Fuzzy approximation by fuzzy convolution type operators
Fuzzy approximation by fuzzy convolution type operators
复制标题
通过模糊卷积类型算子进行模糊逼近
DOI：
10.1016/j.camwa.2004.10.027
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发表时间：
2004
影响因子：
2.9
通讯作者：
G. Anastassiou
中科院分区：
文献类型：
--
作者：
G. Anastassiou
在这里，我们介绍和研究四个自然产生的卷积类型模糊积分算子序列，它们是通过缩放函数定义的已知模糊小波类型算子的积分类似物。它们与模糊单位算子的模糊收敛性是通过涉及模糊连续性模量的模糊不等式建立的。此外，它们的高阶模糊近似也通过涉及所使用的模糊数值函数的 N 阶 (N ≥ 1) H 模糊导数的模糊连续性模来类似地给出。还证明了这些算子的模糊全局平滑性保持特性。
Here we introduce and study four sequences of naturally arising fuzzy integral operatorsof convolution type that are integral analogs of known fuzzy wavelet type operators, defined via a scaling function. Their fuzzy convergence with rates to the fuzzy unit operator is established through fuzzy inequalities involving the fuzzy modulus of continuity. Also, their high-order fuzzy approximation is given similarly by involving the fuzzy modulus of continuity of the Nthorder (N ≥ 1) H-fuzzy derivative of the engaged fuzzy number valued function. The fuzzy global smoothness preservation property of these operators is demonstrated also.