Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 268929, 16 pages
http://dx.doi.org/10.1155/2011/268929
Research Article

Rough Set Approach to Approximation Reduction in Ordered Decision Table with Fuzzy Decision

Xiaoyan Zhang,1 Shihu Liu,2 and Weihua Xu1

1School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China
2School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Received 13 May 2011; Accepted 24 August 2011

Academic Editor: Peter Wolenski

Copyright © 2011 Xiaoyan Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In practice, some of information systems are based on dominance relations, and values of decision attribute are fuzzy. So, it is meaningful to study attribute reductions in ordered decision tables with fuzzy decision. In this paper, upper and lower approximation reductions are proposed in this kind of complicated decision table, respectively. Some important properties are discussed. The judgement theorems and discernibility matrices associated with two reductions are obtained from which the theory of attribute reductions is provided in ordered decision tables with fuzzy decision. Moreover, rough set approach to upper and lower approximation reductions is presented in ordered decision tables with fuzzy decision as well. An example illustrates the validity of the approach, and results show that it is an efficient tool for knowledge discovery in ordered decision tables with fuzzy decision.