On the cardinality of fuzzy sets

It seems that a suitably constructed fuzzy sets of natural numbers form the most complete and adequate description of cardinality of finite fuzzy sets.(see [11]) Nevertheless, in many applications one needs a simple scalar evaluation of that cardinality by nonnegative real number, e.g scalar cardinality. There are many approaches to this evaluation-sigma count of fuzzy set,psigma count of fuzzy sets, cardinality of its core or support, cardinality of its αcut set,etc.(see [2]), [3], [4], [5], [7], [9], [10] for more details). Wygralak in [8] present an axiomatic approach to the scalar cardinality of fuzzy sets which contains as particular cases all standard concepts of scalar cardinality. The best approximation of scalar cardinality of fuzzy set is presented in [12]. The aim of this paper is to select numbers from Wygralak’s best approximation which are coherent with human intuition. This selection is based on the dependency among objects which can be represented by fuzzy compatib...

• Type: Conference
• Year: 2003
• Where: EUSFLAT
• Authors: Pavol Král
• Keywords: E.g Scalar Cardinality, EUSFLAT 2003, EUSFLAT 2007, Fuzzy Set, Scalar Cardinality