模糊离散分式微积分和模糊分式离散方程

IF 3.2 1区 数学 Q2 COMPUTER SCIENCE, THEORY & METHODS Fuzzy Sets and Systems Pub Date : 2024-07-11 DOI:10.1016/j.fss.2024.109073
Ngo Van Hoa , Nguyen Dinh Phu
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引用次数: 0

摘要

本文旨在强调前人在研究基于广义赫库哈拉差分(gH-difference)的模糊分式离散方程(FFDEs)时存在的某些局限性。一般来说,FFDE 与相关的模糊离散分式和方程(FDFSE)之间没有实现等价,需要引入适当的假设来建立这种等价关系。此外,本文通过模糊区间之间的粒度算术运算引入了模糊分数离散微积分的基本理论,以解决前述方法中涉及广义赫库哈拉差分的限制。这些运算是基于多维模糊运算(MFA)中使用的水平成员函数(HMF)概念构建的。此外,论文还提出将分数离散微积分应用于两类右边不为零的时间离散化扩散方程。最后,本文提供了几个数值示例来验证主要结果。
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Fuzzy discrete fractional calculus and fuzzy fractional discrete equations

This paper aims to highlight certain limitations in the study of fuzzy fractional discrete equations (FFDEs) based on the generalized Hukuhara difference (gH-difference) in the previous papers. In general, the equivalence between FFDEs and the associated fuzzy discrete fractional sum equations (FDFSEs) is not achieved, requiring the introduction of an appropriate hypothesis to establish this equivalence. Furthermore, this paper introduces the fundamental theory of fuzzy fractional discrete calculus through granular arithmetic operations between fuzzy intervals to address restrictions in the formerly mentioned approaches involving the generalized Hukuhara difference. These operations are constructed based on the concept of the horizontal membership function (HMF) utilized in multidimensional fuzzy arithmetic (MFA). Additionally, the paper proposes the application of fractional discrete calculus to two types of time-discretization diffusion equations with non-zero right-hand sides. Finally, several numerical examples are provided to validate the main results.

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来源期刊
Fuzzy Sets and Systems
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.
期刊最新文献
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