Foundations of near sets

  • Authors:

  • James F. Peters;Piotr Wasilewski

  • Affiliations:

  • Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Manitoba, Canada R3T 5V6;Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Manitoba, Canada R3T 5V6 and Faculty of Psychology, Warsaw University, Stawki 5/7, 00-183 Warsaw, Poland

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2009

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Abstract

This paper introduces an approach to the foundations of information science considered in the context of near sets. Perceptual information systems (or, more concisely, perceptual systems) provide stepping stones leading to nearness relations, near sets and a framework for classifying perceptual objects. This work has been motivated by an interest in finding a solution to the problem of how one goes about discovering affinities between perceptual granules such as images. Near set theory provides a formal basis for observation, comparison and classification of perceptual granules. This is made clear in this article by considering various nearness relations that define coverings of sets of perceptual objects that are near each other. In the near set approach, every perceptual granule is a set of objects that have their origin in the physical world. Objects that have, in some degree, affinities are considered perceptually near each other, i.e., objects with similar descriptions. This article includes a comparison of near sets with other approaches to approximate knowledge representation and a sample application in image analysis. The main contribution of this article is the introduction of a formal foundation for near sets and a demonstration that the family of near sets is a Gratzer slash lattice.