Attribute reduction in generalized one-sided formal contexts

In this paper, we present a new pair of adjoint mappings between a power set and the direct product of complete lattices. The proposed pair of adjoint mappings form a Galois connection and the corresponding concept lattice is constructed from a generalized one-sided formal context. We also propose a lattice-keep-based attribute reduction approach for generalized one-sided formal contexts. Specifically, we present concrete judgment theorems and an algorithm to calculate the attribute reducts in generalized one-sided formal contexts. Furthermore, according to the importance of attributes, we discuss attributive characteristics for the proposed generalized one-sided concept lattice.