Concept Lattices vs. Approximation Spaces

Abstract

The aim of this paper is to compare concept lattices and approximation spaces. For this purpose general approximation spaces are introduced. It is shown that formal contexts and information systems on one hand and general approximation spaces on the other could be mutually represented e.g. for every information system exists a general approximation space such that both structures determines the same indiscernibility relation. A close relationship between Pawlak’s approximation spaces and general approximation spaces also holds: for each approximation space exists a general approximation space such that both spaces determine the same definable sets. It is shown on the basis of these relationships that an extent of the every formal concept is a definable set in some Pawlak’s approximation space. The problem when concept lattices are isomorphic to algebras of definable sets in approximation spaces is also investigated.

This paper presents results of research, which was done by the author during his Ph.D. studies in the Department of Logic, Jagiellonian University, Kraków, Poland. Research project was supported by the Polish Ministry of Science and Information Society Technologies under grant no. 2 H01A 025 23.