Due to the increasing complexity of the real world, the concept of granular computing came into being. As its key topic, granular clustering still has some problems. First, the existing fuzzy granular data only describe the linear properties of membership. Moreover, the existing methods lack global optimization of granular data boundaries. Last, the existing granular clustering methods generally treat all attributes uniformly, which is not sufficient. Consequently, in this study, we propose an overall architecture for granular modeling and clustering for parabolic granular data, including the PGMO and WKFC-PG algorithms. Innovation is reflected in the following aspects. Novel coverage and specificity functions are designed, and a parabolic granular data structure is established. Whereafter, the idea of PSO is introduced to optimize granular data boundaries. Finally, the attribute weight, the sample weight, and a new distance measure are raised. Experiments verify that our overall archi...

At present, there exist some problems in granular clustering methods, such as lack of nonlinear membership description and global optimization of granular data boundaries. To address these issues, in this study, revolving around the parabolic granular data, we propose an overall architecture for parabolic granular modeling and clustering. To begin with, novel coverage and specificity functions are established, and then a parabolic granular data structure is proposed. The fuzzy c-means (FCM) algorithm is used to obtain the numeric prototypes, and then particle swarm optimization (PSO) is introduced to construct the parabolic granular data from the global perspective under the guidance of principle of justifiable granularity (PJG). Combining the advantages of FCM and PSO, we propose the parabolic granular modeling and optimization (PGMO) method. Moreover, we put forward attribute weights and sample weights as well as a distance measure induced by the Gaussian kernel similarity, and then ...