Affiliations: [a] Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing | [b]
School of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing
Correspondence:
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Corresponding author. Jun Hu. E-mail: hujun@cqupt.edu.cn.
Abstract: The rough set model has been extended to interval rough number decision systems, but the existing studies do not consider interval rough number decision systems with missing values. To this end, a rough set model of incomplete interval rough number decision systems (IIRNDSs) is proposed, and its uncertainty measures are investigated. Firstly, the similarity of two incomplete interval rough numbers (IIRNs) are defined by calculating their optimistic and pessimistic distances of the lower and upper approximation intervals of IIRNs. Then, the rough sets in IIRNDSs are constructed by the induced similarity relation. Next, four uncertainty measures, including approximation accuracy, approximation roughness, conditional entropy, and decision rough entropy are given, which exhibit a monotonic variation with changes in the size of attribute sets, α, and θ. Finally, the experimental results demonstrate the proposed rough set model of IIRNDSs is feasible and effective.
