Granular fuzzy calculus on time scales and its applications to fuzzy dynamic equations

IF 8.1 1区计算机科学 0 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Sciences Pub Date : 2024-10-16 DOI:10.1016/j.ins.2024.121547

Tri Truong , Martin Bohner , Ewa Girejko , Agnieszka B. Malinowska , Ngo Van Hoa

引用次数: 0

Abstract

This paper introduces the foundational theory of fuzzy calculus on time scales, utilizing granular arithmetic operations between fuzzy intervals. These operations are developed based on the concept of the horizontal membership function (HMF), which is applied in multidimensional fuzzy arithmetic (MFA). Furthermore, the paper explores the existence of a unique solution and the continuous dependence of the solution to fuzzy dynamic equations on initial data, employing the Banach fixed-point theorem under a new metric for fuzzy functions in time scales involving the generalized exponential function. Finally, to highlight the practical significance of these results and their potential applications, the paper presents mathematical models relevant to nuclear physics and biology.

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时间尺度上的粒度模糊微积分及其在模糊动态方程中的应用

本文介绍了时间尺度上的模糊微积分基础理论，利用了模糊区间之间的粒度运算。这些运算是在水平成员函数（HMF）概念的基础上发展起来的，并应用于多维模糊运算（MFA）中。此外，论文还在涉及广义指数函数的时间尺度模糊函数新度量下，利用巴拿赫定点定理，探讨了模糊动态方程唯一解的存在性以及解对初始数据的连续依赖性。最后，为了突出这些结果的实际意义及其潜在应用，论文介绍了与核物理和生物学相关的数学模型。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Information Sciences 工程技术-计算机：信息系统

CiteScore

14.00

自引率

17.30%

发文量

1322

审稿时长

10.4 months

期刊介绍： Informatics and Computer Science Intelligent Systems Applications is an esteemed international journal that focuses on publishing original and creative research findings in the field of information sciences. We also feature a limited number of timely tutorial and surveying contributions. Our journal aims to cater to a diverse audience, including researchers, developers, managers, strategic planners, graduate students, and anyone interested in staying up-to-date with cutting-edge research in information science, knowledge engineering, and intelligent systems. While readers are expected to share a common interest in information science, they come from varying backgrounds such as engineering, mathematics, statistics, physics, computer science, cell biology, molecular biology, management science, cognitive science, neurobiology, behavioral sciences, and biochemistry.