The paper discusses an intelligent system for simulation-based modeling of information entities focused on improving the efficiency and accessibility of modeling complex information systems. The system includes an adaptive interface, automated modules designed to generate analytical descriptions and calculation modules, and a mechanism for in-depth analysis of results, which reduces the time for user training and increases the accuracy of the results. One of the key features is the use of logical and linguistic models to select optimal analytical descriptions and create procedural models, which significantly improves the simulation process. Using modern methods of mathematical logic, the system analyzes the structure of analytical formalizations of information objects. It selects optimal solutions based on the similarity of data elements stored in the database. Specialized mathematical models are used to implement operations of logical sequences and build fuzzy relations, significantly improving decisionmaking accuracy and speed while providing high flexibility in settings. The approach allows automation of the processes of developing and adapting models, reducing the time spent on model revision. As a result, the intelligent system ensures high efficiency of the simulation-based modeling of information entities. This is critical in today's digital environment, where speed and accuracy are the main factors of successful work. Intelligent systems, simulation modeling, information objects, analytical descriptions, fuzzy relations, artificial intelligence.
Given information technologies’ rapid development and integration into all spheres of life,
modeling complex systems is becoming increasingly relevant [
With the development of information technology and growing interest in simulation modeling, scientists are actively improving systems for modeling complex objects. Well-known platforms such as MATLAB, Simulink, and Ansys can provide a wide range of simulations but have limitations due to their narrow focus on specific types of tasks. In addition, they require high user qualifications and do not automatically generate analytical descriptions and store results in centralized databases, which complicates the work. These problems can be solved by developing intelligent systems that automate the modeling process, including generating analytical descriptions and model optimization without the need for deep programming knowledge. An important area is integrating artificial intelligence and adaptive interfaces to improve the accuracy of results and facilitate user training.
Well-known scientists who have significantly contributed to developing such intelligent
systems are Liu and Shi [
An essential role in developing intelligent systems is played by the work of S. Oh and J. Byun [13], who have developed methods for contextual risk assessment in cybersecurity, which allows them to be effectively used in modeling complex information objects. These methods will enable the integration of mathematical logic and artificial intelligence to create reliable and fast models. Also worth noting is the study by H. Rong and Z. Yang [14], who applied fuzzy logic to risk management in information systems, which allows for more accurate models for complex and uncertain processes.
Modern research in this area focuses on creating flexible and adaptive systems that can automate many modeling stages and improve the accuracy and speed of decision-making. This is critically important in the rapid development of digital technologies [15, 16]. The combination of modern approaches to mathematical modeling, intelligent systems, and adaptive interfaces is the basis for creating the latest tools for simulation-based modeling of information entities, which can significantly increase efficiency and reduce complexity.
To solve the task set, the paper uses modern methods that ensure effective modeling and analysis of information objects. In particular, system analysis methods are used to evaluate and optimize complex information systems, as well as simulation modeling to study various scenarios of information objects’ behavior under conditions of uncertainty and variable parameters. The theory of fuzzy sets allows us to consider uncertainty in data and decision-making, providing flexibility in processing incomplete or fuzzy information resources. Numerical analysis was used to perform calculations and evaluate the modeling results, which allowed us to obtain accurate numerical indicators of the effectiveness of various decision options. In addition, artificial intelligence methods, such as machine learning and deep learning, are used to automate the decision-making process and predict results, significantly increasing the accuracy and efficiency of simulation-based modeling of information entities.
An intelligent system (IS) for simulation-based modeling of information entities is a comprehensive tool that allows for simulation research and informed decision-making in an interactive mode. Due to the interactive approach to modeling, the system provides the ability to constantly offer the user additional information, instructions, and recommendations for practical work with models, divide the modeling process into separate stages, allowing an individual approach to each stage (automated or manual), which allows for more flexible control of the process and adaptation to specific conditions; reduce the overall time for research by automating routine stages and providing quick access.
