On multi-adjoint concept lattices: definition and representation theorem

Authors:
Jesús Medina;Manuel Ojeda-Aciego;Jorge Ruiz-Calviño
Affiliations:
Dept. Matemática Aplicada. Universidad de Málaga;Dept. Matemática Aplicada. Universidad de Málaga;Dept. Matemática Aplicada. Universidad de Málaga
Venue:
ICFCA'07 Proceedings of the 5th international conference on Formal concept analysis
Year:
2007

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Abstract

Several fuzzifications of formal concept analysis have been proposed to deal with uncertainty or incomplete information. In this paper, we focus on the new paradigm of multi-adjoint concept lattices which embeds different fuzzy extensions of concept lattices, our main result being the representation theorem of this paradigm. As a consequence of this theorem, the representation theorems of the other paradigms can be proved more directly. Moreover, the multi-adjoint paradigm enriches the language providing greater flexibility to the user.