Abstract
Since the rough sets theory based on the double quantification method was proposed, it has attracted wide attention in decision-making. This paper studies the decision-making approach in Incomplete Ordered Information System (IOIS). Firstly, to better extract the effective information in IOIS, combined with the advantages of set-pair dominance relation and generalized multi-granulation, the generalized multi-granulation set-pair dominance variable precision rough sets (GM-SPD-VPRS) and the generalized multi-granulation set-pair dominance graded rough sets (GM-SPD-GRS) are proposed. Moreover, we discuss their related properties. Secondly, considering the GM-SPD-VPRS and the GM-SPD-GRS describe information from relative view and absolute view, respectively, we further combine the two rough sets to obtain six double-quantitative generalized multi-granulation set-pair dominance rough sets (GM-SPD-RS) 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.
Highlights
The acceleration of the information era makes it possible to acquire and process diversified feature data
Example Analysis In Information System (IOIS), five DQGM-SPD-Rough sets (RS) models have been defined in the previous section, and which provide a way for decision-making in IOIS
This paper studies the problem of uncertain decision-making under IOIS
Summary
The acceleration of the information era makes it possible to acquire and process diversified feature data. In the light of granular computing, Zhai et al [49,50] introduced the tolerance relation into VPRS, combined with the multi-granulation, and gave the optimistic and pessimistic variable precision MRS model under the IIS. In consideration that VPRS can reflect the relative quantization information of approximation space, we propose generalized multi-granulation set-pair dominance variable precision rough sets (GM-SPD-VPRS), and the related properties are discussed. (2) Based on the proposed GM-SPD-VPRS, considering the GRS reflect absolute quantization information of approximation space, we defined generalized multi-granulation set-pair dominance graded rough sets (GM-SPD-GRS). (3) To better reflect the relative and absolute quantization information in IOIS, the lower and upper approximation sets of GM-SPD-VPRS and GM-SPD-GRS are fused and combined with logical operators, and five double-quantitative generalized multi-granulation set-pair dominance relation rough sets (DQGM-SPD-RSI to DQGM-SPD-RSV ) are obtained.
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