Generalized one-sided concept lattices with attribute preferences

The main aim of this paper is to introduce the preference relations on generalized one-sided concept lattices, which represent a fuzzy generalization of FCA with classical object clusters and fuzzy attributes. In our case a preference relation is modeled by a linear well quasi-order on the set of all attributes. We describe concept forming operators based on a Galois connection, which is defined between the power set of objects and the fuzzy sets of attributes with lexicographic order induced by the preference relation. The representation theorem for such kind of concept lattices is also presented.