The system is structured based on an information array that includes databases such as the
analytical descriptions database (ADB), the results database (RD), the calculation modules database
(CMDB), and the knowledge base (KB). This array provides storage and processing of data required
for efficient simulation studies and real-time decision-making. The IS is developed using the UML
language, which allows it to clearly describe its structure and interaction between components [
The interface of an intelligent system includes two main components: an innovative user and a
database interface. The clever interface adapts the information from the system components into a
user-friendly form and provides an interactive dialog between the user and the system [
The database of analytical descriptions is used to store analytical descriptions necessary for building models and conducting research. The database of calculation modules contains algorithms, ready-made calculation modules, and individual functions, procedures, and source codes in various programming languages [18]. The results database stores the results of completed tasks in multiple formats (text, graphics, tables), which allows for storing essential data about the conditions and initial parameters of the functions. The knowledge base includes fuzzy rules for selecting calculation procedures and analytical descriptions, which allows the system to adapt flexibly to changing research conditions [17]. Databases (database of analytical descriptions, the database of calculation modules, database of results) are interconnected, which ensures efficient information processing and preservation of logical relationships between tables [19].
An intelligent system for simulation-based modeling of information entities consists of several
integrated subsystems: formation of analytical descriptions, creation of calculation modules, and
analysis of results. The procedural model of the intelligent system defines data processing
algorithms, control logic, decision-making rules, user interaction, and monitoring mechanisms that
are used in decision support systems, automated control systems, robotics, expert systems,
cybersecurity, and big data analysis (Fig. 3). The modeling process is organized in such a way that
at each stage the system adapts to the specific requirements of the study, ensuring the effective use
of mathematical and linguistic models to select the most appropriate analytical tools. The analytical
descriptions generation subsystem selects and generates descriptions necessary for solving the
tasks of the simulation study based on a logical and linguistic model that allows for effective
extraction and analysis of available data from the database of analytical descriptions [
Based on the logical-linguistic model (LLM), the calculation module formation subsystem selects
and adapts procedural models from the database of calculation modules. Without the necessary
procedures, the user can independently develop the required mathematical models or adjust the
existing ones to the specifics of the problem. Thanks to this structure, the calculation module can
be formed based on ready-made components or a new one that meets the requirements of the
study [
After the computational module is generated, it is compiled and run before being used in the
results analysis subsystem. At the analysis stage, the user evaluates the results obtained and, if they
are unsatisfactory, makes adjustments to the analytical description, calculation procedure, or the
module itself, after which the compilation and execution process is repeated until the optimal
result is achieved. At the final stage, all the data obtained are stored in the result databases, and
analytical descriptions, calculation procedures, and modules—in the corresponding databases of
analytical descriptions and databases of calculation modules, thereby providing the possibility of
further processing and use of research results [
To illustrate the mechanisms of analysis and generation of calculation procedures in an intelligent
system, advanced mathematical models can be used to assess the similarity of analytical
descriptions and adaptation of calculation procedures. This makes it possible to detail the process
of selecting the most relevant tools and modules and optimizing modeling efficiency. A multi-level
equation-type index is used to assess the similarity between analytical descriptions [
The LLM for selecting analytical descriptions (LLMVAO) provides an efficient search and
adaptation of analytical descriptions in the database to solve specific modeling or analysis tasks.
The main goal of this model is to optimize the process of finding appropriate solutions by
systematizing and evaluating the parameters that characterize each description. The model’s input
parameters are variables that reflect various aspects of the description’s relevance to the problem.
These are the degree of correspondence to the type of equation ( ), the degree of correspondence
to the subject area ( ), the degree of correspondence to the input ( ) and output ( )
parameters, and the degree of correspondence to the keywords ( ) [14]. The generalized
evaluation of the task description relevance is calculated using the formula:
where is a generalized conformity assessment, and are the
weighting coefficients that determine the significance of each criterion, and
is the value of the relevant criteria. The weighting coefficients are set so that their sum equals one
, and the criteria values are normalized from 0 to 1 [
To adapt the computational procedures, a model is used that considers the sum of the squares of deviations between the values of the input and output parameters of the problem and the selected analytical description. The corresponding formula has the form [14]: (2) (3) where is the overall assessment of the description adaptation, is the input and output parameters of the problem, and
is the corresponding parameters of the selected description. Suppose the value of exceeds the permissible threshold. In that case, this indicates a significant discrepancy between the task parameters and the chosen analytical description. It requires mandatory adjustment of the current description or, if it is not appropriate, additional analysis to find an alternative description that better meets the established criteria. Thus, the LLM for selecting analytical descriptions has several significant advantages that make it particularly effective for modeling tasks. In particular, it provides a high-efficiency level due to the ability to automate the processes of selecting analytical descriptions, which can significantly reduce the time and resources required to analyze large amounts of information. At the same time, the model demonstrates high flexibility by adjusting the weighting coefficients, and it can be adapted to the specific requirements of the task, taking into account the different significance of criteria, such as compliance with the type of equation, subject area, or keywords. In addition, the modular structure of the LLMBAO allows for easy integration of new evaluation criteria or changes to existing ones, which will enable it to be quickly adapted to new conditions or changes in task requirements. Thus, LLMBAO is a versatile tool capable of supporting all stages of working with analytical descriptions, from their search to adaptation and improvement, which is especially important for solving complex and dynamic modeling problems in modern conditions.
