Hierarchical System Modeling

In this study, we present a methodology of building a hierarchical framework of system modeling by engaging concepts and design methodology of granular computing. We demonstrate that it arises as a result of designing and using locally constructed models to develop a model of a global nature. Two main categories of development of hierarchical models are proposed and discussed. In the first one, given a collection of local models, designed is a granular output space and the ensuing hierarchical model produces information granules of the corresponding type depending upon the depth of the hierarchy of the overall hierarchical structure. The crux of the second category of modeling is about selecting one of the original models and elevating its level of information granularity so that it becomes representative of the entire family of local models. The formation of the most "promising" granular model identified in this way involves mechanisms of allocation of information granularity. The focus of the study is on information granules represented as intervals and fuzzy sets (which in case of type-2 information granules lead to so-called granular intervals and interval-valued fuzzy sets) while the detailed models come as rule-based architectures and neural networks. A series of experiments is presented along with a comparative analysis.