基于最大积和最大最小运算的Shepard算子的向量值函数的非线性逼近

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-02-27 DOI:10.1016/j.fss.2025.109332

Oktay Duman , Esra Erkus-Duman

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引用次数: 0

摘要

为了逼近单位超立方体上的向量值函数和连续函数，我们利用极大积和极大极小运算对线性Shepard算子进行了修正。我们还研究了一些正则可和性方法在近似中的作用，如Cesàro可和性和Abel可和性。此外，我们还给出了一些有趣的应用和图形仿真来验证我们的理论结果。例如，我们利用这些修正算子逼近环面曲面、螺旋曲线、模糊点和LogSumExp函数。应用表明，所得结果不仅与经典逼近理论有关，而且与模糊逻辑理论和机器学习算法有关。

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Nonlinear approximation of vector-valued functions by Shepard operators based on max-product and max-min operations

In this paper, to approximate vector-valued and continuous functions on the unit hypercube, we modify the linear Shepard operators by using max-product and max-min operations. We also investigate the effects of some regular summability methods in the approximation, such as Cesàro summability and Abel summability. Furthermore, we give some interesting applications and graphical simulations verifying our theoretical results. For example, we approximate a torus surface, a helix curve, a fuzzy point and the LogSumExp function by means of these modified operators. Our applications show that the results obtained here are connected with not only the classical approximation theory but also the theory of fuzzy logic and machine learning algorithms.

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.