This article proposes an original approach at a mathematical level to the creation of multi- objective quality models for software systems. The research is based on the study and generalization of quality modeling trends of software systems and user needs in order to determine optimal principles for constructing such models. The article provides mathematical explanations that play a key role in identifying and formalizing the principles of creating multi-objective quality models of software. An important aspect is the consideration of quality model construction principles at the mathematical level, allowing for a more precise assessment and analysis of various aspects of software quality. The research results indicate that incorporating mathematical principles into the creation of multi-objective quality models for software systems can have a significant practical impact. It is established that on a practical level of developing multi-objective quality models for software systems, consideration of the principles of creating multi-objective quality models can have numerous practical implications. Specifically, the application of metrics within established principles allows for a comprehensive view of software quality and identifies areas requiring attention and improvement. This helps developers and software quality engineers make informed decisions regarding system improvement and optimization. The research has shown that creating high-quality models of quality requires attention to various aspects, from user needs to testing and continuous improvement, as well as the use of mathematical methods for their formalization and analysis. The developed principles of creating multi-objective quality models at the level of mathematical models allow the use of these models to assess and analyze various aspects of software quality, representing each model using a corresponding function that determines the relationship between quality metrics and the quality of the software itself. It is expected that further development and implementation of these principles will contribute to improving software development processes and ensure high quality of the resulting software.
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