Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 507857, 19 pages
http://dx.doi.org/10.1155/2012/507857
Research Article

Consistency of Probability Decision Rules and Its Inference in Probability Decision Table

Zheng Pei,1 Li Zou,2 Hamid Reza Karimi,3 and Peng Shi4,5

1School of Mathematics and Computer Engineering, Xihua University, Chengdu, Sichuan 610039, China
2School of Computer and Information Technology, Liaoning Normal University, Dalian 116029, China
3Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway
4Department of Computing and Mathematical Sciences, University of Glamorgan, Pontypridd CF37 1DL, UK
5School of Engineering and Science, Victoria University, Melbourne, VIC 8001, Australia

Received 17 January 2012; Accepted 15 March 2012

Academic Editor: Zhan Shu

Copyright © 2012 Zheng Pei 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 most synthesis evaluation systems and decision-making systems, data are represented by objects and attributes of objects with a degree of belief. Formally, these data can be abstracted by the form (objects; attributes; P), where P represents a kind degree of belief between objects and attributes, such that, P is a basic probability assignment. In the paper, we provide a kind of probability information system to describe these data and then employ rough sets theory to extract probability decision rules. By extension of Dempster-Shafer evidence theory, we can get probabilities of antecedents and conclusion of probability decision rules. Furthermore, we analyze the consistency of probability decision rules. Based on consistency of probability decision rules, we provide an inference method to finish inference of probability decision rules, which can be used to decide the class of a new object x′. The conclusion points out that the inference method of the paper not only deals with precise information, but also imprecise or uncertain information as well.