for reducing the likelihood of errors, especially in the context of forensic tasks.
Copyright (c) 2025 Юрій ПОГУЛЯЄВ, Кирило СМЕЛЯКОВ https://creativecommons.org/licenses/by/4.0
A META-MODEL FOR LOW-CODE CONFIGURATION AND DEPLOYMENT OF CONTENT-BASED IMAGE RETRIEVAL SYSTEMS
The object of this study is content-based image retrieval (CBIR) systems with configurable architectures, and the subject is the meta-model for low-code configuration and deployment of CBIR systems. The goal of this work is to develop a meta-model for CBIR systems that enables their low-code configuration and deployment. The proposed meta-model allows users to define a CBIR system by selecting and combining the CBIR components from a predefined catalog, after which deployment artifacts are automatically generated and can be easily deployed. The proposed meta-model formalizes CBIR components: image repository, feature extractor, feature database (logical and physical levels), similarity measure, result aggregator, and user interaction layer; and extends them with two meta-level components: a configuration manager and a deployment engine. The architecture was implemented using Docker for containerization, Spring Boot starters for modularity, and a web-based graphical interface for configuration. A prototype was developed and tested on a dataset of 100 000 images, with systematic variation of component combinations. Experiments confirmed that the meta-model enables rapid reconfiguration and deployment of CBIR systems, allowing the evaluation of performance under different configurations. The examined difference between the best and worst tested configurations highlighting the significant effect of component selection on system performance. Scientific novelty lies in introducing a formalized meta-model that integrates low-code principles into CBIR design, combining modular architecture, containerized deployment, and graphical configuration in a single framework. The practical significance of the solution is in simplifying CBIR experimentation for researchers and practitioners without deep programming expertise, enabling rapid prototyping, testing, and deployment of customized CBIR systems.
Copyright (c) 2025 Станіслав ДАНИЛЕНКО, Сергій СМЕЛЯКОВ https://creativecommons.org/licenses/by/4.0
INFORMATION SYSTEM FOR ADAPTIVE TRANSPORTATION PLANNING WITH CONSIDERATION OF ROAD TRAFFIC VARIABILITY
This paper presents an information system for adaptive transportation planning that integrates the classical linear-programming transportation problem with a time-dependent cost model approximated by a combination of normal probability density functions. The proposed mathematical model implements discretization of the 24-hour interval into equidistant time steps, which enables correct accounting for diurnal variations in road conditions while preserving high computational efficiency. A unified operational algorithm was developed based on the classical Simplex method, and key methods for constructing an initial feasible plan for the transportation problem were implemented to allow comparative analysis of performance and accuracy in dynamic conditions. The outcome of the study includes an intuitive web interface implemented with React, using react-vis for charting, Leaflet for interactive maps and OSRM for routing, together with a server module written in Go that employs the gonum/lp library for solving linear-programming problems. The proposed architecture provides fast interaction between client and server modules, high scalability and straightforward cross-platform deployment. Experimental validation confirmed the correctness of the model both in cases with static cost coefficients and in the enhanced time-dependent transportation formulation. In particular, the system supports automated temporal analysis of solutions and identification of cost-optimal departure times. In the intercity scenario dynamic optimization yielded up to 7.2 % savings relative to the worst static scheduling alternative, while in the urban scenario accounting for time-dependent costs produced savings up to 47.8 % for evening departures compared to the typical morning peak — consistent with observed urban traffic patterns. A comparative analysis with leading commercial transport management systems demonstrated that, despite its streamlined architecture, the proposed system delivers the required level of flexibility and adaptivity while markedly reducing implementation and maintenance costs. Consequently, it constitutes an accessible and transparent tool for educational institutions, research activities and local logistics projects in small and medium-sized enterprises.
