Abstract: In engineering, there are numerous symmetric and asymmetric systems. Common symmetric systems, such as symmetric two-phase circuits, are expressed using complex circuit models and solved through complex number analysis, significantly simplifying the analysis and computation process. However, symmetric circuits also include multi-phase circuits, while asymmetric circuits encompass two-phase and multi-phase circuits. These multi-phase circuits similarly require abstract models for expression and descriptions using a number system analogous to complex number to standardize and streamline the solving process. Based on comprehensive research into multi-phase circuits, this study constructs the Fan numbers (including Merged-number, Roll-number, and Kun-number) to address the description and solving of symmetric multi-phase circuits (differential circuits, three-phase circuits, and four-phase circuits), introduces the Cong Numbers to handle asymmetric two-phase circuits, and develops the Pan numbers (including Dui-number, Hui-number, and Yao-number) for asymmetric multi-phase circuits. Both complex number and Fan Numbers are symmetric number systems, embedding symmetry into their partial identifiers and operational rules as combined number systems. In contrast, Cong Numbers and Pan numbers are asymmetric number systems, where their partial identifiers and operational rules also leverage the formal symmetry of the system, forming combined number systems built upon symmetric number systems. Applied to multi-phase system processing, these methods greatly simplify the description, analysis, and computation of engineering systems. The Fan Numbers, Cong Numbers and Pan numbers provide the most fitting mathematical tools for the deconstruction and analysis of multi-phase systems.