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Attribute reductions in object-oriented concept lattices

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Abstract

Attribute reduction is one of the main issues in the study of concept lattice. This paper mainly deals with attribute reductions of an object-oriented concept lattice constructed on the basis of rough set. Attribute rank of object-oriented concept lattice is first defined, and relationships between attribute rank and object-oriented concepts are then discussed. Based on attribute rank, generating algorithm of object-oriented concepts is investigated. The object-oriented consistent set and object-oriented reduction of an object-oriented concept lattice are defined. Adjustment theorems of the object-oriented consistent set, and the necessary and sufficient conditions for a attribute subset to be an object-oriented consistent set of an object-oriented concept lattice are discussed. Then the object-oriented discernibility matrix of an object-oriented concept lattice is defined and its properties are also studied. Based on the object-oriented discernibility matrix, an approach to object-oriented reductions of an object-oriented concept lattice is proposed, and the attribute characteristics are also analyzed.

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Acknowledgments

The authors would like to thank the anonymous referees for their very constructive comments. This work was supported by a grant from the National Natural Science Foundation of China (No. 10901025) and the Special Fund for Basic Scientific Research of Central Colleges (CHD2012JC003).

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Authors and Affiliations

  1. Department of Mathematics and Information Science, Faculty of Science, Chang’an University, Xi’an, Shaan’xi, 710064, People’s Republic of China

    Jian-Min Ma

  2. Department of Geography and Resource Management, Center for Environmental Policy and Resource Management and Insititute of Space and Earth Information Science, The Chinese University of Hong Kong, Hong Kong, Hong Kong

    Yee Leung

  3. Faculty of Science, Institute for Information and System Sciences, Xi’an Jiaotong University, Xi’an, Shaan’xi, 710049, People’s Republic of China

    Wen-Xiu Zhang

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Correspondence to Jian-Min Ma.

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Ma, JM., Leung, Y. & Zhang, WX. Attribute reductions in object-oriented concept lattices. Int. J. Mach. Learn. & Cyber. 5, 789–813 (2014). https://doi.org/10.1007/s13042-013-0214-0

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