It is known that given a Hilbert function H H, there need not exist a module which has uniquely the smallest graded Betti numbers among all modules attaining H H. In this paper we extend the previous example of this behavior to an infinite family and demonstrate with a second infinite family that ev
Graded numbers and graded convergence of fuzzy numbers
✍ Scribed by JoséA. Herencia
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 795 KB
- Volume
- 88
- Category
- Article
- ISSN
- 0165-0114
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✦ Synopsis
We apply the concept of "graded set" to define several kinds of "graded numbers". We consider the operations, order and convergence for graded numbers. The relationship between these concepts and the corresponding ones for Zadeh's and Hutton's fuzzy numbers gives rise to the definition of "graded convergence" for fuzzy numbers. This convergence avoids some disadvantages presented by the :~-level convergence (which proves to be a specific case of the former).
📜 SIMILAR VOLUMES
The sequence X = {Ark } of fuzzy numbers is statistically convergent to the fuzzy number 3(o provided that for each e ~ 0 lim l{the number ofk~e} = 0. n In this paper we study a related concept of convergence in which the set {k: k<~n} is replaced by {k: kr-1 -~k<~kr} for some lacunary sequence {k~}