Rough Sets and Vague Sets

  • Authors:
  • Zbigniew Bonikowski;Urszula Wybraniec-Skardowska

  • Affiliations:
  • Institute of Mathematics and Informatics, University of Opole, Oleska 48, 45-052 Opole, Poland;Autonomous Section of Applied Logic, Poznań School of Banking, Department in Chorzów, Poland

  • Venue:
  • RSEISP '07 Proceedings of the international conference on Rough Sets and Intelligent Systems Paradigms
  • Year:
  • 2007

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Abstract

The subject-matter of the consideration touches the problem of vagueness. The notion of the rough set, originated by Zdzisław Pawlak, was constructed under the influence of vague information and methods of shaping systems of notions leading to conceptualization and representation of vague knowledge, so also systems of their scopes as some vague sets. This paper outlines some direction of searching for a solution to this problem. In the paper, in connection to the notion of the rough set, the notion of a vague set is introduced. Some operations on these sets and their properties are discussed. The considerations intend to take into account a classical approach to reasoning, based on vague premises, and suggest finding a logic of vague sentences as a non-classical logic in which all counterparts of tautologies of classical logic are laws.