Journal of Applied Mathematics and Decision Sciences
Volume 2007 (2007), Article ID 058248, 13 pages
A Modified Rough Set Approach to Incomplete Information Systems
1Institute of Statistical Studies and Research, Cairo University, Cairo 12613, Egypt
2Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
Received 30 October 2006; Revised 27 January 2007; Accepted 12 March 2007
Academic Editor: James Moffat
Copyright © 2007 E. A. Rady 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.
The key point of the tolerance relation or similarity relation presented in the literature is to assign a “null” value to all missing attribute values. In other words, a “null” value may be equal to any value in the domain of the attribute values. This may cause a serious effect in data analysis and decision analysis because the missing values are just “missed” but they do exist and have an influence on the decision. In this paper, we will introduce the modified similarity relation denoted by MSIM that is dependent on the number of missing values with respect to the number of the whole defined attributes for each object. According to the definition of MSIM, many problems concerning the generalized decisions are solved. This point may be used in scaling in statistics in a wide range. Also, a new definition of the discernibility matrix, deduction of the decision rules, and reducts in the present of the missing values are obtained.