Multi-adjoint t-concept lattices

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 possib...

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Bibliographic Details
Published in:Information sciences 2010-03, Vol.180 (5), p.712-725
Main Authors: Medina, J., Ojeda-Aciego, M.
Format: Article
Language:English
Subjects:
Concept lattice
Galois connection
Implication triple
Multi-adjoint lattice
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Summary: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.
ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2009.11.018