Propagation of knowledge from crisp and soft clustering through a granular hierarchy

Information granules allow us to abstract real world objects using their relevant attributes. Level of abstraction allows us to create a network of information granules that are connected to each other through a real-world relationship. For example, the phone calls are connected to the origin and destination phone numbers. This paper describes the relationship between clustering schemes by propagating the information through the connection between granules. We focus on the hierarchical granular graphs, where phone numbers represent the higher level (coarser) granules that are connected to phone calls which are lower level (finer) granules. The paper studies the effect of transferring crisp and fuzzy clustering schemes through the granular hierarchy. The fuzzy clustering is shown to provide a better technique for such a transfer. Rough clustering derived from fuzzy clustering is shown to be a good instrument for comparing crisp and fuzzy clustering schemes.