## 1 Introduction  
In general, fuzzy sets can effectively represent ambiguous and uncertain information inherent in real-world nonlinear systems. Fuzzy sets also represent dynamic or static characteristics as a membership function and represent the degree of fuzzy membership for given data. A fuzzy inference system (FIS) can be expressed qualitatively to make it easy to understand the system and have robust characteristics for systems with uncertain information. However, FIS has to rely on the knowledge or experience of experts to obtain fuzzy rules. Meanwhile, neural networks (NNs) can analyze the input and output relationships of a system through learning and have a processing function. Hence, NN can perform processing tasks quickly. However, NNs have difficulty understanding a system because they do not have information about the given system. A complementary model, called a neuro-fuzzy system, was proposed by combining the advantages of fuzzy models and neural networks to address the abovementioned issues [1; 2; 3; 4; 5]. Studies are actively being conducted on neuro-fuzzy inference systems [6; 7; 8; 9; 10; 11; 12; 13; 14; 15]. Similar to FIS, neuro-fuzzy inference systems are expressed by fuzzy rules. As the number of input variables increases, the number of fuzzy rules increases exponentially in the grid partitioning.  
Meanwhile, granular computing (GC) is a paradigm for processing an increasing amount of information in computational intelligence and human-centric systems. Researchers have been investigating several design methods for GC [16; 17; 18; 19; 20]. The term GCwas defined as \"subsets computed with words\" in a study by [PERSON] [21]. GC is a set of computational methodologies and approaches derived from property to solve complex and realistic problems, and it encompasses techniques, theories, and methodologies that use the concept of granules to solve real-world complex problems. Among many studies, [PERSON] [22] proposed a granular fuzzy model (GFM) in which the output of this model is expressed as triangular contexts rather than numerical values for a human-centric system. The GFM uses context-based fuzzy c-means (CFCM) clustering [23] to generate the contexts in the output variable and produces cluster centers in the input space with the aid of the generated contexts. Unlike conventional fuzzy c-means (FCM) clustering, CFCM clustering efficiently produces clusters by representing the properties of the data in the input and output variables. Studies are actively being conducted on GFM [24; 25; 26; 27; 28; 29; 30; 31; 32; 33]. However, increasing the number of inputs to GFM can make it difficult for complex system designs to understand the resulting rules. The GFM has overlapping rules as the cluster centers become closer. It also has problems that are difficult to interpret fuzzy if-then rules due to many input variables.  
Therefore, we propose a CFCM-based multi-granular fuzzy model (MGFM) with hierarchical tree structures to design smaller interconnected GFMs that have a smaller number of meaningful rules. The advantage of the proposed model is that it is more computationally efficient and easier to understand fuzzy if-then rules than the GFM itself. Furthermore, we use a new performance index suitable for the output characteristics of GFM. The performance index is obtained by the unique concept of coverage and specificity. Studies on various hierarchical structures are also actively being conducted [34; 35; 36; 37; 38]. This paper is organized as follows. Section 2 describes the concept and procedure of CFCM clustering and CFCM-based GFM. Section 3 provides three hierarchical tree structures and CFCM-based MGFM with hierarchical tree structure. In Section 4, experiments on automobile fuel consumption and the Boston housing database are described. Finally, conclusions are provided in Section 5.