Nearness of Objects: Extension of Approximation Space Model

The problem considered in this paper is the extension of an approximation space to include a nearness relation. Approximation spaces were introduced by Zdzisław 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. ∗Address for correspondence: Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6 Canada 498 J.F. Peters et al. / Nearness