Calculi of Approximation Spaces

  • Authors:

  • Andrzej Skowron;Jarosław Stepaniuk;James Peters;Roman Swiniarski

  • Affiliations:

  • Institute of Mathematics Warsaw University, Banacha 2 02-097 Warszawa, Poland. E-mail: skowron@mimuw.edu.pl;Department of Computer Science Białystok University of Technology Wiejska 45a, 15-351 Białystok, Poland. E-mail: jstepan@ii.pb.bialystok.pl;Department of Electrical and Computer Engineering University of Manitoba Winnipeg Manitoba R3T 5V6, Canada. E-mail: jfpeters@ee.umanitoba.ca;Department of Mathematical and Computer Sciences San Diego State University 5500 Campanile Drive, San Diego CA 92182, USA. E-mail: rswiniar@sciences.sdsu.edu

  • Venue:
  • Fundamenta Informaticae - SPECIAL ISSUE ON CONCURRENCY SPECIFICATION AND PROGRAMMING (CS&P 2005) Ruciane-Nide, Poland, 28-30 September 2005
  • Year:
  • 2006

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Abstract

This paper considers the problem of how to establish calculi of approximation spaces. Approximation spaces considered in the context of rough sets were introduced by Zdzisław Pawlak more than two decades ago. In general, a calculus of approximation spaces is a system for combining, describing, measuring, reasoning about, and performing operations on approximation spaces. An approach to achieving a calculus of approximation spaces that provides a basis for approximating reasoning in distributed systems of cooperating agents is considered in this paper. Examples of basic concepts are given throughout this paper to illustrate how approximation spaces can be beneficially used in many settings, in particular for complex concept approximation. The contribution of this paper is the presentation of a framework for calculi of approximation spaces useful for approximate reasoning by cooperating agents.