A novel method for constructing the optimal hierarchical structure based on fuzzy granular space

Abstract

Granular computing serves as a general framework for complex problem solving in broad scopes and at various levels. The granularity was constructed via many ways, however, for complex systems there remain two challenges including determining a reasonable granularity and extracting the hierarchical information. In this paper, a new method is presented for constructing the optimal hierarchical structure based on fuzzy granular space. Firstly, the inter-class deviations and intra-class deviations were introduced, whose properties were investigated in depth and approved mathematically. Secondly, the fuzzy hierarchical evaluation index is developed, followed with a novel model for extracting the global optimal hierarchical structure established. An algorithm is then proposed, which reliably constructs the multi-level structure of complex system. Finally, to reduce the complexity, the granular signatures are extracted according to the nearest-to-center principle; with the use of the signatures, a classifier is designed for verifying our method. The validation of this method is approved by an application to the H1N1 influenza virus system. The theories and methodologies on granular computing presented here are helpful for capturing the structural information of complex system, especially for data mining and knowledge discovery.