This is the groundbreaking book on formal concept analysis (FCA), whose aim is to mathematize the notion of concept and its corresponding hierarchy. Being a branch of applied lattice theory, first mathematical order and lattice theory are surveyed, in order to be able to define so-called concept lattices from an easy data representation as a standard cross table (contingency table or double entry table). These concepts, just extracted from a data context, can be represented in a diagram and can be further analyzed to identify hidden structures and tolerance relations using suitable mathematical tools, which can be used to decompose complex lattices into possible overlapping parts and to construct larger lattices by direct product and substitution. More advanced techniques includes distributive law generalizations, dimensionality issues, morphism comparison using structural maps, and concept scaling techniques.

https://doi.org/10.1007/978-3-642-59830-2

B. Ganter, R. Wille (1999), Formal Concept Analysis: Mathematical Foundations. Springer-Verlag, ISBN 9783540627715.

Pablo Guerrero-Garcia

University of Malaga