The method of transforming bridge is an effective method in Extenics used to solve antithetical problems. The study addresses the problem in the application of the transforming bridge, refines and improves the existing transforming bridge, optimizes the general steps, and applies it to the planning and design of a golf course to obtain a variety of effective design strategies. The further refinement of the transforming bridge will provide more specific methods for the solution of antithetical problems in various fields, and has very important application value for the formal and quantitative study of antithetical problems.

Currently, the amount of both information and knowledge is growing rapidly, and many problems faced by enterprises, organizations and individuals are characterized by non-linearity, high uncertainty and dynamism. Problems with relatively definite goals and domains and uncertain or insufficient boundary conditions leading to unclear problem expression and difficult goal achievement are called ill-defined problems. In this research, based on the method of constructing the extension model and solving the contradictory problem in Extenics, the method of constructing the initial extension model of the ill-defined problems and the method of solving the single-goal ill-defined problems are proposed by using the extensible analysis method and the extension transformation method. Finally, the feasibility of the method is demonstrated by a case study. Since this study applies a combination of formal and quantitative methods, it also lays the foundation for the intelligent solution of single-goal ill-defined problems and the study of multi-goal ill-defined problems.

In the research of extension innovation design, many innovative design elements can be formalized by multi-dimensional complex-elements, and many of them belong to heterogeneous multi-dimensional compound-elements (HMdCes) , and there are various complex relationships among them. At present, there is a lack of research on the conductive rules among these HMdCes. Based on the conductive rules of basic-element transformations, the conductive rules among HMdCes without basic-elements’ operations internally and HMdCes with multiple basic-elements or basic-element’ operations internally are established, which can provide more reasoning basis for the ideas generation of extension innovative design. Taking the design for the function and structure of ZDY series reducer as an example, the conductive rules among HMdCes established in this research are used to verify the universality and effectiveness of the rules.