Attribute Reduction Based on Equivalence Classes with Multiple Decision Values in Rough Set
For the attribute reduction problem of decision information systems, the concept of the equivalence class only including the condition attributes is introduced. The necessary condition of implementing attribute reduction and the attribute reduction method
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Attribute Reduction Based on Equivalence Classes with Multiple Decision Values in Rough Set Dongwen Zhang, Jiqing Qiu and Xiao Li
Abstract For the attribute reduction problem of decision information systems, the concept of the equivalence class only including the condition attributes is introduced. The necessary condition of implementing attribute reduction and the attribute reduction method based on the equivalence classes with the multiple decision values are presented. After sorting the condition attributes by the cardinalities of the equivalence classes with the multiple decision value in ascending order, these ordered condition attributes are united one by one until the positive region of the united attribute subset is equal to the full region. Furthermore, if the attribute subset is independent and its indiscernibility relation is the same as the indiscernibility relation in original information system, then the subset is an attribute reduction of the information system. Finally, the experiment result demonstrates that our method is efficient. Keywords Attribute reduction decision values
Rough set
Equivalence class
Multiple
63.1 Introduction We have witnessed a very rapid growth of rough set theory in recent years; rough set theory has been successfully applied in such fields as knowledge discovery, decision analysis, pattern classification, fault diagnosis, etc., [1]. Attribute reduction is one of D. Zhang (&) School of information Science and Engineering, Hebei University of Science and Technology, Shijiazhuang, China e-mail: [email protected] J. Qiu X. Li School of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, China
Z. Zhong (ed.), Proceedings of the International Conference on Information Engineering and Applications (IEA) 2012, Lecture Notes in Electrical Engineering 219, DOI: 10.1007/978-1-4471-4853-1_63, Springer-Verlag London 2013
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the key issues in rough set theory. Reference [2] proposed a discernibility matrix method, in which any two objects determine one feature subset that can distinguish them and could obtain all attribute reducts of a given data set. According to the discernibility matrix viewpoint, Ref. [3] provided a technique of attribute reduction for interval ordered information systems, set-valued ordered information systems, and incomplete ordered information systems, respectively. The idea of attribute reduction using positive region, which remains the positive region of target decision unchanged originated by Refs. [4, 5], gave an extension of this positive region reduction for hybrid attribute reduction in the framework of fuzzy rough set. In heuristic search strategies among attribute reduction methods, some attribute significance measures such as dependency function, information gain, consistency, and other measures are employed to select a feature subset. In fact, several authors [6] have applied variants entropies, combination entropy, or mutual information to measure uncertainty of an information syst
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