Ordinally equivalent data: A measurement-theoretic look at formal concept analysis of fuzzy attributes

摘要

We show that if two fuzzy relations, representing data tables with graded attributes, are ordinally equivalent then their concept lattices with respect to the Goedel operations on chains are (almost) isomorphic and that the assumption of Goedel operations is essential. We argue that measurement-theoretic results like this one are important for pragmatic reasons in relational data modeling and outline issues for future research.