Abstract: Ill-defined problems, with relatively defined goals and problem domains but expandable boundary conditions, are ubiquitous in life. It is of significant importance to provide directions for the intelligent expansion of knowledge under theoretical guidance, there by forming a comprehensive knowledge network for solving such open-ended problems. This research identifies three primary knowledge categories that constitute the foundation of complete knowledge network: descriptive knowledge of strategy generation materials, domain knowledge that delineates the initial goals and conditions of the problems, and methodological knowledge suitable for the tools employed in strategy generation. The completeness of knowledge network is validated through the achievement of the initial objectives. Finally, the feasibility of the proposed approach is demonstrated through a case study on the design of the ergonomic office chair. By adopting a hybrid approach that integrates formalization and quantification within the extension innovation methodology system, this research offers a novel pathway for establishing a comprehensive knowledge network for solving open-ended problems in an artificial intelligence context.