## 1 Introduction  
A fuzzy set means a set in which each element has a degree of membership for a set. Studies on methodologies, algorithms, and structures are being conducted in various fields of application in the real world based on the fuzzy set [1; 2; 3]. Real-world problems with complex nonlinear characteristics need a hybrid intelligent model that has integrated the theories, structures, and technologies of various models. Integrating various computational techniques has an advantage over individual models for designing hybrid intelligent systems. A representative method that is frequently used with the hybrid intelligent system is the neuro-fuzzy reasoning system. The neuro-fuzzy inference system is a combined system that complements the shortcomings of the two models as a model that combines the parallel computation and learning capabilities of artificial neural networks and the human knowledge expression and explanation capabilities of the fuzzy system [4; 5; 6; 7; 8]. On the other hand, granular computing (GrC) is a computing paradigm that is newly emerging in the information processing field. GrC is a computational theory about using information granules (IGs) such as clusters, subsets, sections, groups, and classes for effective computation model design using information and knowledge about real-world applications [9; 10; 11; 12; 13]. Research related to GrC is being conducted in various fields, including information hiding in programming, granularity in artificial intelligence, divide and conquer algorithms in computational science, section computing, cluster analysis, fuzzy and rough set theory, and database. Here, using the established concept of IGs formed in the fuzzy and rough set theory helps solve problems that arise in real-world applications. [PERSON] [14] proposed a granular model (GM) that represents the model output as a fuzzy number in the form of a triangle, instead of a numerical value, based on GrC. GM generates IGs using the Context-based Fuzzy C-Means (CFCM) clustering that applies the conventional FCM clustering. The CFCM clustering generates clusters by considering data characteristics in an output space and the input space. Studies on GM are being actively conducted now [15; 16; 17; 18; 19; 20]. An analysis of the above-mentioned research trends indicates the need for research on methodology and optimization to generate rational IGs because the performance varies significantly according to the shape, size, and number of IGs. Optimization, which is a process of finding solutions closest to the correct answer under certain constraints, is widely used in service management, product development, etc. Optimization algorithms are classified into global and local optimization techniques according to the required solution level. The global optimization technique [21] aims at finding the best solution in the entire search area even though it takes time to process, whereas the local optimization technique [22] aims at finding the best solution in a partial search area within a short time. There are various methodologies for optimization techniques, and the representative methods are genetic algorithm (GA) and particle swarm optimization (PSO). GA is a computational model using [PERSON]'s theory of survival of the fittest, which explains the evolution of the biological system and a global optimization technique developed by [PERSON] [23]. After expressing the problem to be solved by GA as data structures of a given format, and then they are gradually transformed to produce progressively better solutions. The PSO algorithm is an iterative optimization algorithm that attempts at social behavior simulation developed by [PERSON] and [PERSON] [24]. It started from the movements of entities that live in groups, such as ants, fish, and birds. Optimization is performed by converting the characteristic of these entities that move in groups when sharing information among them into a simple mathematical formula (GA [25; 26; 27; 28; 29], PSO [30; 31; 32; 33; 34]).