On the Inverse Problem for Generalized One-Sided Concept Lattices

Abstract

Generalized one-sided concept lattices represent a generalization of the classical concept lattices convenient for analysis of object-attribute models with different types of attributes. Formally, to each objectattribute model (represented by the notion of formal context) there is assigned a pair of concept-forming operators. Fixed points of these operators form a hierarchical structure consisting of extent-intent pairs. From the algebraic point of view this structure forms a complete lattice, called the generalized one-sided concept lattice. In this paper we deal with the inverse problem for generalized one-sided concept lattices. For a given generalized one-sided concept lattice we describe an algorithm for finding the corresponding formal context.