Cardinalities of Fuzzy Sets:
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...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2003
|
| Schriftenreihe: | Studies in Fuzziness and Soft Computing
118 |
| Schlagworte: | |
| Online-Zugang: | FHI01 BTU01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | 1 Online-Ressource (XIV, 195 p) |
| ISBN: | 9783540363828 |
| DOI: | 10.1007/978-3-540-36382-8 |
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| 520 | |a 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 | ||
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Datensatz im Suchindex
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| author | Wygralak, Maciej |
| author_facet | Wygralak, Maciej |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.1 |
| dewey-search | 511.1 |
| dewey-sort | 3511.1 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-540-36382-8 |
| format | Electronic eBook |
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| id | DE-604.BV045149129 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:10:03Z |
| institution | BVB |
| isbn | 9783540363828 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030538828 |
| oclc_num | 1050943738 |
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| physical | 1 Online-Ressource (XIV, 195 p) |
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| publishDate | 2003 |
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| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Studies in Fuzziness and Soft Computing |
| spelling | Wygralak, Maciej Verfasser aut Cardinalities of Fuzzy Sets by Maciej Wygralak Berlin, Heidelberg Springer Berlin Heidelberg 2003 1 Online-Ressource (XIV, 195 p) txt rdacontent c rdamedia cr rdacarrier Studies in Fuzziness and Soft Computing 118 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 Mathematics Discrete Mathematics Complexity Math Applications in Computer Science Group Theory and Generalizations Systems Theory, Control Computer science / Mathematics Group theory System theory Discrete mathematics Complexity, Computational Erscheint auch als Druck-Ausgabe 9783642535147 https://doi.org/10.1007/978-3-540-36382-8 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Wygralak, Maciej Cardinalities of Fuzzy Sets Mathematics Discrete Mathematics Complexity Math Applications in Computer Science Group Theory and Generalizations Systems Theory, Control Computer science / Mathematics Group theory System theory Discrete mathematics Complexity, Computational |
| title | Cardinalities of Fuzzy Sets |
| title_auth | Cardinalities of Fuzzy Sets |
| title_exact_search | Cardinalities of Fuzzy Sets |
| title_full | Cardinalities of Fuzzy Sets by Maciej Wygralak |
| title_fullStr | Cardinalities of Fuzzy Sets by Maciej Wygralak |
| title_full_unstemmed | Cardinalities of Fuzzy Sets by Maciej Wygralak |
| title_short | Cardinalities of Fuzzy Sets |
| title_sort | cardinalities of fuzzy sets |
| topic | Mathematics Discrete Mathematics Complexity Math Applications in Computer Science Group Theory and Generalizations Systems Theory, Control Computer science / Mathematics Group theory System theory Discrete mathematics Complexity, Computational |
| topic_facet | Mathematics Discrete Mathematics Complexity Math Applications in Computer Science Group Theory and Generalizations Systems Theory, Control Computer science / Mathematics Group theory System theory Discrete mathematics Complexity, Computational |
| url | https://doi.org/10.1007/978-3-540-36382-8 |
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