Affiliations: Key Laboratory of Intelligent Information Processing,
Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190,
P.R.China and Graduate University of Chinese Academy of Sciences, Beijing
100039, P.R.China. leiyuxia@ict.ac.cn | Institute of Computing Technology, Chinese Academy of
Sciences, Beijing 100190, P.R.China
Note: [] Address for correspondence: Institute of Computing Technology,
Chinese Academy of Sciences, Beijing, 100190, P.R.China
Abstract: Formal Concept Analysis (FCA) is a valid tool for data mining and
knowledge discovery, which identifies conceptual structures from (formal)
contexts. As many practical applications involve non-binary data, non-binary
attributes are introduced via a many-valued context in FCA. In FCA, conceptual
scaling provides a complete framework for transforming any many-valued context
into a context, in which each non-binary attribute is given a scale, and the
scale is a context. Each relation in relational databases is a many-valued
context of FCA. In this paper, we provide an approach toward normalizing
scales, i.e., each scale can be represented by a nominal scale and/or a set of
statements. One advantage of normalizing scales is to avoid generating huge
(binary) derived relations. By the normalization, the concept lattice of a
derived relation is reduced to a combination of the concept lattice of a
derived nominal relation and a set of statements. Hence, without transforming a
relation into a derived relation, one can not only determine concepts of the
derived relation from concepts of given scales, but also determine concepts of
the derived relation from concepts of a derived nominal relation and a set of
statements. The connection between the concept lattice of a derived nominal
relation and the concept lattice of a derived relation is also considered.
