Concept lattices and order in fuzzy logic

The theory of concept lattices (i.e. hierarchical structures of concepts in the sense of Port-Royal school) is approached from the point of view of fuzzy logic. The notions of partial order, lattice order. and formal concept are generalized for fuzzy setting. Presented is a theorem characterizing the hierarchical structure of formal fuzzy concepts arising in a given formal fuzzy context. Also, as an application of the present approach, Dedekind-MacNeille completion of a partial fuzzy order is described. The approach and results provide foundations for formal concept analysis of vague data-the propositions "object x has attribute y", which form the input data to formal concept analysis, are now allowed to have also intermediate truth values, meeting reality better. (C) 2004 Elsevier B.V. All rights reserved.