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Preface of the special issue on concept lattices and their applications

This special issue is devoted to selected revised papers of the 2015 International Conference on Concept Lattices and their Applications (CLA’2015) held in Clermont-Ferrand (France). The first attempt to define a lattice theory, as a mathematic model, was made by Birkhoff (1940). An underlying deep concept is the notion of Galois connection that emerged in the early 1940s, after a long gestation since the beginning of the twentieth century. Over the last two decades, research has demonstrated how concept lattices formalize conceptual structures by coding any kind of duality, such as the duality between the intent and the extent of a concept. Application in data analysis using this duality for analyzing questionnaire data was done by Barbut and Monjardet in the domain of social sciences (Barbut and Monjardet 1970). The concept lattice also named “Galois lattice” was then promoted by R. Wille, and then extended as a discipline called formal concept analysis (Ganter and Wille 1999). Formal concept analysis (FCA) is a mathematical tool for analyzing data and formally representing conceptual knowledge. FCA helps forming conceptual structures from data. Such structures consist of units, which are formal abstractions of concepts of human thought allowing meaningful and comprehensible interpretation. FCA is a mathematical discipline whose features include: