منابع مشابه
Cardinality for Infinite Sets
How can we determine whether two sets have the same cardinality (or “size”)? The answer to this question, reassuringly, lies in early grade school memories: by demonstrating a pairing between elements of the two sets. More formally, we need to demonstrate a bijection f between the two sets. The bijection sets up a one-to-one correspondence, or pairing, between elements of the two sets. We know ...
متن کاملOn Cardinality of Fuzzy Sets
In this article, we would like to revisit and comment on the widely used definition of cardinality of fuzzy sets. For this purpose we have given a brief description of the history of development of fuzzy cardinality. In the process, we can find that the existing definition fails to give a proper cardinality while dealing with complementation of fuzzy sets. So there arises the need of defining t...
متن کاملOn the cardinality of fuzzy sets
It seems that a suitably constructed fuzzy sets of natural numbers form the most complete and adequate description of cardinality of finite fuzzy sets.(see [11]) Nevertheless, in many applications one needs a simple scalar evaluation of that cardinality by nonnegative real number, e.g scalar cardinality. There are many approaches to this evaluation-sigma count of fuzzy set,psigma count of fuzzy...
متن کاملCardinality of Fuzzy Sets: An Overview
In this article, we would like to stress on the new definition of cardinality of fuzzy sets which can be contributed to the definition of complementation of fuzzy sets on the basis of reference function. As a consequence of which we would like to discard those results which are based on the existing definition of cardinality of fuzzy sets particularly when it involves complementation.
متن کاملPartitioning into Sets of Bounded Cardinality
We show that the partitions of an n-element set into k members of a given set family can be counted in time O((2− )), where > 0 depends only on the maximum size among the members of the family. Specifically, we give a simple combinatorial algorithm that counts perfect matchings in a given graph on n vertices in time O(poly(n)φ), where φ = 1.618 . . . is the golden ratio; this improves a previou...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1983
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1983-0702311-9