There are intro-duced two types of fuzzy cardinalities, namely µ-cardinality and µ-cardinality equipollence) of fuzzy sets and shown some of their properties and represen-tations (for the flnite cases) with regard to needs of the following chapters. Cardinalities of Fuzzy Sets by Maciej Wygralak and Publisher Springer. the sigma count of a fuzzy set, the cardinality of its core or support, and the cardinality of its t -level set. In the next three sections, we deal with triangular norm-based operations on fuzzy sets as well as other basic elements of the language of fuzzy sets. Pris: 1079 kr.
Save up to 80% by choosing the eTextbook option for ISBN: 9783540363828, 3540363823. 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. Other identities are related to the fuzzification of the (symmetric) difference of fuzzy sets.
For a possible example of such a set consider the set of your eight closest friends in the set of "tall people" (or your "Top Eight" in your MySpace page if you had one a few years ago). An important such identity is the valuation property. The print version of this textbook is ISBN: 9783540363828, 3540363823. 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.
Cardinality of a fuzzy set: Cardinality of a non-fuzzy set, Z, is the number of elements in Z. An axiomatic approach to scalar cardinalities of finite fuzzy sets involving t-norms and t-conorms is presented.
We like to investigate their properties, including the valuation property, the cartesian product rule and the complementarity rule.
A characterization theorem for these cardinalities is proved and it is also proved that some standard properties remain true. The last section of this chapter contains an introduction to the problem of cardinalities of fuzzy sets with triangular norm-based operations. Cardinalities of Fuzzy Sets - 9783642535147 By Maciej Wygralak: Buy its Paperback Edition at lowest price online for Rs 8557 at BuyHatke.com. Many approaches to fuzzy quantiflers are based on the concept of scalar or fuzzy cardinalities. Scalar cardinality comes as the relevant concept here. Counting is one of the basic elementary mathematical activities. 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.
Therefore, it is interesting to investigate the relation-ship between equipollences and cardinalities of fuzzy sets. The existing methods to assess the cardinality of a fuzzy set with finite support are intended to preserve the properties of classical cardinality.
The first approach claims that the cardinality of a fuzzy set is measured by means of a scalar value, either integer or real, whereas the second approach assumes the cardinality of a fuzzy set is just another fuzzy set over the non-negative integers. The infinite family of possible scalar cardinalities of a fuzzy set generated by the postulates contains as particular cases all standard concepts of scalar cardinality, e.g. At the same time, Salii (1965) defined a more general kind of structure called an L-relation, which he studied in an abstract algebraic context. An introduction of equipollence of fuzzy sets was the second goal of this the-sis. Cardinalities of Fuzzy Sets by Maciej Wygralak, 9783540003373, available at Book Depository with free delivery worldwide. Chapter 3 is devoted to cardinalities of flnite fuzzy sets. There's an entire book on cardinality in fuzzy set theory actually.
In order to study An axiomatic approach to scalar cardinalities of finite fuzzy sets involving t-norms and t-conorms is presented.
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