Granular Fuzzy Modeling Guided Through the Synergy of Granulating Output Space and Clustering Input Subspaces

As an augmentation of classic fuzzy models, granular fuzzy models (GFMs) have been applied to many fields being in rapport with experimental data, models, and users. However, most of the existing methods used to construct GFMs are based on the principle of optimal allocation of information granularity, which requires that a numeric model be provided in advance. In this paper, a straightforward and convincing modeling method is proposed to directly construct GFM on a basis of experimental data. The method first granulates the output space to form some interval information granules with distinct semantics and then uses them to partition the entire input space into a series of input subspaces. Subsequently, an initial GFM is emerged by using "If-Then" rules to relate with those interval information granules positioned in the output space and structures expressed in prototypes that are produced by clustering individual input subspaces. Further, the initial GFM is also refined by continuously migrating prototypes in individual input subspaces. The experimental studies using the synthetic dataset and several real-world datasets are reported. They offer a useful insight into the feasibility and effectiveness of the proposed modeling method and reveal the impact of parameters on the performance of the ensuing GFMs. An application example is also presented to exhibit the advantages of the resulting GFM.