Vagueness and Roughness

  • Zbigniew Bonikowski
  • Urszula Wybraniec-Skardowska
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5390)


The paper proposes a new formal approach to vagueness and vague sets taking inspirations from Pawlak’s rough set theory. Following a brief introduction to the problem of vagueness, an approach to conceptualization and representation of vague knowledge is presented from a number of different perspectives: those of logic, set theory, algebra, and computer science. The central notion of the vague set, in relation to the rough set, is defined as a family of sets approximated by the so called lower and upper limits. The family is simultaneously considered as a family of all denotations of sharp terms representing a suitable vague term, from the agent’s point of view. Some algebraic operations on vague sets and their properties are defined. Some important conditions concerning the membership relation for vague sets, in connection to Blizard’s multisets and Zadeh’s fuzzy sets, are established as well. A classical outlook on a logic of vague sentences (vague logic) based on vague sets is also discussed.


vagueness roughness vague sets rough sets knowledge vague knowledge membership relation vague logic 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Zbigniew Bonikowski
    • 1
  • Urszula Wybraniec-Skardowska
    • 2
  1. 1.Institute of Mathematics and InformaticsUniversity of OpoleOpolePoland
  2. 2.Autonomous Section of Applied Logic, Poznań School of Banking, Faculty in ChorzówPoland

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