Details

Autor(en) / Beteiligte

• Ganter, Bernhard
• Hanika, Tom
• Hirth, Johannes
• Dürrschnabel, Dominik
• López Rodríguez, Domingo

Titel

Scaling Dimension

Ist Teil von

• Formal Concept Analysis, p.64-77

Ort / Verlag

Cham: Springer Nature Switzerland

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the FCA monograph, still has room for improvement. As it stands, even some of the basic definitions are in flux. Our contribution was triggered by the study of concept lattices for tree classifiers and the scaling methods used there. We extend some basic notions, give precise mathematical definitions for them and introduce the concept of scaling dimension. In addition to a detailed discussion of its properties, including an example, we show theoretical bounds related to the order dimension of concept lattices. We also study special subclasses, such as the ordinal and the interordinal scaling dimensions, and show for them first results and examples.