Rough Approximation Operators in Group Mapping and Their Applications to Coding Theory

Article type: Research Article

Authors: Xu, Jiuping^* | Qiu, Rui | Tao, Zhimiao

Affiliations: Uncertainty Decision-Making Laboratory, Sichuan University, Chengdu 610064, P. R. China. xujiuping@scu.edu.cn; qiurui2015@163.com; zhimiaotao@scu.edu.cn

Correspondence: [*] Address for correspondence: Uncertainty Decision-Making Laboratory, Sichuan University, Chengdu 610064, P. R. China.

Abstract: This paper focuses on rough approximation operators in group mapping. The relationships between rough set theory and group theory are considered from a novel perspective. The necessary and sufficient conditions for the upper approximation and lower approximation of a group to be groups are analyzed. In addition, the homomorphism and isomorphism between two groups which have related upper or lower approximations are investigated. Finally, the applications of rough approximation operators in group mapping to coding theory are developed.

Keywords: rough set, lower approximation, upper approximation, group mapping, coding theory

DOI: 10.3233/FI-2016-1348

Journal: Fundamenta Informaticae, vol. 145, no. 1, pp. 93-109, 2016