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Double-Quantitative Generalized Multi-Granulation Set-Pair Dominance Rough Sets in Incomplete Ordered Information System

by Zhan-ao Xue 1,2,*, Min Zhang 1,2,*, Yong-xiang Li 1,2, Li-ping Zhao 1,2 and Bing-xin Sun 1,2
1
College of Computer and Information Engineering, Henan Normal University, Xinxiang 453007, China
2
Engineering Lab of Henan Province for Intelligence Business & Internet of Things, Henan Normal University, Xinxiang 453007, China
*
Authors to whom correspondence should be addressed.
Symmetry 2020, 12(1), 133; https://doi.org/10.3390/sym12010133 (registering DOI)
Received: 4 December 2019 / Revised: 2 January 2020 / Accepted: 7 January 2020 / Published: 9 January 2020
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. View Full-Text
Keywords: double quantification; set-pair dominance relation; generalized multi-granulation; variable precision rough sets; graded rough sets double quantification; set-pair dominance relation; generalized multi-granulation; variable precision rough sets; graded rough sets
MDPI and ACS Style

Xue, Z.-A.; Zhang, M.; Li, Y.-X.; Zhao, L.-P.; Sun, B.-X. Double-Quantitative Generalized Multi-Granulation Set-Pair Dominance Rough Sets in Incomplete Ordered Information System. Symmetry 2020, 12, 133.

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