An axiomatic definition of cardinality for finite interval-valued hesitant fuzzy sets

Abstract

Recently, some extensions of the classical fuzzy sets are studied in depth due to the good properties that they present. Among them, in this paper finite interval-valued hesitant fuzzy sets are the central piece of the study, as they are a generalization of more usual sets, so the results obtained can be immediately adapted to them. In this work, the cardinality of finite intervalvalued hesitant fuzzy sets is studied from an axiomatic point of view, along with several properties that this definition satisfies, being able to relate it to the classical definitions of cardinality given by Wygralak or Ralescu for fuzzy sets