Influences of Three-Way Concept Lattice Caused by Variations of Attribute Values

Three-way concept lattices have been widely used in various types of applications. As the construction of three-way concept lattices is rather time consuming, especially for large formal contexts, it is not applicable to construct the lattices from the beginning when changes are made to the contexts. Motivated by this problem, the influences of three-way concept lattices caused by variations of attribute values are explored in this study. Specifically, we discuss two types of changes. One is changing the value of a specific incidence relation from 0 to 1, and the other is from 1 to 0. Furthermore, two types of three-way concept lattices are investigated. One is the object-induced three-way concept lattice, and the other is the attribute-induced three-way concept lattice. Both the mathematical proofs and the examples show the effectiveness of our proposed methods.