Cuts of IF-sets respecting fuzzy connectives

  • Authors:

  • Davide Martinetti;Vladimír Janiš;Susana Montes

  • Affiliations:

  • Department of Statistics and O.R., University of Oviedo, Spain;Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Slovak Republic;Department of Statistics and O.R., University of Oviedo, Spain

  • Venue:
  • WILF'11 Proceedings of the 9th international conference on Fuzzy logic and applications
  • Year:
  • 2011

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Abstract

Intuitionistic fuzzy sets (IF-sets) are a suitable tool to describe cases where it is useful to account not only the grade of membership to a collection, but also the grade of its non-membership. We consider the a-cuts of an IF-set A as crisp sets consisting of those elements x for which the truth value (in fuzzy logic) of the statement "x belongs to A and it is not true that x does not belong to A" is at least α. We describe properties of such cuts depending on the chosen type of conjunction and negation.