On the Size of $\exists$-Generalized Concepts

Abstract: Formal Concept Analysis (FCA) offers several tools for qualitative data analysis. One possibility is to group objects that share common attributes together and get a concept lattice that describes the data. Quite often the size of this concept lattice is very large. Many authors have investigated methods to reduce the size of this lattice. In \cite{KMBV14} the authors consider putting together some attributes to reduce the size of the attribute sets. But this reduction does not always carry over the set of concepts. They have provided some counter examples where the size of the concept lattice increases by one after putting two attributes together. Then they asked the following question: "How many new concepts can be generated by an $\exists$-generalization on just two attributes?" The present paper provides a family of contexts for which the size increases on more than one concept after putting solely two attributes together.