Spectral lattices of (R)over-bar(max),(+)-Formal contexts

Abstract

In [13] a generalisation of Formal Concept Analysis was introduced with data mining applications in mind, K-Formal Concept Analysis, where incidences take values in certain kinds of semirings, instead of the standard Boolean carrier set. Subsequently, the structural lattice of such generalised contexts was introduced in [15], to provide a limited equivalent to the main theorem of K-Formal Concept Analysis, resting on a crucial parameter, the degree of existence of the object-attribute pairs phi. In this paper we introduce the spectral lattice of a concrete instance of K-Formal Concept Analysis, as a further means to clarify the structural and the K-Concept Lattices and the choice of p. Specifically, we develop techniques to obtain the join- and meet-irreducibles of a (R) over bar (max),+-Concept Lattice independently of phi and try to clarify its relation to the corresponding structural lattice.