## 5 Conclusions  
In this paper, we proposed the optimized fuzzy-based granular model based on a hierarchical structure and optimal information granule allocation. Conventional fuzzy clustering generates clusters by calculating the distance between the center of the cluster and the data using the Euclidean distance. However, there is a problem in that the performance decreases when the data points have geometric characteristics. To improve this problem, GK clustering is used. GK clustering uses Mahalanobis distance to calculate the distance between the center of the cluster and the data to generate a geometrical cluster. On the basis of GK clustering, we proposed context-based GK (CGK) clustering, which generates the contexts in the output space and estimates the clusters each context. The advantages of the proposed CGK-based granular model can be summarized as follows:  
Firstly, it is possible to automatically generate the explainable and meaningful fuzzy if-then rules that can be expressed linguistically by generating information granules in the input space and output space from numerical input and output data. Next, it is effective to process numerical input data points with specific geometric features. Since the output of the CGK-based granular model can be presented by the fuzzy number, it is possible to express the prediction result linguistically. Finally, we improved the performance by designing the CGK-based granular model with the aggregate structure that combines the linear regression model, neural network with multilayer, and radial basis function neural network. In the future, based on the rational information granule generation principle, we plan to conduct the studies on generating various types of information granules and optimally allocating the information granules created in the input space and output space. In addition, we plan to design information granules that combine not only aggregated structures but also other types of hierarchical structures and predictive models. Conceptualization, C.-U.Y. and K.-C.K. ; Methodology, C.-U.Y. and K.-C.K. ; Software, C.-U.Y. and K.-C.K. ; Validation, K.-C.K. ; Formal Analysis, C.-U.Y. and K.-C.K. ; Investigation, C.-U.Y. and K.-C.K. ; Resources, K.-C.K. ; Data Curation, C.-U.Y. ; Writing-Original Draft Preparation, C.-U.Y. ; Writing-Review and Editing, C.-U.Y. and K.-C.K. ; Visualization, C.-U.Y. ; Supervision, K.-C.K. ; Project Administration, K.-C.K. ; Funding Acquisition, K.-C.K. All authors have read and agreed to the published version of the manuscript. This study was supported by research fund from Chosun University, 2022. Institutional Review Board Statement: Not applicable. * [PERSON] and [PERSON] (2018) [PERSON], [PERSON]; [PERSON], K.C. Performance comparison of ANFIS models by input space partitioning methods. _Symmetry_**2018**, _10_, 12. [CrossRef]
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