Spectral Lattices of \(\mathbb{\overline R}_{\rm max,+}\)-Formal Contexts

  • Francisco J. Valverde-Albacete
  • Carmen Peláez-Moreno
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4933)


In [13] a generalisation of Formal Concept Analysis was introduced with data mining applications in mind, \(\mathcal K\)-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 \(\mathcal K\)-Formal Concept Analysis, resting on a crucial parameter, the degree of existence of the object-attribute pairs ϕ. In this paper we introduce the spectral lattice of a concrete instance of \(\mathcal K\)-Formal Concept Analysis, as a further means to clarify the structural and the \(\mathcal K\)-Concept Lattices and the choice of ϕ. Specifically, we develop techniques to obtain the join- and meet-irreducibles of a \(\mathbb{\overline R}_{\rm max,+}\)-Concept Lattice independently of ϕ and try to clarify its relation to the corresponding structural lattice.


Closure Operator Natural Order Concept Lattice Formal Context Confusion Matrice 
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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Francisco J. Valverde-Albacete
    • 1
  • Carmen Peláez-Moreno
    • 1
  1. 1.Dpto. de Teoría de la Señal y de las ComunicacionesUniversidad Carlos III de MadridLeganésSpain

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