本文選題：不確定變量　切入點(diǎn)：不確定過程　出處：《河北大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：自然界中存在著各種各樣的不確定現(xiàn)象,隨著時代的發(fā)展與科技的進(jìn)步,現(xiàn)實(shí)生活中的不確定現(xiàn)象也越來越多,概率論和模糊理論不能解決的問題也隨之增加.為了更好地處理不確定現(xiàn)象,產(chǎn)生了不確定理論.不確定理論是一種新的處理人的主觀不確定性的公理化體系方法.在不確定理論的框架下,本文通過對強(qiáng)同單調(diào)不確定過程進(jìn)行研究,得出了關(guān)于強(qiáng)同單調(diào)不確定過程及其積分的一些性質(zhì).通過對復(fù)不確定過程及其分布函數(shù)的研究,得出了不確定積分與復(fù)不確定積分的一些性質(zhì).最后,對復(fù)不確定微分方程的求解方法進(jìn)行研究,得出了復(fù)不確定微分方程解的存在唯一性定理.本文的主要內(nèi)容有:1.定義并討論了強(qiáng)同單調(diào)不確定過程的加法和數(shù)乘性質(zhì)以及關(guān)于強(qiáng)同單調(diào)不確定過程積分的非負(fù)性、單調(diào)性和幾個積分不等式.2.引入了復(fù)不確定過程分布函數(shù)的概念,給出了復(fù)不確定過程分布的一個充要條件,研究了復(fù)不確定過程的獨(dú)立性、期望和方差等,討論了不確定積分與復(fù)不確定積分的存在性問題,同時研究了其它不確定積分的一些基本性質(zhì).3.探討了復(fù)不確定微分方程的解并證明了復(fù)不確定微分方程解的存在唯一性定理.
[Abstract]:There are various kinds of uncertainties in nature. With the development of the times and the progress of science and technology, there are more and more uncertainties in real life. The number of problems that cannot be solved by probability theory and fuzzy theory increases. In order to better deal with uncertainties, Uncertainty theory is a new axiomatic system method to deal with human's subjective uncertainty. Under the framework of uncertainty theory, this paper studies the strongly isomorphic monotone uncertain process. Some properties of strongly isomorphic monotone uncertain processes and their integrals are obtained. By studying complex uncertain processes and their distribution functions, some properties of uncertain integrals and complex uncertain integrals are obtained. The method of solving complex uncertain differential equations is studied. The existence and uniqueness theorems of solutions for complex uncertain differential equations are obtained. The main contents of this paper are: 1.Defining and discussing the additive and multiplicative properties of strongly identical monotone uncertain processes and the nonnegativity of integrals for strongly isomorphic uncertain processes. The concept of distribution function of complex uncertain processes is introduced, a sufficient and necessary condition for the distribution of complex uncertain processes is given, and the independence, expectation and variance of complex uncertain processes are studied. This paper discusses the existence of uncertain integrals and complex uncertain integrals, studies some basic properties of other uncertain integrals, discusses the solutions of complex uncertain differential equations and proves the existence and uniqueness theorems of solutions of complex uncertain differential equations.
【學(xué)位授予單位】：河北大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

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本文編號：1623817