Taming Non-Commutativity in the Framework of Multi-Adjoint Concept Lattices

J. Medina and M. Ojeda-Aciego (Spain)

Keywords

Concept lattices, multi-adjoint lattices, Galoisconnection,implicationtriples.

Abstract

Sometimes, in real applications, we have to consider the use of non-commutative operators. However, it is in teresting to be able to “balance” of “soften” the noncommutative character of the involved operators. There exist some approaches to the construction of concept lattices based on non-commutative conjunctors L × L → L, but are based on the fact that the supports (or carriers) of the fuzzy subsets of both objects and attributes have to coincide. Our contribution in this work is to present sufficient conditions in order to be able to construct concepts in a generalized fuzzy context in which the domain of the underlying conjunctors can be L1 × L2 with L1 = L2.

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