An application of fuzzy hypergraphs and hypergraphs in granular computing

Granular computing emphasizes the exploitation of useful structures known as granular structures characterized by multi-level and multi-view. This paper studies the construction of granular structures models using fuzzy hypergraph and hypergraph, so that granules could be represented more intuitively and visually. In fuzzy hypergraph model and hypergraph model of granular computing, a vertex refers to an object, a fuzzy hyperedge or hyperedge corresponds to a granule. In particular, in the hypergraph model, the hyperedge is a partition of the universe, which is got from fuzzy equivalence relation. A fuzzy hypergraph or hypergraph relates to a set of granules and their relations in a specific granularity, and a series of hypergraphs correspond to a hierarchical structure. Based on granular structures, the mapping between fuzzy hypergraphs or hypergraphs presents the relations of the granules in different levels. The results show that it is efficient to represent the partition by means of fuzzy hypergraph and hypergraph, and it is a useful way to represent granular structures through fuzzy hypergraph model or hypergraph model.