期刊
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
卷 50, 期 5, 页码 695-707出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ijar.2008.12.002
关键词
Formal concept analysis; Rough set theory; Concept lattice; Complete residuated lattice; Fuzzy closure system; Fuzzy opening system; The law of double negation
资金
- Natural Science Foundation of China [10771147]
This paper presents a comparative study of concept lattices of fuzzy contexts based on formal concept analysis and rough set theory. It is known that every complete fuzzy lattice can be represented as the concept lattice of a fuzzy context based on formal concept analysis [R. Belohlavek, Concept lattices and order in fuzzy logic, Ann. Pure Appl. Logic 128 (2004) 277-298]. This paper shows that every complete fuzzy lattice can be represented as the concept lattice of a fuzzy context based on rough set theory if and only if the residuated lattice (L, *, 1) satisfies the law of double negation. Thus, the expressive power of concept lattices based on rough set theory is weaker than that of concept lattices based on formal concept analysis. (C) 2009 Elsevier Inc. All rights reserved.
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