## 2 Design of the CGK-Based Fuzzy Granular Model
### Optimal Assignment of IGs
When the original numerical data are input to the sub-model, the output becomes a type 1 IG. When type 1 IG that combines the output calculated in the sub-model is input to the upper model, type 2 IG is generated through context-based GK clustering. The higher the number of types, the higher the level of abstraction; thus, it can represent a more meaningful IG that is verbally explainable. The CGK-based fuzzy granular model of the aggregated structure generates IGs of the context shape in the output space and IGs of geometric shape in the input space. In this study, the IGs of the context shape generated in the output space of the CGK-based fuzzy granular model of the aggregated structure is optimally assigned through the GA [45; 46] based on biological genetics. GA sets the number of generations, cross-operation ratio, and mutation ratio and optimizes by creating a new group using genetic operators. It calculates the goodness of fit to confirm whether the new group has the optimal solution. The goodness of fit is evaluated using the PI obtained through training and validation data after the generation is created. The goodness of fit can quantitatively indicate how much the generated solution is fit for solving the problem. The sequence of GA is as follows. The initial chromosome is generated by using the upper and lower limits of the context to be optimized. The goodness of fit of each chromosome is calculated through the PI. The current chromosome becomes a parent chromosome, and from these, the offspring chromosome is generated through crossover and mutation operations. After calculating the goodness of fit of the generated child chromosomes, the above process is stopped if it is a satisfactory value; otherwise, the child chromosomes are generated again, and the above process is repeated. Figure 6 shows the flowchart of the genetic algorithm. The lower and upper limits of the context are set as candidate solutions, the fitness computation of each chromosome is calculated, and the result is repeated until satisfactory. Figure 5: Variable assignment process of IGs generated in the output space for the generation of rational IGs. The IGs of the optimally assigned output space, i.e., the IGs of the optimal context shape, are updated in the CGK-based GM to modify the spacing between contexts in the output space. In addition, IGs of the geometric shape are generated from the input space connected with each modified context to produce the optimal IGs in the input space and output space. Figure 7 shows the structure of the optimized CGK-based fuzzy granular model. Figure 8 shows the structure of the optimized CGK-based fuzzy granular model of the aggregated structure. This figure shows that IGs of the context shape are generated through the context-based GK clustering. Here, contexts are updated by optimizing the upper and lower limits of the context using GA, and through this, the optimized IGs of the geometric shape are generated in the input space. Figure 7 shows the structure of the optimized CGK-based fuzzy granular model. If you look at the output space in the figure, you can see a black context and a red context. Here, the black context is the existing context and the red context is the context optimized using GA.  
Figure 6: Flowchart of GA process. Figure 7: Structure of the optimized CGK-based fuzzy granular model.