模糊微分方程可约的条件

doi:10.3969/j.issn.1000-1565.2020.04.001

河北大学学报(自然科学版) ›› 2020, Vol. 40 ›› Issue (4): 337-343.DOI: 10.3969/j.issn.1000-1565.2020.04.001

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模糊微分方程可约的条件

吉利业,尤翠莲

收稿日期:2019-11-27 出版日期:2020-07-25 发布日期:2020-07-25
通讯作者: 尤翠莲(1977—),女,河北唐山人,河北大学教授,主要从事不确定理论与规划研究. E-mail:yycclian@163.com
作者简介:吉利业(1996—),女,河北唐山人,河北大学在读硕士研究生,主要从事模糊微分方程理论与应用研究. E-mail:1334620331@qq.com
基金资助:
国家自然科学基金资助项目(61773150);河北省教育厅重点基金资助项目(ZD2020172);河北省教育厅青年基金资助项目(QN2020124)

Reducibility conditions for fuzzy differential equation

JI Liye, YOU Cuilian

College of Mathematics and Information Science, Hebei University, Baoding 071002, China

Received:2019-11-27 Online:2020-07-25 Published:2020-07-25

摘要/Abstract

摘要： 模糊微分方程是在模糊环境下研究动态系统的重要工具,所以对方程进行求解是一项必不可少的工作.为了能使更多的模糊微分方程更容易求解,通过对非线性模糊微分方程进行变量替换判断方程是否可约,并在此过程中试图找到非线性模糊微分方程转化成线性模糊微分方程的方法.最后给出了2种形式的模糊微分方程是否可约的充分条件,同时推导出非线性模糊微分方程转化为线性模糊微分方程的具体方法,使可约模糊微分方程更容易辨别和求解,并且给出算例验证了结果的有效性.

关键词: 模糊变量, 模糊过程, 模糊积分, 变量替换, 可约模糊微分方程

Abstract: Fuzzy differential equation is an important tool for studying dynamic system in fuzzy environment. Therefore, finding the solutions to these equations is essential. In order to make more fuzzy differential equations easier to solve, variables substitution is performed in nonlinear fuzzy differential equation to judge whether the equation is reducible. In this process, we try to find out the method to reduce a nonlinear fuzzy differential equation to a linear fuzzy differential equation. In the last, the conditions of two types of fuzzy differential equations being reducible are given. Therefore, it becomes easy to distinguish reducible fuzzy differential equations and solve them. In addition, some examples are given to verify the effectiveness of the results.

Key words: fuzzy variable, fuzzy process, fuzzy integral, variables substitution, reducible fuzzy differential equation

中图分类号:

O519

吉利业,尤翠莲. 模糊微分方程可约的条件[J]. 河北大学学报(自然科学版), 2020, 40(4): 337-343.

JI Liye, YOU Cuilian. Reducibility conditions for fuzzy differential equation[J]. Journal of Hebei University (Natural Science Edition), 2020, 40(4): 337-343.

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模糊微分方程可约的条件

Reducibility conditions for fuzzy differential equation

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