Rough Lattice: A Combination with the Lattice Theory and the Rough Set Theory

被引：0

作者：

Shao, Yingchao ^{[1
]}

Fu, Li ^{[2
]}

Hao, Fei ^{[3
]}

Qin, Keyun ^{[4
]}

机构：

[1] Guizhou Univ Finance & Econ, Sch Informat, Guiyang 550025, Guizhou, Peoples R China

[2] Qinghai Nationalities Univ, Sch Math & Stat, Xining 810007, Qinghai, Peoples R China

[3] Soonchunhyang Univ, Dept Comp Software Engn, Asan 58217, South Korea

[4] Southwest Jiaotong Univ Chengdu, Sch Math, Sichuan 610031, Peoples R China

来源：

PROCEEDINGS OF THE 2016 INTERNATIONAL CONFERENCE ON MECHATRONICS, CONTROL AND AUTOMATION ENGINEERING (MCAE) | 2016年 / 58卷

关键词：

rough set; lattice; rough lattice; lower approximation; upper approximation; FUZZY; APPROXIMATIONS; REDUCTION; IDEALS;

D O I：

暂无

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The rough set theory, introduced by Pawlak in 1982, is a formal for dealing with the uncertainties. But it cannot directly deal with the uncertainties with order structure. The lattice theory, introduced by Peirce and Schr$\ddot{o}$der towards the end of the nineteenth century, is a mathematical tool with order structure, algebraic structure and topological structure. In this paper, the rough theory is applied to the lattice theory, and the concept of the rough lattice is presented in order that a tool is presented which can deal with the uncertainties with lattice structure. For this purpose, an equivalence relation on a lattice is defined and then the notions of rough lattice and lower and upper approximations are introduced and some related properties are investigated. At last, some related algebraic structures are studied.

引用

页码：91 / 95

页数：5

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