Granular Fuzzy Modeling for Multidimensional Numeric Data: A Layered Approach Based on Hyperbox

Abstract

At present, the development of most of the granular fuzzy models depends upon some well-established numeric ones. In this study, a layered approach used to directly construct granular fuzzy models based on multidimensional numeric data is presented by engaging design methodology of granular computing. The crux of the approach involves a construction of interval information granules in the output space and the corresponding hyperbox information granules in the input space. A method of constructing these information granules and the hyperbox-based granular fuzzy model formed around them is studied in detail. Two different schemes to decode the formed hyperbox-based granular fuzzy model are also presented. Furthermore, a measure of a composite quality of the formed hyperbox-based granular fuzzy model is proposed along with the concept of coverage and specificity of resulting information granules. A number of experimental studies are reported, which offer a useful insight into the effectiveness of the presented approach, as well as reveal the impact of critical parameters on the performance of the established models.