Copyright (c) 2025 Гліб ІЩЕНКО , Олександр ШЕВЧУК https://creativecommons.org/licenses/by/4.0
CONSTRUCTION OF A FORMAL MODEL OF THE EXCURSION SELECTION PROCESS FOR STUDENTS: A CASE STUDY OF THE “PUSH” SCHOOL IN KHARKIV IN THE FORM OF A LOGICAL AFP-NETWORK
The article is devoted to the study of the finite predicate algebra toolkit for constructing a network model aimed at formalizing the process of selecting educational excursions for students of general secondary education institutions, in particular for the “Push” School in Kharkiv. The objective of this work is to develop a corresponding mathematical model in the form of a logical AFP-network. The organization of excursions constitutes an important component of the educational process, as it enables the integration of learning, recreation, social interaction, and career guidance for students. In the context of modern challenges—such as ensuring safety, aligning with educational objectives, and optimizing costs—there is a clear need for the development of effective methods for planning and selecting excursions, which determines the practical relevance of the research problem. The application of predicate algebra in this domain has made it possible to formalize the excursion selection process while accounting for a wide range of parameters, including cost, duration, safety level, student categories, interests, educational objectives, accommodation conditions, and others. The methodology for constructing logical networks provides a systematic analysis of the subject area and enables the creation of a mathematical model in the form of a complex polyadic relation through the composition of corresponding binary relations derived from the subject area analysis, thereby optimizing the processing of input knowledge. The mathematical model of the excursion selection process is represented as a polyadic predicate dependent on a set of variables, each associated with a specific domain of definition. Knowledge processing is carried out in the network nodes through conjunction and disjunction operations, with knowledge represented as predicates corresponding to subsets of the respective domains. Each binary predicate is described in the form of bipartite graphs and the corresponding formulas. The conjunction of all constructed binary predicates forms a logical network that enables iterative processing of information until a stable result is achieved. The scientific novelty lies in the developed model, which facilitates the automation of the excursion selection process while accounting for the individual characteristics of students and the resources of the school. The results of this study represent an effective tool for optimizing educational programs.
Copyright (c) 2025 Ірина ВЕЧІРСЬКА, Аліна CОКОЛОВА, Наталія ВАЛЕНДА https://creativecommons.org/licenses/by/4.0
ANALYSIS OF EFFICIENCY OF HARDWARE PLATFROMS FOR SPATIAL ORIENTATION SYSTEMS USING A UNIFIED ENERGY CONSUMPTION MODEL
This paper addresses the problem of evaluating the efficiency of hardware platforms for spatial orientation systems, with a specific focus on mobile and assistive technologies for visually impaired users. The primary purpose is to conduct a systematic comparison between two classes of compact computing devices - single-board computers and smartphones - using a unified model and method for forecasting energy consumption in distributed computing systems that was developed and validated in our previous research. The methodology integrates both simulation and experimental measurements to provide a reliable assessment of computational performance, energy efficiency, and subsystem contributions under conditions representative of real-world computer vision workloads. The chosen experimental task was based on object detection using the SSD MobileNetV1 neural network, applied to video stream processing with standardized preprocessing and postprocessing stages, enabling reproducible and cross-platform evaluation. Energy consumption was decomposed into idle, computing, and camera subsystems, with measurements obtained through controlled power supply instrumentation over extended periods to eliminate short-term deviations. Results show that Apple smartphones consistently outperform single-board computers in both computational power and energy efficiency, with CPUs delivering significantly higher throughput and lower overall energy consumption during real-time inference, while GPU acceleration via CoreML further amplifies this advantage. Smartphones also demonstrate superior thermal stability and lower idle consumption, though their advanced camera subsystems introduce additional energy costs not observed in simpler USB cameras used with single-board platforms. The experiments shown that running similar task smartphones were underloaded and had a room for running better models, unreachable for single-board computers. The overall conclusion emphasizes that for computer vision tasks in spatial orientation systems, even older-generation smartphones represent a more efficient and practical hardware base than the most advanced single-board computers, offering not only higher performance per unit of energy but also a richer set of integrated sensors and connectivity options. These findings underline the strategic importance of smartphones as the optimal hardware foundation for next-generation assistive technologies, while pointing to future research directions involving Android platforms and peripheral expansions for single-board devices
Copyright (c) 2025 Олександр МАМЧИЧ, Олеся БАРКОВСЬКА , Андрій КОВАЛЕНКО, Антон ГАВРАШЕНКО https://creativecommons.org/licenses/by/4.0
ANALYSIS OF OPTIMIZER AND HYPERPARAMETER INFLUENCE ON YOLO IN THERMAL LANDMINE DETECTION
This paper investigates the impact of optimizer choice and hyperparameter tuning on the performance of the YOLO deep learning model for landmine detection in thermal images. The aim of this work is to study the effect of different optimizers and parameter configurations on model accuracy and training stability. The object of the study is the process of detecting landmines in thermal imagery using deep neural networks. A dataset of thermal landmine images annotated in YOLO format was used for training. The experiments were conducted with the YOLOv11n architecture initialized with pre-trained weights. The varied parameters included the optimizer (SGD or Adam), learning rate, and batch size. Each model was trained for 50 epochs, and performance was evaluated using mAP, precision, and recall metrics. The study provides a comparative analysis of the influence of Adam and SGD optimizers on the accuracy and stability of YOLO when trained on a limited dataset of thermal landmine images. The results suggest that, given appropriate configuration, SGD is capable of achieving performance competitive with adaptive methods, despite their popularity. The experiments also confirm the feasibility of achieving high detection accuracy even with a relatively small dataset. All configurations achieved high mAP values. The Adam optimizer enabled a faster initial reduction in loss functions, whereas SGD provided smoother and more stable training dynamics. The highest precision and recall were obtained in the experiment with SGD at a learning rate of 0.01 and batch size of 64, making this configuration the most promising for further research. The findings on optimizer and hyperparameter selection can be applied to improve the efficiency of automated thermal image analysis systems based on unmanned aerial vehicles, contributing to safer and faster detection of explosive hazards.
