1.Department of Basic Courses, Zhejiang Shuren University, Hangzhou 310015 2.College of Information Science and Engineering, Zhejiang Normal University, Jinhua 321004
Abstract:Let φ be a surjective homomorphic mapping from group G to group K. Through the congruence relation ρ from K to G by φ, the property, that the surjective homomorphic mapping φ can commutate with the upper (lower) approximation of the congruence relation, is obtained. It is shown that a homomorphic mapping keeps upper (lower) rough subgroups, and upper (lower) rough left (right, twosided) ideally unchanged.
[1] Pawlak Z. Rough Sets: Theoretical Aspect of Reasoning about Data. Boston, USA: Kluwer Academic,1991 [2] Pawlak Z. Rough Sets. International Journal of Information and Computer Science, 1982, 11: 341-356 [3] Pawlak Z. Rough Classification. International Journal of Man-Machine Studies, 1984, 20: 469-483 [4] Tentush I. On Rough Mereological Cech Topologies. Bulletin of the Polish Academy of Science: Computer Science, 1995, 43(1): 75-85 [5] Pawlak Z. Rough Sets and Fuzzy Sets. Fuzzy Sets and Systems, 1985, 17: 99-102 [6] Iwinski T B. Algebraic Approach to Rough Sets. Bulletin of Polish Academy of Sciences: Mathematics, 1987, 35: 673-683 [7] Han S Q. Homomorphism and Isomorphism of Rough Group. Journal of Shanxi University (Natural Science Edition), 2001, 24(4): 303-305 (in Chinese) (韩素青.粗糙群的同态与同构.山西大学学报(自然科学版), 2001, 24(4): 303-305) [8] Zhang W X, Wu W Z, Liang J Y, et al. Rough Set Theory and Approaches. Beijing, China: Science Press, 2001(in Chinese) (张文修,吴伟志,梁吉业,等.粗糙集理论与方法.北京:科学出版社, 2001) [9]Tao X H, Hao Z F. Properties of Rough Groups. Computer Engineering and Applications, 2003, 39(32): 58-59,115 (in Chinese) (陶鲜花,赫志峰.粗糙群的性质.计算机工程与应用, 2003, 39(32): 58-59,115) [10]Tao X H, Hao Z F. Properties of Compatible Homomorphism of Rough Groups. Journal of South China University of Technology (Natural Science Edition), 2004, 32(3): 74-76 (in Chinese) (陶鲜花,赫志峰.粗糙群相容同态的性质.华南理工大学学报(自然科学版), 2004, 32(3): 74-76) [11]Li D Y, Miao D Q. Properties of Rough Subgroups. Computer Science, 2001, 28(5): 42-43 (in Chinese) (李德玉,苗夺谦.粗糙半群的性质.计算机科学, 2001, 28(5): 42-43)