MATHEMATICAL MODELS FOR DETERMINING THE COMPLEXITY OF OBJECT-ORIENTED DESIGN DUE TO THE RELATIONSHIPS BETWEEN CLASSES OF OPEN-SOURCE WEB APPLICATIONS CREATED USING PHP FRAMEWORKS
DOI:
https://doi.org/10.32782/mathematical-modelling/2025-8-1-17Keywords:
mathematical model, prediction ellipse, complexity, object-oriented design, relationships between classes, web application, normalizing transformation, Box-Cox transformationAbstract
The problem of determining the object-oriented design complexity of the open-source software, including Web applications created using the PHP frameworks, is important because nowadays open-source software is growing in popularity and using the PHP frameworks making application development faster. The object of the study is the process of determining the object-oriented design complexity due to the relationships between classes of the open-source web applications created using the PHP frameworks. The subject of the study is the mathematical models to determine the object-oriented design complexity due to the relationships between classes of the open-source web applications created using the PHP frameworks. The goal of the work is the build two mathematical models for determining the object-oriented design complexity due to the relationships between classes of the open-source web applications created using the PHP frameworks based on the two-variate Box-Cox normalizing transformation to increase confidence in evaluating the object-oriented design complexity of these apps.To determine the object-oriented design complexity due to the relationships between classes of open-source web applications created using PHP frameworks, two mathematical models in the form of a prediction ellipse were constructed based on the two-variate Box-Cox transformation for the normalized metrics RFC (the Response for Class) and CBO (Coupling Between Objects). The maximum likelihood method is used to compute the parameter estimates of the two-variate Box-Cox transformation. The above models are built using two test statistics based on the quantiles of the Chi-square distribution and the F-distribution, respectively. To build these mathematical models using the PhpMetrics tool (https://phpmetrics.org/), we obtained data from metrics for 125 open-source web applications created using five well-known PHP frameworks: CakePHP, Laravel, Symfony, CodeIgniter, and Yii. These applications are hosted on GitHub. The results of determining the complexity of object-oriented design due to the relationships between classes of open-source web applications created using PHP frameworks were compared.
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