This study delves into the foundational underpinning of general system component methodologies, constituting the core methodologies that underlie problem-solving approaches. It seeks to elucidate the most prevalent concepts and fundamental problem-solving methods upon which applied methodologies are constructed. These core methodologies serve as the basis for the development of practical models, techniques, and problem-solving schemes, as depicted in Figure 1. The research provides a comprehensive exploration of the fundamental building blocks of problem-solving methodologies and their critical role in shaping applied methodologies.