Dual Three-way Concept Lattice Based on Composition of Concepts and Its Concept Reduction

Three-way concept lattice not only represents the information jointly owned, but also represents the information that is not owned by each other by combining positive operators and negative operators.It is an extension of the classical concept lattice.However, when dealing with some practical problems, we sometimes start from the reverse, considering the information that the complementary sets may not have and the information that they may have, so the dual three-way concept lattice came into being.In this paper, a novel method to construct dual three-way concept lattices based on the composition of dual concepts in formal context and its complementary context is proposed.It is proved that the dual three-way concepts obtained by concepts composition are the same as those obtained by dual three-way operators.Then, we discuss the attribute reduction method of dual three-way concept lattices based on discernibility matrices.With the help of this idea, this paper proposes an approach to reducing the dual three-wa