Affiliations: Department of Electrical and Computer Engineering,
University of Manitoba, Winnipeg, Manitoba R3T 5V6 Canada.
E-mail: jfpeters@ee.umanitoba.ca | Institute of Mathematics, Warsaw University, Banacha
2, 02-097 Warsaw, Poland. E-mail: skowron@mimuw.edu.pl | Department of Computer Science, Bialystok University
of Technology Wiejska 45A, 15-351 Bialystok, Poland.
E-mail: jstepan@ii.pb.bialystok.pl
Abstract: The problem considered in this paper is the extension of an
approximation space to include a nearness relation. Approximation spaces were
introduced by Zdzis?aw Pawlak during the early 1980s as frameworks for
classifying objects by means of attributes. Pawlak introduced approximations as
a means of approximating one set of objects with another set of objects using
an indiscernibility relation that is based on a comparison between the feature
values of objects. Until now, the focus has been on the overlap between sets.
It is possible to introduce a nearness relation that can be used to determine
the "nearness" of sets of objects that are possibly
disjoint and, yet, qualitatively near to each other. Several members of a
family of nearness relations are introduced in this article. The contribution
of this article is the introduction of a nearness relation that makes it
possible to extend Pawlak's model for an approximation space and to
consider the extension of generalized approximations spaces.
