Concept lattices of fuzzy contexts: Formal concept analysis vs. rough set theory

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. Bělohlávek, 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.