On relationship between three-way concept lattices

By reformulating and extending the properties of three-way operators, this paper investigates the relationship between different kinds of three-way concept lattices. Three-way operators are defined through eight kinds of two-way operators which are connected by the complement operation. To examine the interrelations systematically, we study (a) the relationship between two-way operators, (b) the relationship between two-way concepts, (c) the relationship between three-way operators, and (d) the relationship between three-way concepts. The results show that the four kinds of object-induced three-way concept lattices are order isomorphic to each other and the four kinds of attribute-induced three-way concept lattices are also order isomorphic to each other. (C) 2020 Elsevier Inc. All rights reserved.