Cuts of intuitionistic fuzzy sets respecting fuzzy connectives

Authors:
Davide Martinetti;VladimíR Janiš;Susana Montes
Affiliations:
Department of Statistics and OR, University of Oviedo, Spain;Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Slovak Republic;Department of Statistics and OR, University of Oviedo, Spain
Venue:
Information Sciences: an International Journal
Year:
2013

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Abstract

Intuitionistic fuzzy sets (IF-sets) create a suitable tool to describe cases where it is useful to account not only the grade of membership to a certain 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 @a. We describe properties of such cuts depending on the chosen type of conjunction and negation.