Publication at Faculty of Mathematics and Physics |
2013
Abstract
Often, both in practice and theory, it is impossible to describe the sets under consideration precisely. The paper examines the basic mathematical background of methods for handling such situations; in particular, it is concerned with the possibilities of describing a set qualitatively by nonnumeric techniques that are frequently used in the theory of rough sets and in the analysis of formal concepts.
The paper demonstrates that the basic mathematical ideas underlying these techniques are closely related to those applied in various studies of set-valued set-functions appearing in the Preston Hammer concept of extended topology, Galois correspondences, Boolean algebras with operators, and modal logics.