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The Scientific World Journal
Volume 2014 (2014), Article ID 109706, 9 pages
http://dx.doi.org/10.1155/2014/109706
Research Article

Attribute Reduction Based on Property Pictorial Diagram

School of Mathematics, Northwest University, Xi’an, Shaanxi 710069, China

Received 28 June 2014; Revised 23 July 2014; Accepted 23 July 2014; Published 27 August 2014

Academic Editor: Yunqiang Yin

Copyright © 2014 Qing Wan and Ling Wei. 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

This paper mainly studies attribute reduction which keeps the lattice structure in formal contexts based on the property pictorial diagram. Firstly, the property pictorial diagram of a formal context is defined. Based on such diagram, an attribute reduction approach of concept lattice is achieved. Then, through the relation between an original formal context and its complementary context, an attribute reduct of complementary context concept lattice is obtained, which is also based on the property pictorial diagram of the original formal context. Finally, attribute reducts in property oriented concept lattice and object oriented concept lattice can be acquired by the relations of attribute reduction between these two lattices and concept lattice of complementary context. In addition, a detailed illustrative example is presented.