The effectiveness of the LLM for selecting analytical descriptions largely depends on its ability to find relevant descriptions and adapt them to the specific requirements of the task. Adjusting calculation procedures or developing new ones is often necessary when working with a large amount of data and various analytical descriptions. To ensure such adaptability, an approach is used that considers the descriptions’ main characteristics and ensures optimal compliance with the task at hand. To adapt computational procedures based on LLMs, a model can be used that includes a set of criteria that take into account the type of equation, subject area, input and output parameters, and keywords. The mathematical model of adaptation can be described as follows: where is adapted calculation procedures, is a function for assessing the correspondence of the type of equation , is a function for assessing the correspondence of the subject area , is a function that takes into account the relationship between input ( ) and output ( ) parameters, is keyword matching function, is an integral function that takes into account all the relationships between the parameters, are weighting coefficients that determine the importance of the corresponding functions in the overall model [13]. The and function can be nonlinear, which allows for complex dependencies between parameters. For example, the function can be represented as: (4) (5) where is the value of the input and output parameters for the level of the problem, is the weighting coefficient for the level, is an integral function that takes into account all the relationships between the parameters, is the number of parameter levels [10]. The values of the weighting coefficients ( ) are determined empirically or based on historical data, which allows the model to be adapted to specific conditions and tasks. This formula describes a multifactorial process of adaptation of calculation procedures in which model parameters affect the final result individually and through interaction. Depending on the values of the weighting coefficients, the system can prioritize specific criteria, ensuring the model’s flexibility.
The integral function allows us to consider non-linear dependencies that may arise in realworld problems. Thus, the model improves the efficiency of procedure selection and enables the development of new ones that meet complex research requirements. The following model can be used to evaluate the modeling results and make adjustments: where is the result of the evaluation, which determines the degree of compliance of the obtained results with the expected ones, is the obtained results of the simulation, is the expected result. The function defines a metric that can be used to compare the two data sets, such as the mean square error (MSE) or other relevant criteria. In the case of unsatisfactory results, the system can return to previous steps, such as adjusting the analytical description or computational procedures, to improve the result.
In the modeling process, after each stage of compilation and execution, it is necessary to evaluate the results and decide on further steps. This can be described as an iterative process: where is the optimal modeling result, is a function representing the step in adaptation and correction, and is the iteration index. The iterative process will continue until the desired result is achieved, with the system constantly adapting based on the received at each stage.
A similarity index is used to evaluate the similarity between analytical descriptions, considering
the difference between the corresponding elements of the analytical description and the type of
equation. This approach allows us to quantify the degree of similarity between the descriptions. If
the index value is small, this indicates a high correspondence between the descriptions. The
improved mathematical model of the similarity index is as follows [
The elements of the two methods (original and adapted) are compared to adjust the calculation
procedures. If the difference between them exceeds a specified threshold, the user can adjust the
corresponding procedures [
is the element of the adapted calculation procedure, is the number of elements in the procedure. If the difference exceeds a certain threshold, it signals that the procedure needs to be adjusted. The user can make changes to the calculation procedure using functional elements from the calculation module database.
