不確定過程與積分
發(fā)布時(shí)間：2018-10-09 12:59
【摘要】：自然界中普遍存在著各種各樣的不確定現(xiàn)象,基于對(duì)這些不確定現(xiàn)象的研究,產(chǎn)生了不確定理論.不確定理論是概率論,可信性理論,信賴性理論的統(tǒng)稱,是處理人的信度的數(shù)學(xué)體系.在不確定理論的框架下,把不確定過程定義為一族隨時(shí)間變化的不確定變量.基于不確定理論,本文主要對(duì)復(fù)不確定過程進(jìn)行了討論,得出了相關(guān)性質(zhì),并將不確定微積分推廣到復(fù)情形,進(jìn)一步研究了復(fù)不確定微積分的性質(zhì),給出了不確定無窮積分的定義.為了研究不確定向量,本文還提出了不確定向量的熵.這些結(jié)果擴(kuò)展了不確定理論的研究內(nèi)容.本文的內(nèi)容有:1.研究了復(fù)不確定過程的一些特性,包括復(fù)不確定過程的期望和獨(dú)立性以及復(fù)不確定微積分的性質(zhì).2.定義了不確定無窮積分,把不確定過程關(guān)于典范過程的積分區(qū)間由有限區(qū)間推廣到了無窮區(qū)間.3.提出正則不確定向量的聯(lián)合分布函數(shù)以及不確定向量的熵,為度量不確定向量的不確定性提供了工具.
[Abstract]:There are many kinds of uncertain phenomena in nature. Based on the study of these uncertain phenomena, uncertainty theory is produced. Uncertainty theory is the general term of probability theory, credibility theory and reliability theory, and it is a mathematical system to deal with human reliability. Under the framework of uncertainty theory, the uncertain process is defined as a family of uncertain variables varying with time. Based on the uncertainty theory, this paper mainly discusses the complex uncertain process, obtains the related properties, and extends the uncertain calculus to the complex case, and further studies the properties of the complex uncertain calculus. The definition of indefinite infinite integral is given. In order to study the uncertain vector, the entropy of the uncertain vector is also proposed in this paper. These results extend the research content of uncertainty theory. The content of this article is 1: 1. Some properties of complex uncertain processes are studied, including the expectation and independence of complex uncertain processes and the properties of complex uncertain calculus. The indefinite infinite integral is defined, and the integral interval of uncertain process for canonical process is extended from finite interval to infinite interval. 3. The joint distribution function of the regular uncertain vector and the entropy of the uncertain vector are proposed, which provide a tool for measuring the uncertainty of the uncertain vector.
【學(xué)位授予單位】：河北大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：O21;O172.2
本文編號(hào)：2259421
[Abstract]:There are many kinds of uncertain phenomena in nature. Based on the study of these uncertain phenomena, uncertainty theory is produced. Uncertainty theory is the general term of probability theory, credibility theory and reliability theory, and it is a mathematical system to deal with human reliability. Under the framework of uncertainty theory, the uncertain process is defined as a family of uncertain variables varying with time. Based on the uncertainty theory, this paper mainly discusses the complex uncertain process, obtains the related properties, and extends the uncertain calculus to the complex case, and further studies the properties of the complex uncertain calculus. The definition of indefinite infinite integral is given. In order to study the uncertain vector, the entropy of the uncertain vector is also proposed in this paper. These results extend the research content of uncertainty theory. The content of this article is 1: 1. Some properties of complex uncertain processes are studied, including the expectation and independence of complex uncertain processes and the properties of complex uncertain calculus. The indefinite infinite integral is defined, and the integral interval of uncertain process for canonical process is extended from finite interval to infinite interval. 3. The joint distribution function of the regular uncertain vector and the entropy of the uncertain vector are proposed, which provide a tool for measuring the uncertainty of the uncertain vector.
【學(xué)位授予單位】：河北大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：O21;O172.2
【相似文獻(xiàn)】
相關(guān)碩士學(xué)位論文 前1條
1 李香誼;不確定過程與積分[D];河北大學(xué);2016年
，本文編號(hào)：2259421
本文鏈接：http://sikaile.net/kejilunwen/yysx/2259421.html
最近更新
教材專著
