Higher-order derivative of uncertain process and higher-order uncertain differential equation

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

Fuzzy Optimization and Decision Making Pub Date : 2024-04-08 DOI:10.1007/s10700-024-09422-0

Kaixi Zhang, Baoding Liu

引用次数: 0

Abstract

This paper initializes higher-order uncertain calculus that deals with higher-order differentiation and multiple integration of uncertain process based on uncertainty theory. Fubini theorem and fundamental theorem of higher-order uncertain calculus are derived. Finally, this paper rigorously defines higher-order uncertain differential equations and introduces some analytic methods for solving these equations.

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不确定过程的高阶导数和高阶不确定微分方程

本文以不确定性理论为基础，初步提出了处理不确定过程的高阶微分和多重积分的高阶不确定微积分。推导出了 Fubini 定理和高阶不确定微积分基本定理。最后，本文严格定义了高阶不确定微分方程，并介绍了求解这些方程的一些解析方法。

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.