We use the optimality index, which compares the calculated results with theoretical values to
evaluate the effectiveness of the calculated results. The greater the difference between them, the
less optimal the results are [
Each analytical description is formed through equations, input, and output variables to perform simulation-based modeling of information entities. The classification of analytical descriptions by the type of equations is carried out using a logical model of key search, which allows the assessment of the degree of similarity between two descriptions and determines the optimal parameters for their combination within the simulation modeling (Fig. 4). This ensures automated selection of the most relevant models for further modeling and analysis of information objects.
The logical key search model improves the accuracy of simulation modeling by optimally matching input and output variables.
For this purpose, each analytical description is assigned an equation-type index, which is
determined by the hierarchical distribution of equations. At the first level of the hierarchy, the type
of equation is determined, after which the first digit of the index is set; similarly, at each
subsequent level, the following numbers of the index are determined. For example, for
deterministic algebraic linear systems of equations, the equation type index will be “1111” [
Each analytical description is assigned an index that determines the type of equation. The index
is formed through the hierarchical distribution of equations, where at each level the index number
is determined according to the type of equation [
The difference between their equation-type indices determines the similarity between the two
analytical descriptions. The difference is calculated modulo [
If the number of index bits does not match, it is necessary to supplement them with zeros of the
same length to compare them correctly [
, we add zeros to the lowercase index: where
is a parameter vector with the following components and belongs to the set , and the dimension of the vector is defined as
If the indices have a different number of digits, zeros are added to the smaller index to ensure a correct comparison. This avoids errors in the similarity assessment since both indexes have the same number of elements.
A more minor difference between the indices indicates greater similarity between analytical descriptions. The difference determines how close a description is to another, and this allows us to optimize the process of developing descriptions: where is the similarity score between two analytical descriptions, and is the difference between the equation type indices. The similarity score can be defined as the inverse function of the difference . The smaller the difference, the higher the similarity between the descriptions. This definition helps to reduce the time required to develop new descriptions because, with high similarity, the system can use existing descriptions with only minor adjustments.
The development of intelligent systems for simulation-based modeling of information entities involves using modern mathematical tools, including fuzzy logic, to formalize complex processes and make decisions in a multifactorial environment. One of the key steps in building such a solution is to define a membership function that allows us to display a fuzzy relation for each rule. This relation is defined as:
T-implication is a more general and flexible type of implication that is often used in fuzzy sets and fuzzy logic systems to model logical relationships between elements. It includes mathematical operations that take into account fuzziness and fuzzy relationships between components and is formalized as follows: where , and is a parameter whose value is determined by solving an optimization problem, which, having an optimal value, ensures accurate adaptation of the model to changing conditions.
The membership function for the fuzzy set is given as: where is the norm, the expression is used, subject to
The resulting membership function that describes the output of the model is defined as: (18) (19) (20) (21) (23) (24)
The proposed model allows for effective adaptation to changing conditions and optimization of system parameters. Thanks to modern algorithms and fuzzy logic methods, the system ensures accuracy and reliability in the simulation-based modeling of information entities, which is vital for analyzing complex technical systems and decision-making.
Simulation-based modeling of information entities is a crucial tool for analyzing complex systems. A logic-linguistic model (LLM) is used to automate the selection of calculation algorithms, which is based on the use of rules, fuzzy sets, and mathematical formulas to determine optimal solutions. Its advantages include fast decision-making, high accuracy due to the adaptation of algorithms, and flexibility in selecting procedures depending on input conditions. The LLM works with four main parameters:
1. (logical key) defines the structure and organization of the data used in the system. It allows the system to identify the information required for computation and analysis. is critical for correctly selecting algorithms based on a particular data type.
2. (method accuracy) shows how accurate the algorithm results are. This parameter depends on the absolute error. The lower the absolute error, the higher the accuracy, which allows the model to reflect real processes more accurately (22) 3. (calculation procedure execution time) determines the performance of the algorithm. The execution time characterizes the efficiency of using computing resources. The following formula is used to calculate it where is the actual execution time, is the optimal time for this task.
4. (compliance of the procedure with the analytical description) reflects the level of coincidence between theoretical calculations and practical results. The integral indicator calculates it where is a membership function that characterizes the quality of the matching results.
Analyzing the values of these parameters allows us to determine one of three possible scenarios of system operation:
1. If the values of all parameters are high, the system operates in optimal conditions. In this case, a ready-made calculation procedure is used, which ensures fast and efficient execution of the task without the need for additional configuration.
