DoubleQuantitative Generalized MultiGranulation SetPair Dominance Rough Sets in Incomplete Ordered Information System Since the rough sets theory based on the double quantification method was proposed, it has attracted wide attention in decisionmaking. This paper studies the decisionmaking approach in Incomplete Ordered Information System (IOIS). Firstly, to better extract the effective information in IOIS, combined with the advantages of setpair dominance relation and generalized multigranulation, the generalized multigranulation setpair dominance variable precision rough sets (GMSPDVPRS) and the generalized multigranulation setpair dominance graded rough sets (GMSPDGRS) are proposed. Moreover, we discuss their related properties. Secondly, considering the GMSPDVPRS and the GMSPDGRS describe information from relative view and absolute view, respectively, we further combine the two rough sets to obtain six doublequantitative generalized multigranulation setpair dominance rough sets (GMSPDRS) models. Among them, the first two models fuse the approximation operators of two rough sets, and investigate the extreme cases of optimistic and pessimistic. The last four models combine the two rough sets by the logical disjunction operator and the logical conjunction operator. Then, we discuss relevant properties and derive the corresponding decision rules. According to the decision rules, an associated algorithm is constructed for one of the models to calculate the rough regions. Finally, we validate the effectiveness of these models with a medical example. The results indicate that the model is effective for dealing with practical problems.

An Acceleration Method for Computing Dominace Classes in Ordered Information System In rough set theory, two crisp sets (i.e., the lower and upper approximates of a target concept) is used to describe uncertainties in given information systems. However, the traditional rough set models are built based on equivalence relations which do not consider the preference relationship of attribute values. Dominance relationbased rough set approach effectively solve this problem which uses dominance relations to substitute equivalence relations to deal with ordered data. In this kind of approach, the computing of dominance class is a necessary step to attribute reduction which is very timeconsuming. In order to reduce the computational cost in calculating dominance classes, this paper presents a method to compute dominance classes by gradually reducing the search space in the domain. The corresponding algorithm is proposed. In each step of the algorithm, the inferior classes of the objects in a given information system are removed in the universe with the increase of the attributes. Experiments using six UCI data show that the proposed method improves the efficiency of computing dominance classes with the increasing of attributes and objects.