¹The College of Computer Science and Technology, Henan Polytechnic Unviersity, JiaoZuo, China, 464000
²The Intelligent Control and Development Center, Southwest Jiaotong University, Chengdu, China, 610031
³The School of Mathematics & Information Engineering, Jiaxing University, Jiaxing, China, 314001

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Abstract—Rough sets, a tool for data mining, deal with the vagueness and granularity in information systems. Rough approximations on a complete completely distributive lattice(CCD lattice for short) and brings generalizations of rough sets into a unified framework are discussed in [3]. This paper is devoted to the discussion of the relationship between approximations and topologies on a CCD lattice. It is proved that the set of all upper approximations (or of lower approximations) with respect to a partition consists of a clopen topology; and conversely, a clopen topology which obey disjoint axiom can be induced by approximations. Furthermore, the axiomatic characterizations of upper and lower approximations are presented.

Index Terms—Rough sets, complete completely distributive lattice, approximations, clopen topology.

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Cite: Yan Gao, Jilin Yang, Weifeng Du, "The Topological Properties of the Approximation Operators on a CCD Lattice," Journal of Software vol. 5, no. 9, pp. 950-957, 2010.