The Complementary Equivalence Relation Based Rough Set
MA Zhou-Ming1,2,3, LI Jin-Jin1,2
1.School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000 2.Laboratory of Granular Computing, Minnan Normal University, Zhangzhou 363000 3.College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024
Abstract A binary relation can be regarded as a set, and thus its complementary set is taken into account. Based on the set attribute of the equivalence relations, the definition of the complementary equivalence relation is given firstly, and its characterization of the relationship among the internal elements is probed. Firstly, the rough set based on the complementary equivalence relation is constructed, and the basis of its axiomatization is discussed as well. Secondly, the mutual relation between the rough set based on the complementary equivalence relation and the classical rough set is studied. And by the proposed rough set, the corresponding calculations of the classical approximation operators is predigested,and the key knowledge like basic accurate set is also fixed.
[1] Pawlak Z. Rough Sets. International Journal of Computer and Information Sciences, 1982, 11(5): 341-356 [2] Yao Y Y. Constructive and Algebraic Methods of the Theory of Rough Sets. Information Sciences, 1998, 109(1/2/3/4): 21-47 [3] Yao Y Y. Two Views of the Theory of Rough Sets in Finite Universes. International Journal of Approximate Reasoning, 1996, 15(4): 291-317 [4] Mi J S, Wu W Z, Zhang W X. Constructive and Axiomatic Approaches of the Theory of Rough Sets. Pattern Recognition and Artificial Intelligence, 2002, 15(3): 280-284 (in Chinese) (米据生,吴伟志,张文修.粗糙集的构造与公理化方法.模式识别与人工智能, 2002, 15(3): 280-284) [5] Zhu F, He H C. The Axiomatization of the Rough Set. Chinese Journal of Computers, 2000, 23(3): 330-333 (in Chinese) (祝 峰,何华灿.粗集的公理化.计算机学报, 2000, 23(3): 330-333) [6] Li J J. Topological Methods on the Theory of Covering Generalized Rough Sets. Pattern Recognition and Artificial Intelligence, 2004, 17(1): 7-10 (in Chinese) (李进金.覆盖广义粗集理论中的拓扑学方法.模式识别与人工智能, 2004, 17(1): 7-10) [7] Chen J K, Li J J. An Application of Rough Sets to Graph Theory. Information Sciences, 2012, 201: 114-127 [8] Lin G P, Qian Y H, Li J J. NMGRS: Neighborhood-Based Multigranulation Rough Sets. International Journal of Approximate Reasoning, 2012, 53(7): 1080-1093 [9] Kang X P, Li D Y, Wang S G, et al. Rough Set Model Based on Formal Concept Analysis. Information Sciences, 2013, 222: 611-625 [10] Wang J, Miao D Q, Zhou Y J. Roughs Set Theory and Its Application: A Survey. Pattern Recognition and Artificial Intelligence, 1996, 9(4): 337-344 (in Chinese) (王 珏,苗夺谦,周育健.关于Rough Set理论与应用的综述.模式识别与人工智能, 1996, 9(4): 337-344)
2014, Vol. 27 
