Requirements elicitation using goal-oriented requirements engineering (GORE) has two phases: goal decomposition and goal selection. If the goal graph, which is the artifact of the first phase, is unsatisfactory, the requirements elicited in the second phase will also be of low quality, irrespective of the goal selection method used. In this study, we focus on the first phase and propose a novel mathematical model, with the aim of producing a high-quality goal graph. Our model is based on case-based decision theory (CBDT), which can automate both goal decomposition and the selection of optimal viewpoint. We report three applications conducted to evaluate the scalability of our GDM-CBDT model. The results demonstrate that GDM-CBDT achieves its design goals but identifies a special case in which GDM-CBDT is unable to determine the optimal viewpoint. In the future, the model will be extended to treat such cases.