Nearness of Objects: Extension of Approximation Space Model

  • Authors:

  • James F. Peters;Andrzej Skowron;Jaroslaw Stepaniuk

  • 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

  • Venue:
  • Fundamenta Informaticae - Special Issue on Concurrency Specification and Programming (CS&P)
  • Year:
  • 2007

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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.