On uncertain partial differential equations

IF 4.8 2区计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Fuzzy Optimization and Decision Making Pub Date : 2023-11-19 DOI:10.1007/s10700-023-09418-2

Yuanguo Zhu

引用次数: 0

Abstract

Uncertain partial differential equation (UPDE) was introduced in literature. But the solution of a UPDE was not defined well. In this article, we will rigorously give a suitable concept of a UPDE and define its solution by an integral equation. Then, some examples are given to show the rationality of the definition. Uncertain heat conduction equation is presented as an application of UPDE. For those UPDEs having no analytic solutions, \(\alpha\)-path method is introduced to obtain the inverse uncertainty distributions of solutions to UPDEs.

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不确定偏微分方程

文献中介绍了不确定偏微分方程(UPDE)。但UPDE的解并没有得到很好的定义。在本文中，我们将严格地给出一个合适的UPDE概念，并用积分方程来定义它的解。然后，通过实例说明了该定义的合理性。给出了不确定热传导方程作为UPDE的应用。对于不存在解析解的upde，引入\(\alpha\) -path方法获得upde解的逆不确定性分布。

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

Fuzzy Optimization and Decision Making 工程技术-计算机：人工智能

CiteScore

11.50

自引率

10.60%

发文量

审稿时长

6 months

期刊介绍： The key objective of Fuzzy Optimization and Decision Making is to promote research and the development of fuzzy technology and soft-computing methodologies to enhance our ability to address complicated optimization and decision making problems involving non-probabilitic uncertainty. The journal will cover all aspects of employing fuzzy technologies to see optimal solutions and assist in making the best possible decisions. It will provide a global forum for advancing the state-of-the-art theory and practice of fuzzy optimization and decision making in the presence of uncertainty. Any theoretical, empirical, and experimental work related to fuzzy modeling and associated mathematics, solution methods, and systems is welcome. The goal is to help foster the understanding, development, and practice of fuzzy technologies for solving economic, engineering, management, and societal problems. The journal will provide a forum for authors and readers in the fields of business, economics, engineering, mathematics, management science, operations research, and systems.