The clinical diagnosis decision-making process of integrated traditional Chinese medicine and Western medicine is essentially a type of group decision-making (GDM) problem, which is transparently characterized by the multiformity of data types and the diversity of knowledge structures among experts. However, most existing GDM methods are designed based on single data types and cannot address GDM problems involving multiple data types and diversified attributes. Moreover, the preference-approval structure provides a simple framework to simulate the preference information regarding an individual's ranking and approval. But it only considers two categories: approval and disapproval, without accounting for the indecision of individuals. In reality, three-way decision (TWD) is common. Given the deficiencies above, this paper puts forward a novel preference-approval structure-based three-way group consensus decision-making approach for a class of GDM problems with the characteristics of incompleteness, multi-granularity, diversity, and compound. To represent the information in these complex GDM problems, we firstly present the concept of incomplete multi-granularity diversified compound decision systems (IMGDCDSs). Secondly, according to the data characteristics, we construct a non-additive TWD model over the framework of granular computing. On the one hand, using the reference point of each attribute, an acquisition method of relative loss functions is given by considering three kinds of states. On the other hand, we present a new fuzzy measure to calculate non-additive conditional probabilities. The above work enriches the existing TWD theory. Based on the three-way classification and ranking results obtained, this paper subsequently defines a preference-approval structure and establishes a new group consensus decision-making approach. Thereby, the TWD model is integrated into preference-approval structures, which further enriches the GDM theory. More importantly, some existing group consensus methods are special cases of our study. Whereafter, we demonstrate the feasibility of the approach using an illustrative example. Finally, the stability and effectiveness of the approach are verified through an empirical study in the context of medical diagnosis.