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Studies in Fuzziness and Soft Computing

Cardinalities of Fuzzy Sets

Authors: Wygralak, Maciej

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About this book

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.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $79.99
price for USA in USD
  • ISBN 978-3-540-36382-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA in USD
  • ISBN 978-3-540-00337-3
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $99.99
price for USA in USD
  • ISBN 978-3-642-53514-7
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Cardinalities of Fuzzy Sets
Authors
Series Title
Studies in Fuzziness and Soft Computing
Series Volume
118
Copyright
2003
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-36382-8
DOI
10.1007/978-3-540-36382-8
Hardcover ISBN
978-3-540-00337-3
Softcover ISBN
978-3-642-53514-7
Series ISSN
1434-9922
Edition Number
1
Number of Pages
XIV, 195
Topics

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