Copyright (c) 2025 Наталія МЕЛЬНИКОВА, Анна ВЕЧІРСЬКА https://creativecommons.org/licenses/by/4.0
EFFICIENCY ANALYSIS OF FINANCIAL TIME SERIES FORECASTING MODELS UNDER MARKET TURBULENCE CONDITIONS
This paper presents a comparative analysis of financial time series forecasting models' effectiveness under market turbulence conditions. The study focuses on evaluating the adaptability of statistical ARIMA model and recurrent LSTM neural network across different prediction horizons during periods of high market volatility. Daily OHLC data from five major technology companies (Google, Apple, Amazon, Meta, Oracle) for the period 2020-2025 was analyzed, with particular emphasis on the turbulent April-June 2025 period. Three model architectures were implemented: ARIMA(2,1,0), LSTM Bidirectional Autoencoder (100 units), and simple LSTM (20 units). Testing was conducted on 5, 15, and 30-day forecasting horizons using MAPE, RMSE, and MAE metrics. Additionally, residual analysis through autocorrelation function examination was applied to validate model quality. Results demonstrate that ARIMA excels in short-term forecasts (5 days) with MAPE ≤ 0.06, but its effectiveness diminishes on medium-term horizons due to inability to adapt to market turbulence. Simple LSTM (20 units) achieved optimal balance between accuracy and stability, outperforming ARIMA by 30.75% on medium and long-term forecasts. Complex LSTM Autoencoder proved least effective due to overfitting on market noise. The scientific novelty lies in comprehensive analysis of model adaptability to extreme market turbulence using residual analysis as additional validation method. It was proven that simpler LSTM architectures outperform complex ones under high volatility conditions. The practical significance includes optimization of algorithmic trading strategies and risk management systems during market instability periods, particularly valuable for financial institutions and investment funds.
Copyright (c) 2025 Олег ПАСТУХ, Юрій ПЕТРОВ https://creativecommons.org/licenses/by/4.0
RESULTS OF APPLICATION OF INFORMATION TECHNOLOGY FOR PROCESSING AND ANALYSING ELECTROCARDIOGRAM SIGNALS TAKING INTO ACCOUNT THEIR MORPHOLOGICAL AND RHYTHMIC CHARACTERISTICS
This paper presents an information technology for comprehensive processing and analysis of electrocardiographic signals considering their morphological and rhythmic characteristics based on a cyclic random process mathematical model for improved cardiac pathology detection. The proposed information technology utilizes a cyclic random process (CRP) model that naturally accounts for the quasi-periodic structure of ECG signals with variable rhythm. The system implements sequential and parallel processing through interconnected functional blocks: preprocessing (baseline drift removal, noise filtering), automatic segmentation for cycle boundary detection, rhythm function formation using cubic spline interpolation, cyclic signal transformation ensuring equal sample counts per cycle, and separate statistical processing of morphological and rhythmic features. Experimental verification was performed on real ECG signals from patients diagnosed with atrial fibrillation and atrial flutter. The technology successfully segmented ECG signals and quantified both amplitude and temporal variability. For atrial fibrillation, the rhythm function demonstrated significant variability (400-800 ms range) with sharp transitions between adjacent values. For atrial flutter, the rhythm function showed greater stability (150-230 ms range) with smoother fluctuations. Statistical analysis revealed distinct patterns of morphological variability, with dispersion values reaching 0.004 mV² for atrial fibrillation and 0.025 mV² for atrial flutter. The key innovation lies in the simultaneous yet separate analysis of morphological and rhythmic characteristics through rhythm function incorporation, enabling comprehensive assessment of both amplitude variability and beat-to-beat dynamics within a unified CRP framework. The developed technology enables automated differentiation between various cardiac pathologies through independent classification of rhythmic and morphological abnormalities, supporting clinical decision-making in cardiac diagnostics and real-time monitoring applications.
