Theoretical-multiset model of integration of heterogeneous information systems of the university in the context of digital transformation

In the changing digital environment, universities face the necessity of integrating heterogeneous information systems. This study focuses on a set-theoretic approach to modeling the integration of these systems. It considers the construction of a model that will effectively facilitate interaction among various information resources within the university, belonging to different platforms and formats. Special attention is paid to optimizing data exchange processes and ensuring information integrity within the common digital space of the university. This work proposes a formal integration model that allows minimizing architectural coupling and ensuring the evolutionary development of the university's digital platform. The set-theoretic apparatus is used to formalize the IT landscape. A decomposition method based on the concept of "architectural quanta" (Architectural Quantum) is applied. Metrics of structural autonomy are proposed to assess effectiveness. A formal model describing the university's information system as a collection of loosely coupled quanta is introduced. An architectural integrity condition is established, prohibiting integration through shared databases. A structural autonomy coefficient (K_sa) is developed to quantitatively assess architectural quality. The model serves as a theoretical basis for implementing automated architecture control systems based on specialized metrics (Fitness Functions) in CI/CD pipelines, which helps reduce technical debt and accelerate the launch of new educational services (Time-to-Market). The main research method employed is a set-theoretic approach to modeling the integration of heterogeneous information systems in the context of digitalization. The scientific novelty lies in applying the set-theoretic apparatus to describe and model the processes of data integration from various sources with differing structures and formats. The developed model provides a formalized representation of the integration relationships between information systems, allowing for the optimization of data exchange processes and enhancing the efficiency of the university's information resources. The research results indicate the high effectiveness of the proposed approach for creating a unified information space within the university, contributing to improved quality of education, scientific research, and managerial processes. Practical implementation of the model will enhance the university’s competitiveness in the digital economy. The feasibility of building a flexible and scalable system capable of adapting to new requirements and changes in the university's information environment is proven.