Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable ...Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.展开更多
In this paper,the pointwise characterizations of fuzzy mappings are given. Based of this definition,we give a few of new properties of fuzzy cardinal numbers.
A simple recursive algorithm to generate the set of natural numbers, based on Mersenne numbers: M<sub>N</sub> = 2<sup>N</sup> – 1, is used to count the number of prime numbers within the preci...A simple recursive algorithm to generate the set of natural numbers, based on Mersenne numbers: M<sub>N</sub> = 2<sup>N</sup> – 1, is used to count the number of prime numbers within the precise Mersenne natural number intervals: [0;M<sub>N</sub>]. This permits the formulation of an extended twin prime conjecture. Moreover, it is found that the prime numbers subsets contained in Mersenne intervals have cardinalities strongly correlated with the corresponding Mersenne numbers.展开更多
The concepts of quasi-cardinality, possibility and expectation of a fuzzy set on a measurable set, as a generalization of the quasi-cardinality of a fuzzy set on a finite universe of discourse is proposed. Also some p...The concepts of quasi-cardinality, possibility and expectation of a fuzzy set on a measurable set, as a generalization of the quasi-cardinality of a fuzzy set on a finite universe of discourse is proposed. Also some properties of them are given out and thus some relevant results are elucidated.展开更多
文摘Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.
文摘In this paper,the pointwise characterizations of fuzzy mappings are given. Based of this definition,we give a few of new properties of fuzzy cardinal numbers.
文摘A simple recursive algorithm to generate the set of natural numbers, based on Mersenne numbers: M<sub>N</sub> = 2<sup>N</sup> – 1, is used to count the number of prime numbers within the precise Mersenne natural number intervals: [0;M<sub>N</sub>]. This permits the formulation of an extended twin prime conjecture. Moreover, it is found that the prime numbers subsets contained in Mersenne intervals have cardinalities strongly correlated with the corresponding Mersenne numbers.
文摘The concepts of quasi-cardinality, possibility and expectation of a fuzzy set on a measurable set, as a generalization of the quasi-cardinality of a fuzzy set on a finite universe of discourse is proposed. Also some properties of them are given out and thus some relevant results are elucidated.
基金国家自然科学基金(the National Natural Science Foundation of China under Grant No.60773209)陕西省自然科学基金(the NaturalScience Foundation of Shaanxi Province of China under Grant No.2006F18)
