Multi-adjoint t-concept lattices

  • Authors:
  • J. Medina;M. Ojeda-Aciego

  • Affiliations:
  • Dept. Matemáticas, Universidad de Cádiz, Spain;Dept. Matemática Aplicada, Universidad de Málaga, Spain

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2010

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Abstract

The t-concept lattice is introduced as a set of triples associated to graded tabular information interpreted in a non-commutative fuzzy logic. Following the general techniques of formal concept analysis, and based on the works by Georgescu and Popescu, given a non-commutative conjunctor it is possible to provide generalizations of the mappings for the intension and the extension in two different ways, and this generates a pair of concept lattices. In this paper, we show that the information common to both concept lattices can be seen as a sublattice of the Cartesian product of both concept lattices. The multi-adjoint framework can be applied to this general t-concept lattice, and its usefulness is illustrated by a working example.