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

DOI

10.2991/mcae-16.2016.23How to use a DOI?

Keywords

rough set; lattice; rough lattice; lower approximation; upper approximation

Abstract

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.

Copyright

© 2016, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Yingchao Shao
AU  - Li Fu
AU  - Fei Hao
AU  - Keyun Qin
PY  - 2016/07
DA  - 2016/07
TI  - Rough Lattice: A Combination with the Lattice Theory and the Rough Set Theory
BT  - Proceedings of the 2016 International Conference on Mechatronics, Control and Automation Engineering
PB  - Atlantis Press
SP  - 91
EP  - 95
SN  - 2352-5401
UR  - https://doi.org/10.2991/mcae-16.2016.23
DO  - 10.2991/mcae-16.2016.23
ID  - Shao2016/07
ER  -