An Algebraic Approach to the Approximation of Information

Abstract

This paper is based on the notion of an information system <U,Ω,V,f> in the sense of Pawlak. Every set of knowledge $\mathit{P}\subseteq \mathrm{\Omega }$ determines a closure operator on U. The class of Boolean algebras with added operations determined by all sets of know ledge are axiomatixed. As a consequence of the representation theorem information systems can be constructed that have a prescribed lattice of functional dependencies.