本文選題：模糊數(shù) + 模糊值函數(shù)��； 參考：《南京信息工程大學(xué)》2017年碩士論文

【摘要】：模糊微分方程是模糊數(shù)學(xué)的重要組成部分,其求解法在實(shí)際中應(yīng)用廣泛.本文主要研究了三種解模糊微分方程邊值問(wèn)題的方法,推廣和改進(jìn)了已有文獻(xiàn)的相關(guān)結(jié)論.全文分為六章,第六章為本文的結(jié)論,其余五章內(nèi)容如下:第一章簡(jiǎn)述了問(wèn)題的研究現(xiàn)狀與基本方法.第二章列出了本文所需要的預(yù)備知識(shí).第三章考慮了線(xiàn)性模糊微分方程邊值問(wèn)題在強(qiáng)廣義可微性概念下推廣了模糊Laplace變換公式,利用逆變換定理與卷積的性質(zhì),提出模糊微分方程邊值問(wèn)題的Laplace變換求解法.第四章以二階線(xiàn)性模糊微分方程為例,利用模糊微分方程的刻畫(huà)方程與模糊邊值之間的關(guān)系,研究了模糊微分方程三角模糊數(shù)邊值條件下的求解法.第五章考慮了帶模糊邊值的三階線(xiàn)性微分方程利用線(xiàn)性變換的性質(zhì)分離模糊邊值,得出了三階線(xiàn)性微分方程模糊邊值問(wèn)題的一種求解方法.
[Abstract]:Fuzzy differential equation is an important part of fuzzy mathematics, and its solution method is widely used in practice. In this paper, three methods for solving boundary value problems of fuzzy differential equations are studied. This paper is divided into six chapters, the sixth chapter is the conclusion of this paper, the other five chapters are as follows: the first chapter describes the research status and basic methods of the problem. The second chapter lists the preparatory knowledge needed in this paper. In chapter 3, the boundary value problem of linear fuzzy differential equation is considered. The fuzzy Laplace transformation formula is generalized under the concept of strong generalized differentiability. By using the property of inverse transformation theorem and convolution, the Laplace transform method for solving the boundary value problem of fuzzy differential equation is proposed. In the fourth chapter, taking the second order linear fuzzy differential equation as an example, by using the relation between the description equation of fuzzy differential equation and the fuzzy boundary value, we study the solution method under the condition of triangular fuzzy number boundary value of fuzzy differential equation. In chapter 5, we consider the third order linear differential equation with fuzzy boundary value and use the property of linear transformation to separate fuzzy boundary value, and obtain a method to solve the fuzzy boundary value problem of third order linear differential equation.
【學(xué)位授予單位】：南京信息工程大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O175.8

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