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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.
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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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Cardinalities of Fuzzy Sets (Studies in Fuzziness and Soft Computing, 118)
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Cardinalities of Fuzzy Sets (eng)
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Cardinalities of Fuzzy Sets (Studies in Fuzziness and Soft Computing)
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Hardcover. Condition: Very Good. Signed. No DJ. Signed by the author and inscribed on the front free page to Professor Lotfi A. Zadeh. Lotfi Zadeh (1921-2017) electrical engineer, computer scientist, artificial intelligence researcher and professor emeritus of computer science at the University of California, Berkeley, and founder of fuzzy mathematics. Seller Inventory # mon0000019573
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Cardinalities of Fuzzy Sets
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Cardinalities of Fuzzy Sets
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 212 pp. Englisch. Seller Inventory # 9783540003373
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Cardinalities of Fuzzy Sets
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Cardinalities of Fuzzy Sets
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Gebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. First monograph presenting cardinality theory of fuzzy sets with triangular norms, including its scalar and fuzzy streamsSelf-contained, systematic presentation equipped with many examplesCounting is one of the basic elementary mathematica. Seller Inventory # 4877099
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