Research on the application of mathematical modeling in artificial intelligence decision-making systems

The rapid evolution of Artificial Intelligence and its increasing application in decision-making processes across various domains necessitates the integration of advanced mathematical models to enhance accuracy and reliability. This paper explores the synergy between mathematical modeling and AI in decision-making systems, highlighting how graph theory and probability theory can significantly improve the functionality and efficiency of AI algorithms. The study begins with a comprehensive review of related works, establishing the context and relevance of integrating mathematical models in AI. In the methodology section, we delve into the fundamentals of graph theory and probability theory, laying the groundwork for their application in AI. This is followed by a detailed exposition on the design and optimization of AI algorithms, with a focus on a Deep Learning Neural Network and a Support Vector Machine (SVM). Experimental design and procedures are meticulously outlined, providing clarity on the implementation of the proposed methods.