Rough approximation operations based on IF sets

  • Authors:

  • Anna Maria Radzikowska

  • Affiliations:

  • Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland

  • Venue:
  • ICAISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Soft Computing
  • Year:
  • 2006

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Abstract

Intuitionistic fuzzy sets, originally introduced by Atanassov, allow for representation both degrees of membership and degrees of non–membership of an element to a set. In this paper we present a generalisation of Pawlak's rough approximation operations taking Atanassov's structures as a basis. A special class of residuated lattices is taken as a basic algebraic structure. In the signature of these algebras we have abstract counterparts of two main classes of fuzzy implications. We show that basing on these lattices we can express degrees of weak and strong certainties and possibilities of membership and non–membership of an element to a set.