Tolerance Granular Computing based on incomplete information system

At present GrC mainly is divided into three categories: computing with words (CW), rough set (RS) and quotient space (QS). From the perspective of essential characteristic of GrC, this demarcation is not comprehensive and accurate. In fact, CW is based on fuzzy granules (fuzzy subset) and both RS and QS are based on disjoint granules, which essentially are equivalence classes, either equal to each other or with empty overlap. In practical application, intersecting granules however need to be handled. Therefore there is another kind of GrC which is based on intersecting granules. This kind of GrC is referred to as tolerance GrC (TGrC) in our work. By constructing a Boolean algebra on super-granular space and a decision algebraic system, this paper will present an incomplete information system-based TGrC. With the TGrC, an example about extracting rules incomplete information is given, so as to show its basic principle.