On L-fuzzy Chu correspondences

Abstract

In this paper, we focus on the framework of Chu correspondences introduced by Mori for a classical formal concept analysis, and we propose a suitable extension of the framework in a more general and flexible environment based on L-fuzzy sets, and define the notions of L-Chu correspondence and of L-bond. After introducing the generalized framework, the sets of L-Chu correspondences and of L-bonds are proved to have the structure of complete lattice and, furthermore, there exists a natural anti-isomorphism between them.

Keywords:

• L-fuzzy sets
• Chu correspondence
• bond
• concept lattices
• formal concept analysis

2010 AMS Subject Classifications :

• 03B52
• 06B23

Acknowledgements

O. Krídlo was partially supported by the grant VEGA 1/0131/09, and M. Ojeda-Aciego was partially supported by projects P06-FQM-02049, TIN06-15455-C03-01, and TIN09-14562-C05-01.