| Cardinalities of Fuzzy Sets 2003 Edition Contributor(s): Wygralak, Maciej (Author) |
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ISBN: 3540003371 ISBN-13: 9783540003373 Publisher: Springer OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: March 2003 Annotation: This is the first book presenting cardinality theory of fuzzy sets with triangular norms, including its scalar and "fuzzy" streams. This theory constitutes not only a powerful basis but also a useful tool for modelling and processing vague and imprecise quantitative information. The multiple application areas of the theory encompass computer science, soft computing, computing with words, and decision-making. Starting with a presentation of the fundamentals of triangular norms a fuzzy set theory, the book offers a self-contained, concise and systematic exposition of cardinalities of fuzzy sets that includes many examples. |
| Additional Information |
| BISAC Categories: - Mathematics | Set Theory - Mathematics | Group Theory - Technology & Engineering | Engineering (general) |
| Dewey: 511.322 |
| LCCN: 2002044662 |
| Series: Studies in Fuzziness and Soft Computing |
| Physical Information: 0.67" H x 6.56" W x 9.44" (0.95 lbs) 195 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |