Definability of approximations in reflexive relations

Yu Ru Syau, Lixing Jia, En Bing Lin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

Considering a reflexive relation R on a fixed nonempty set U, four different constructions of lower and upper approximations are described by using the so-called R-successor or/and R-predecessor sets of each object of the set U. The first two of the four constructions of lower and upper approximations are well known, and one pair is presented in this paper for the first time. The lower and upper approximations in each pair are mutually dual, and all the four upper approximations discussed in this paper are extensive and monotonic. If the reflexive relation R is further assumed to be symmetric, the four constructions of lower and upper approximations are induced to the commonly used lower and upper approximations. The primary goal of this paper is to study definability of approximations in reflexive relations via a special kind of neighborhood systems, called total pure reflexive neighborhood systems. It is shown that such neighborhood systems give a unified framework for definability of the four constructions.

Original languageEnglish
Title of host publicationProceedings - 2013 IEEE International Conference on Granular Computing, GrC 2013
PublisherIEEE Computer Society
Pages276-280
Number of pages5
ISBN (Print)9781479912810
DOIs
StatePublished - 2013
Event2013 IEEE International Conference on Granular Computing, GrC 2013 - Beijing, China
Duration: Dec 13 2013Dec 15 2013

Publication series

NameProceedings - 2013 IEEE International Conference on Granular Computing, GrC 2013

Conference

Conference2013 IEEE International Conference on Granular Computing, GrC 2013
Country/TerritoryChina
CityBeijing
Period12/13/1312/15/13

Keywords

  • definability
  • lower and upper approximations
  • neighborhoods
  • reflexive relations
  • rough sets

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