A new type of generalized one-sided concept lattices and its knowledge reduction

In this paper, we introduce a new pair of adjoint mappings between the power sets and the products of complete lattices. The proposed pair of adjoint mappings forms a Galois connection and the corresponding concept lattice is constructed for a generalized one-sided formal context. Moreover, we propose a lattice-keep-based attribute reduction approach for a generalized one-sided formal context. Specifically, we present the concrete judgement theorems and algorithms to calculate the attribute reducts of generalized one-sided formal contexts.