# A Design of CGK-Based Granular Model Using Hierarchical Structure
## 1 Introduction
[PERSON] [21] proposed recurrent self-evolving fuzzy neural network (RSEFNN), which adopts online gradient descent learning rules to solve brainwave regression problems in brain dynamics, to predict driving fatigue. [PERSON] [22] proposed prediction neural network (PNN), which is based on fully connected neural networks and CNNs, and is used for internal image prediction. [PERSON] [23] proposed an embedded backpropagation neural network comprising two hidden layers for earthquake magnitude prediction. The aforementioned fuzzy inference systems and ANNs have different processes and solve various prediction problems. In addition, studies are being conducted on solving problems by combining two or more different methods, rather than using one method. Inference systems that combine different methods are called hybrid systems, and the granular computing (GrC) [24; 25] method is adopted as a method for constructing hybrid systems. GrC is a computing theory related to the processing of information objects, called \"information granules\" (IG), that occur during the process of extracting knowledge from data and information, as well as abstractifying the data. In the computing performed in general-used fuzzy inference systems, ANNs, and deep learning methods, the model output appears in a crisp form or as numbers. If the model output is in a crisp form or a number with a clear value, the numerical error relative to the actual output value can be calculated; however, difficulties occur when the difference between the model and actual output is expressed linguistically. However, in GrC, the model output is expressed in a soft form or as a fuzzy set; hence, GrC is effective at handling and processing data and information that are uncertain, incomplete, or with vague boundaries. In the actual world, people mainly use linguistic expressions rather than numerical expressions, and the brain, which makes inferences in uncertain and incomplete environments, utilizes linguistic values instead of numerical values to perform inferences and make decisions. Accordingly, GrC can represent the process by which humans think and make decisions. The following studies on GrC have been conducted [26; 27; 28; 29]. [PERSON] [30] proposed a novel approach that develops and analyzes a granular input space and designed a granular model accordingly. [PERSON] [31] proposed fuzzy possibilistic C-means (FPCM) clustering and a GrC method to solve anomalous value-detection problems. [PERSON] [32] proposed three types of granular fuzzy regression-domain adaptative methods, to apply GrC to transfer learning. [PERSON] [33] proposed a method that adopts GrC to granularize fuzzy rule-based models and assess the proposed models. [PERSON] [34] made long-term predictions about energy systems in the steel industry by designing a granular model based on IGs created via fuzzy clustering. By analyzing the aforementioned research, it has become possible to create IGs that are generated via GrC, and to use these to design a granular model (GM), as well as calculate soft form output and express it linguistically. In addition, performance evaluation methods are proposed to evaluate the prediction performance of soft form output. However, studies are required to improve the prediction performance of granular models by creating optimal IGs, including methods for generating IGs and setting their form and size. Conventional fuzzy clustering creates circle-shaped clusters starting at the cluster's center in the input space. However, when the input space's data exhibits geometric features, a problem emerges in which the clustering is not properly performed. To address this problem, Gustafuson-Kessel (GK) clustering is employed, as it can generate clusters while considering the geometric features of the data. This study proposes context-based GK (CGK) clustering, which considers both the input space and also the output space during existing GK clustering to generate geometrically-shaped clusters.