Articles liés à Cardinalities of Fuzzy Sets

Cardinalities of Fuzzy Sets - Couverture rigide

Wygralak, MacIej

 
9783540003373: Cardinalities of Fuzzy Sets
Couverture rigide
ISBN 10 : 3540003371 ISBN 13 : 9783540003373
Editeur : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2003

Synopsis

Counting is one of the basic elementary mathematical activities. It comes with two complementary aspects: to determine the number of elements of a set - and to create an ordering between the objects of counting just by counting them over. For finite sets of objects these two aspects are realized by the same type of num­ bers: the natural numbers. That these complementary aspects of the counting pro­ cess may need different kinds of numbers becomes apparent if one extends the process of counting to infinite sets. As general tools to determine numbers of elements the cardinals have been created in set theory, and set theorists have in parallel created the ordinals to count over any set of objects. For both types of numbers it is not only counting they are used for, it is also the strongly related process of calculation - especially addition and, derived from it, multiplication and even exponentiation - which is based upon these numbers. For fuzzy sets the idea of counting, in both aspects, looses its naive foundation: because it is to a large extent founded upon of the idea that there is a clear distinc­ tion between those objects which have to be counted - and those ones which have to be neglected for the particular counting process.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de la quatrième de couverture

Counting is one of the basic elementary mathematical activities. It comes with two complementary aspects: to determine the number of elements of a set - and to create an ordering between the objects of counting just by counting them over. For finite sets of objects these two aspects are realized by the same type of num­ bers: the natural numbers. That these complementary aspects of the counting pro­ cess may need different kinds of numbers becomes apparent if one extends the process of counting to infinite sets. As general tools to determine numbers of elements the cardinals have been created in set theory, and set theorists have in parallel created the ordinals to count over any set of objects. For both types of numbers it is not only counting they are used for, it is also the strongly related process of calculation - especially addition and, derived from it, multiplication and even exponentiation - which is based upon these numbers. For fuzzy sets the idea of counting, in both aspects, looses its naive foundation: because it is to a large extent founded upon of the idea that there is a clear distinc­ tion between those objects which have to be counted - and those ones which have to be neglected for the particular counting process.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Date d'édition
2003
Langue
anglais
ISBN 10 
3540003371
ISBN 13 
9783540003373
Reliure
Relié
Nombre de pages
200
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