Inconsistent incomplete decision system(IIDS) has strong superiority in modeling and expressing complex data
compared with other decision systems, which shows its important value. Therefore, based on existed research results, this
paper investigates the definition method of reduction in IIDS. Five kinds of reduction in IIDS, such as possible reduct, are
presented and the relationships between them are also found out. This work can form the foundation for further studying
related theory and method of reduction in IIDS.