JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (08): 92-96.doi: 10.6040/j.issn.1671-9352.1.2014.151

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On invariance properties of covering-based rough sets under consistent function

ZHANG Yan-lan1, LI Chang-qing2   

  1. 1. College of Computer, Minnan Normal University, Zhangzhou 363000, Fujian, China;
    2. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, Fujian, China
  • Received:2014-06-02 Revised:2014-07-08 Published:2014-09-24

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Abstract: Invariance properties of covering-based rough sets under consistent function are discussed. It is proved that there exist one-to-one correspondences between covering upper approximations of original approximation space and covering upper approximations of image approximation space under consistent function. Furthermore, the image of reduction of original approximation space is the reduction of image approximation space.

Key words: covering upper (lower) approximation operator, consistent function, reduction

CLC Number: 

  • TP18
[1] PAWLAK Z. Rough sets [J]. International Journal of Computer and Information Science, 1982, 11:341-356.
[2] ZAKOWSKI W. Approximation in the space (U,Π) [J]. Demonstratio Mathematica, 1983, 16:761-769.
[3] BONIKOWSKI Z, BRYNIARSKI E, WYBRANIEC U. Extensions and intentions in the rough set theory [J]. Information Sciences, 1998, 107:149-167.
[4] BRYNIARSKI E. A calculus of rough sets of the first order [J]. Bulletin of the Polish Academy of Sciences, 1987, 37(16):71-77.
[5] POMYKALA J A. Approximation operations in approximation space [J]. Bulletin of the Polish Academy of Sciences, 1987, 35(9-10):653-662.
[6] 李进金. 覆盖广义粗集理论中的拓扑学方法 [J]. 模式识别与人工智能, 2004, 17(1):7-10. LI Jinjin. Topological methods on the theory of covering generalized rough sets [J]. Pattern Recognition and Artificial Intelligence, 2004, 17(1):7-10.
[7] ZHU William. Topological approaches to covering generalized rough sets [J]. Information Sciences, 2007, 177:1499-1508.
[8] XU Weihua, ZHANG Wenxiu. Measuring roughness of generalized rough sets induced by a covering [J]. Fuzzy Sets and Systems, 2007, 158(22):2443-2455.
[9] ZHU William, WANG Feiyue. On three types of covering-based rough sets [J]. IEEE Transactions on Knowledge and Data Engineering, 2007, 19(8):1131-1144.
[10] 黄兵, 何新, 周献中. 基于广义粗集覆盖约简的粗糙熵 [J]. 软件学报, 2004, 15(2):215-220. HUANG Bing, HE Xin, ZHOU Xianzhong. Rough entropy based on generalized rough sets covering reduction [J]. Journal of Software, 2004, 15(2):215-220.
[11] CHEN Degang, WANG Changzhong, HU Qinghua. A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets [J]. Information Sciences, 2007, 177:3500-3518.
[12] TSANG E, CHENG D, LEE J, et al. On the upper approximations of covering generalized rough sets [C]//Proceedings of the Third International Conference on Machine Learning and Cybernetics.Shanghai: IEEE Computer Society. 2004:4200-4203.
[13] ZHANG Yanlan, LUO Maokang. Relationships between covering-based rough sets and relation-based rough sets [J]. Information Sciences, 2013, 225:55-71.
[14] WANG Changzhong, CHEN Degang, WU Chong, et al. Data compression with homomorphism in covering information systems [J]. International Journal of Approximate Reasoning, 2011, 52: 519-525.
[15] WANG Changzhong, CHEN Degang, SUN Baiqing, et al. Communication between information systems with covering based rough sets[J]. Information Sciences, 2012, 216:17-33.
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