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 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. Key words: concept lattice, multi-adjoint lattice, implication triple, Galois connection.

• Type: Journal
• Year: 2010
• Where: ISCI
• Authors: Jesús Medina, Manuel Ojeda-Aciego
• Keywords: Concept Lattices, ISCI 2010, Non-commutative Fuzzy Logic, T-concept Lattice