2. If one or more parameters have average values, the system suggests an algorithm that needs to be adjusted. This allows us to adapt the existing approach to the current conditions and ensure it meets the objectives.
3. If all parameters have low values, this indicates significant deviations from optimal
conditions. In such a situation, the system recommends developing a new algorithm that considers
the task’s specifics and current constraints [
Integrating such mechanisms into simulation modeling provides efficiency and flexibility in solving complex problems, allowing algorithms to adapt to changing conditions and achieve high accuracy of results [14].
The optimality criterion is used to determine the optimal algorithm:
where and are weighting factors that reflect the importance of each parameter [
The system’s adaptability is also taken into account, which characterizes its ability to respond quickly to changes in input parameters: where is the algorithm adaptation speed
For decision-making, LLM uses membership functions based on fuzzy sets [
is determined by the following formula:
In this case, the fuzzy relation is used to calculate the supremum: where is the intersection operation of fuzzy sets [20].
Normalization of input parameters is a crucial step to ensure the correct use of
and values. For this purpose, the parameter values are normalized on the interval [
The triangular membership function is used to evaluate the boolean key are the minimum and maximum values, (25) (26) (27) (28) (29) (30) (31) : (32) where are the points that define the shape of the triangle.
To improve the stability of the model, a modified T-implication formula is used: where is a parameter that controls the level of smoothing [18].
The aggregation of membership functions to determine the complex membership of all parameters is carried out by the method of summing weight functions [9]: where is the weighting factor of the parameter where .
The weighting coefficients are calculated based on the Analytic Hierarchy Process (AHP) [22]: where is the parameter importance score.
Shannon entropy is used to determine the level of uncertainty of the result [19]: The gradient descent method is used to select the optimal values of the model parameters: where are the model parameters, is the learning coefficient, and is the loss function.
The quadratic loss function is used to assess the model’s accuracy: where is the real value, is the predicted value.
A heuristic criterion is used to determine the best solution:
In general, the LLM ensures the efficiency and accuracy of the choice of algorithms for simulation modeling. It is based on clearly defined rules, mathematical models, and criteria that allow adapting solutions to the specific conditions of the task [17].
The development of an intelligent system for simulation-based modeling of information entities
includes hardware, software, and information software, as well as integration with modern web
technologies for access via the Internet. The system is implemented through a web interface, which
ensures cross-platform compatibility with various operating systems [
Developing an intelligent system for simulation-based modeling of information entities is essential for optimizing processes and improving decision-making efficiency. The basis of such a system is the integration of modern technologies, including adaptive interfaces and automated modules designed to generate analytical descriptions and calculation modules, significantly reducing time costs and user qualification requirements. This provides quick access to customized solutions for new tasks and increases the efficiency of simulation modeling. One of the key innovations is the (33) (34) (35) (36) (37) (38) (39) model of logical key formation, which is based on the analysis of analytical formalizations of research objects and uses modern mathematical logic methods to optimize data use. This ensures a reliable and flexible approach to information processing, automating critical research stages and improving the accuracy of results.
The developed LLM for selecting analytical descriptions through similarity analysis and using fuzzy relations simplifies and speeds up the selection of optimal solutions for modeling. The mechanism of implication using one-parameter G-norms (Greenberg norms), which are aimed at improving the decision-making process in complex and uncertain conditions, allows automation of the process of adapting procedural models, which reduces the time spent on model revision and enhances the quality of results. The basis of such a system is the ability to efficiently process and analyze a set of input parameters that affect the efficiency and accuracy of the tasks performed. Since such systems often face large amounts of data and the need to adapt to dynamic changes in conditions, using G-norms allows solving these problems with the help of fuzzy logic and mathematical models.
The use of fuzzy logic in the system allows for effective taking into account uncertainty and ambiguity, reducing the uncertainty of results and increasing the system’s stability in the face of changing input parameters. The model adapts to evolving conditions and optimizes parameters, which are vital for analyzing complex technical systems and making real-time decisions.
Thus, an intelligent system for simulation-based modeling of information entities significantly improves the efficiency of scientific research, reduces the time for calculations and modeling, and increases the accuracy and reliability of the results, making it an essential tool for many information systems.
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