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Advances in Fuzzy Systems
Volume 2013, Article ID 372091, 10 pages
Research Article

Extended Tolerance Relation to Define a New Rough Set Model in Incomplete Information Systems

Department of Management and Information Systems Engineering, Nagaoka University of Technology, Nagaoka 940-2188, Japan

Received 18 December 2012; Accepted 27 August 2013

Academic Editor: Eyke Huellermeier

Copyright © 2013 Do Van Nguyen 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.


This paper discusses and proposes a rough set model for an incomplete information system, which defines an extended tolerance relation using frequency of attribute values in such a system. It first discusses some rough set extensions in incomplete information systems. Next, “probability of matching” is defined from data in information systems and then measures the degree of tolerance. Consequently, a rough set model is developed using a tolerance relation defined with a threshold. The paper discusses the mathematical properties of the newly developed rough set model and also introduces a method to derive reducts and the core.