Lattice CST(L1) Obtained By The Substitution Sum In Formal Context

Abstract

Formal Concept Analysis (FCA) is an applied branch of Lattice theory, widely used in computer science, which derives implicit relationships between objects described through a set of attributes on one hand and these attributes on the other. Any finite lattice can be represented by a formal concept, which can be obtained from the formal context of ob- jects and attributes. Let T be a (0, 1) sublattice of a lattice L₁.  In this paper, a concept lattice CS_T(L₁) is constructed by the  substitution- sum in the formal context, where T is a formal context of a (0, 1) sublattice of the lattice L₁. The structural properties of the concept lattice are studied and a characterization for the meet and join irreducible elements of CS_T(L₁) is given. Further, some congruence relations are defined on the lattice CST(L₁).