Type-2 Fuzzy Hypergraphs Using Type-2 Fuzzy Sets
Seihwan Park and Hyung Lee-Kwang
Division of Computer Science, Department of Electrical Engineering & Computer Science Advanced Information Technology Research Center (AITrc) Korea Advanced Institute of Science and Technology (KAIST) 373-1, Kusong-dong, Yusong-gu, Taejon 305-701, Korea
Hypergraphs have been applied to analyze system architecture and to represent system partitions. The concept of ordinary hypergraphs was extended to fuzzy and interval-valued fuzzy hypergraphs. In this paper, we extend fuzzy hypergraphs to type-2 fuzzy hypergraphs. Type-2 fuzzy hypergraphs are defined using type-2 fuzzy sets and satisfy the properties of hypergraphs as well as additional properties. We also show that interval-valued fuzzy hypergraphs are a special case of proposed type-2 fuzzy hypergraphs. The properties of type-2 fuzzy hypergraphs are explained using simple examples.