Incomplete Multigranulation Rough Set

• Published in: IEEE transactions on systems, man and cybernetics. Part A, Systems and humans Vol. 40; no. 2; pp. 420 - 431
• Main Authors: Qian, Yuhua, Liang, Jiye, Dang, Chuangyin
• Format: Journal Article
• Language: English
• Published: IEEE 01.03.2010
• Subjects: Algorithm design and analysis; Algorithms; Approximation; Approximation algorithms; Artificial intelligence; Attribute reduction; Cybernetics; Data mining; Fuzzy sets; granular computing; Human; Information systems; information systems (ISs); Knowledge representation; Management information systems; Mathematical models; Preserves; Research and development; rough set; Tolerances; Uncertainty; Universe
• ISSN: 1083-4427; 1558-2426
• DOI: 10.1109/TSMCA.2009.2035436

The original rough-set model is primarily concerned with the approximations of sets described by a single equivalence relation on a given universe. With granular computing point of view, the classical rough-set theory is based on a single granulation. This correspondence paper first extends the rough-set model based on a tolerance relation to an incomplete rough-set model based on multigranulations, where set approximations are defined through using multiple tolerance relations on the universe. Then, several elementary measures are proposed for this rough-set framework, and a concept of approximation reduct is introduced to characterize the smallest attribute subset that preserves the lower approximation and upper approximation of all decision classes in this rough-set model. Finally, several key algorithms are designed for finding an approximation reduct.