Evidence-theory-based numerical algorithms of attribute reduction with neighborhood-covering rough sets

• Published in: International journal of approximate reasoning Vol. 55; no. 3; pp. 908 - 923
• Main Authors: Chen, Degang, Li, Wanlu, Zhang, Xiao, Kwong, Sam
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.03.2014; Elsevier
• Subjects: Applied sciences; Artificial intelligence; Attribute reduction; Belief and plausibility functions; Computer science; control theory; systems; Covering rough sets; Data processing. List processing. Character string processing; Evidence theory; Exact sciences and technology; Information theory; Information, signal and communications theory; Learning and adaptive systems; Logical, boolean and switching functions; Memory organisation. Data processing; Neighborhood; Rough sets; Software; Telecommunications and information theory; Theoretical computing; Covering rough sets; Evidence theory; Belief and plausibility functions; Rough sets; Attribute reduction; Neighborhood; Belief; Data analysis; Knowledge acquisition; Decision support system; Information system; Universe; Data reduction; Dimension reduction; Rough set theory; Discernability; Dempster Shafer theory; Closure operator; Selection criterion; Set covering; Proof theory; Numerical algorithm
• ISSN: 0888-613X; 1873-4731
• DOI: 10.1016/j.ijar.2013.10.003

Covering rough sets generalize traditional rough sets by considering coverings of the universe instead of partitions, and neighborhood-covering rough sets have been demonstrated to be a reasonable selection for attribute reduction with covering rough sets. In this paper, numerical algorithms of attribute reduction with neighborhood-covering rough sets are developed by using evidence theory. We firstly employ belief and plausibility functions to measure lower and upper approximations in neighborhood-covering rough sets, and then, the attribute reductions of covering information systems and decision systems are characterized by these respective functions. The concepts of the significance and the relative significance of coverings are also developed to design algorithms for finding reducts. Based on these discussions, connections between neighborhood-covering rough sets and evidence theory are set up to establish a basic framework of numerical characterizations of attribute reduction with these sets.