Copyright (c) 2025 Андрій СВЕРСТЮК, Любомир МОСІЙ https://creativecommons.org/licenses/by/4.0
ANALYSIS OF FRESCHET AND HAUSDORF METRICS AND THEIR MODIFICATIONS FOR IMAGE COMPARISON
This paper provides a comprehensive analysis of classical and modern metric approaches used for quantitative evaluation of image similarity, including the Fréchet and Hausdorff distances as well as their modifications – the Gromov-Fréchet and Gromov-Hausdorff metrics. The relevance of this research is determined by the wide use of image comparison methods in computer vision systems, where they form the basis for segmentation, classification, and object detection in various application domains, particularly in medicine. Images are represented as polygons, which unifies computational procedures and simplifies the formal description of distance measurement algorithms. The properties of the considered metrics were compared, and computational experiments demonstrated that the Fréchet distance effectively reflects the similarity of polygon contours, while the Hausdorff distance is more suitable for comparing inner regions. The Gromov-based modifications provide minimal distances and more flexible results when dealing with objects of complex structure. Algorithmic solutions for each metric are described, with an emphasis on their computational complexity and possible practical applications. Special attention is given to isometric transformations, which reduce matching errors. The results were validated through experiments implemented in Java with the OpenCV library, proving the adequacy and efficiency of the proposed approaches. The practical value of the research lies in the potential integration of the obtained results into automated medical diagnostic systems for the analysis of histological, cytological, and immunohistochemical images. The proposed algorithms may serve as a basis for developing effective segmentation and classification methods for biomedical data.
Copyright (c) 2025 Микола БЕРЕЗЬКИЙ https://creativecommons.org/licenses/by/4.0
SYNTHESIS OF RECURSIVE DEVICES FOR VERTICAL-GROUP CALCULATION OF BASIC MULTI-OPERAND NEUROOPERATIONS
The operational basis of artificial neural networks has been determined, comprising groups of the following neurooperations: preprocessing, processing, and computation of transfer functions. A set of basic multi-operand neurooperations was selected for hardware implementation, including: finding maximum and minimum values in a one-dimensional data array, calculation of the sum of squared differences, scalar product calculation. The methods of vertical-group computation of basic multi-operand neurooperations (finding for maximum and minimum values in a one-dimensional array, calculation of the sum of squared differences, and scalar product calculation) have been improved. Using the selection of number of bits for operands group for single-cycle processing, these methods enable synchronization of data arrival time with calculation time and ensure high hardware utilization efficiency during the hardware implementation. It's proposed a recursive devices design for vertical-group computation of basic multi-operand neurooperations based on an integrated approach. This approach leverages the capabilities of modern element base, incorporates vertical methods, algorithms, and recursive device structures for implementing basic neurooperations and considers the requirements of specific applications. The principles for designing recursive devices for vertical-group calculation of basic multi-operand neurooperations have been chosen. These include: the use of a basis of elementary arithmetic operations and a multi-operand approach; modularity; pipelining and spatial parallelism; homogeneity and regularity of the structure; synchronization between data arrival time and neurooperation calculation time; specialization and adaptation of structure to specific application requirements. A format converter has been developed to transform a flow of serial input data from a one-dimensional array into a parallel-serial data output by group of bits. Basic structures have been developed. They represent calculation algorithms in terms of hardware and serve as the foundation for synthesizing of recursive devices for vertical-group calculation of basic multi-operand neurooperations with specified parameters. The method for synthesis of recursive devices for calculation of basic multi-operand neurooperations with vertical-group data processing has been improved. Through the use of mechanisms for synchronizing calculation time with data arrival time, this method provides the selection of structure which performs real-time data processing and with high hardware utilization efficiency. It has been demonstrated that the use of the improved vertical-group methods, designed basic structures of devices for finding maximum and minimum numbers in one-dimensional arrays, calculation of the sum of squared differences and scalar product, as well as the improved synthesis method, enables real-time mode and the implementation of devices for calculation of basic multi-operand neurooperations with vertical-group data processing with high hardware utilization efficiency.
Copyright (c) 2025 Іван ЦМОЦЬ, Олег БЕРЕЗЬКИЙ, Тарас МАМЧУР https://creativecommons.org/licenses/by/4.0