A DecisionTheoretic Rough Set Approach to LatticeValued Information System The decisiontheoretic rough set utilizes Bayesian decision to interpret the thresholds of probabilistic rough set model. That provides a novel semantic description for rough regions in the viewpoint of threeway decision theory and has been applied to numerous fields. However, it lacks the ability to deal with latticevalued information system (LvIS), in which the condition attribute set consists of multiple types of attributes and their domain constitute lattice. Therefore, this study concentrates on the decisiontheoretic rough approach in a LvIS. Then, the total decision cost associated with rough regions is addressed and an attribute reduction algorithm will be designed based on minimum decision cost. Finally, a case study on medical diagnosis is conducted to illustrate the decision procedure and attribute reduction approach.

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.