The dissertation solves the actual scientific and applied problem of reducing the computational complexity of structural and parametric identification of interval models of complex objects while simultaneously ensuring the guaranteed accuracy of these models within the limits necessary for solving decision-making problems and researching the properties of these objects.
An analysis of methods and means of constructing models of the characteristics of complex objects under conditions of uncertainty was carried out. There are cases in which the use of the inductive approach and interval data analysis methods are justified for the construction of models of the characteristics of complex objects. The problems of structural and parametric identification of interval discrete models of complex objects in the form of difference equations are considered. An analysis of these methods was carried out and the use of a knowledge-oriented approach to both the description of the subject area of the researched object and the area of construction of this class of mathematical models was justified in order to reduce the computational complexity of their implementation.
The concept of identification of interval discrete models of complex objects is proposed and substantiated, which involves a combination of interval data analysis methods, a knowledge-oriented approach to both the description of the subject area of the object under study and the area of construction of a given class of mathematical models using an ontology, which collectively created the possibility of developing new, more computationally efficient methods of structural and parametric identification of interval discrete models of objects.
A new hybrid method of structural and parametric identification of interval discrete models of complex objects is proposed and substantiated, which, unlike the existing ones, is based on combined methods of interval analysis, behavioral models of bee colonies, and a knowledge-oriented approach to the description of the subject area of objects based on an ontology, which in the aggregate provided a reduction in the computational complexity of structural identification.
When developing a computer environment for interval modeling, a model verification method based on a combination of a data filtering method and a metric for evaluating the relevance of information is proposed and substantiated, which collectively ensures the completeness of the model and reduces the computational complexity of its identification.
An interval discrete model was developed in the form of a difference equation that describes the dynamics of user reactions to messages in thematic groups of social networks, which, unlike the existing ones, takes into account the reactions of users to informational messages, which made it possible to build a stable portrait of them and an optimal schedule of publications of a specialized group for maximizing the number of responses to messages.
The method of structural identification of interval discrete models of complex objects has been improved, which, unlike the existing ones, contains computational procedures for adaptive adjustment of the selection of structural elements in a way of establishing for each element of a set of structural elements the probability of selecting any element and based on the change of this distribution at different phases behavioral model of a bee colony, which collectively reduces the computational complexity of implementing the method.
Computer environments for interval modeling and analysis have gained further development, in which, unlike the existing ones, an open software architecture is implemented, which collectively ensures a reduction in the time complexity of the procedures for both the development and application of interval mathematical models.
The repository of interval discrete models of air pollution by motor vehicles and interval models of the visualization of the recurrent laryngeal nerve during thyroid surgery underwent further development, which, unlike the existing ones, contains an ontological description of both the subject area of their application and the conditions for the development of these models, which overall simplifies procedures for developing the specified class of mathematical models for users.
A software complex was developed for modeling based on interval analysis and an ontological approach, in particular, an object-oriented approach to programming was used, using the Spring Framework technology in the Java programming language, as well as the Python interpreter. Jython was chosen as the Python interpreter, which is completely written in Java and well suited for implementing specialized applets.
A number of studies were carried out, which allowed to confirm the effectiveness of the methods and tools proposed in the work.
Keywords: mathematical modeling, knowledge-oriented systems, ontology, interval system, decision support system.
