International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 12714, 13 pages
Research Article

Decision Analysis via Granulation Based on General Binary Relation

M. M. E. Abd El-Monsef1 and N. M. Kilany2

1Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
2Commercial Technical Institute for Computer Sciences, Suez, Egypt

Received 10 May 2006; Revised 22 November 2006; Accepted 26 November 2006

Academic Editor: Lokenath Debnath

Copyright © 2007 M. M. E. Abd El-Monsef and N. M. Kilany. 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.


Decision theory considers how best to make decisions in the light of uncertainty about data. There are several methodologies that may be used to determine the best decision. In rough set theory, the classification of objects according to approximation operators can be fitted into the Bayesian decision-theoretic model, with respect to three regions (positive, negative, and boundary region). Granulation using equivalence classes is a restriction that limits the decision makers. In this paper, we introduce a generalization and modification of decision-theoretic rough set model by using granular computing on general binary relations. We obtain two new types of approximation that enable us to classify the objects into five regions instead of three regions. The classification of decision region into five areas will enlarge the range of choice for decision makers.