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Abstract and Applied Analysis
Volume 2014, Article ID 679037, 7 pages
http://dx.doi.org/10.1155/2014/679037
Research Article

Granular Space Reduction to a β Multigranulation Fuzzy Rough Set

1School of Economics and Management, Jiangsu University of Science and Technology, Zhenjiang 212003, China
2Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information, Nanjing University of Science and Technology, Ministry of Education, Nanjing 210094, China
3School of Electronics and Information, Jiangsu University of Science and Technology, Zhenjiang 212003, China

Received 2 January 2014; Accepted 24 February 2014; Published 30 March 2014

Academic Editor: Hao Shen

Copyright © 2014 Junyi Zhou 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

Multigranulation rough set is an extension of classical rough set, and optimistic multigranulation and pessimistic multigranulation are two special cases of it. β multigranulation rough set is a more generalized multigranulation rough set. In this paper, we first introduce fuzzy rough theory into β multigranulation rough set to construct a β multigranulation fuzzy rough set, which can be used to deal with continuous data; then some properties are discussed. Reduction is an important issue of multigranulation rough set, and an algorithm of granular space reduction to β multigranulation fuzzy rough set for preserving positive region is proposed. To test the algorithm, experiments are taken on five UCI data sets with different values of β. The results show the effectiveness of the proposed algorithm.