基于区间概率上的模糊问题探究

1、基于区间概率上的模糊问题探究    基于区间概率上的模糊问题探究区间概率基础上的模糊概率的研究     目录：中文摘要 5-6ABSTRACT 6-7第1章引言 10-121.1研究背景 10-111.2论文的研究内容与结构 11-12第2章模糊数学基础 12-162.1截集与分解定理 12-132.1.1截集 122.1.2分解定理 12-132.2模糊数 13-152.2.1闭区间数及其运算 

2、13-142.2.2模糊数的概念与运算 14-152.3本章小结 15-16第3章区间概率 16-283.1区间概率 16-203.1.1可行性区间 16-193.1.2区间概率 19-203.2离散型区间概率随机变量 20-233.2.1离散型区间概率随机变量的相关定义和性质 20-213.2.2离散型区间概率随机变量的数字特征 21-233.3连续型区间概率随机变量 23-263.3.1连续型区间概率随机变量的相关定义 23-243.3.2连续型区间概率随机变量的数字特征 

3、;24-263.4本章小结 26-28第4章精确事件模糊概率 28-404.1精确事件的定义 28-294.2离散型精确事件模糊概率定义 29-304.3离散型精确事件模糊概率随机变量及其数字特征 30-364.3.1离散型精确事件模糊概率随机变量 31-324.3.2离散型精确事件模糊概率随机变量的数字特征 32-364.4连续型精确事件模糊概率随机变量及其数字特征 36-384.4.1连续型精确事件模糊概率随机变量 36-384.4.2连续型精确事件模糊概率随机变量的数字特征 384.5本章

4、小结 38-40第5章模糊事件模糊概率的初步讨论 40-485.1模糊事件的定义 40-415.1.1模糊事件的实际背景 405.1.2模糊事件的定义 40-415.2离散型模糊事件的模糊概率定义 41-425.3离散型模糊事件模糊概率随机变量及其数字特征 42-455.3.1离散型模糊事件模糊概率随机变量 42-435.3.2离散型模糊事件模糊概率随机变量的数字特征 43-455.4连续型模糊事件模糊概率随机变量及其数字特征 45-475.4.1连续型模糊事件模糊概率随机变量 45-

5、465.4.2连续型模糊事件模糊概率随机变量的数字特征 46-475.5本章小结 47-48第6章总结与展望 48-49参考文献 49-51致谢 51-52攻读学位期间发表的论文 52 【摘要】 模糊概率按模糊情况分为三类：Fuzzy事件-精确概率、精确事件Fuzzy概率、Fuzzy事件Fuzzy概率。近几年来,不少学者对第一类问题作了大量研究,取得了很多成果。对第二类问题也有一些文献作了探索,取得了一定的进展,但研究还很不深入,主要是因为Fuzzy概率运算方法还不成熟。1998年,王柏生提出了一种模糊数源的思想,该思想对探

6、索模糊数的合理运算具有极大的启发性。基于这种思想,区间概率随机变量极其数字特征得到了相对详细的研究.在此基础上一些文献对第二类模糊概率问题的研究做了一些探索,主要是离散型模糊随机问题。在连续型随机问题中,概率密度函数完全刻画了随机变量,但要得到准确的概率密度函数不是一件容易的事。所以在数据不充分、概率密度函数不能完全确定的情况下,用模糊值函数来描述概率密度函数将更具有实际意义,并称此模糊值函数为模糊概率密度函数,相应的随机变量称为连续型精确事件模糊概率随机变量。在此基础上连续型第二类模糊概率随机问题也得到了一定的研究。本文首先介绍了区间概率及其随机问题的有关知识,然后在此基础上详细的总结了第二

7、类模糊概率及其随机问题的有关结论：包括离散型和连续型。离散型区间概率随机问题是基于模糊数源思想,建立了有限源区间概率空间,并且给出了区间概率随机变量(向量)及其分布函数、分布列、期望区间、方差区间等的定义,并研究了其中的一些特定性质和运算规律。离散型第二类模糊概率随机问题就是以离散型区间概率随机问题为基础得出一系列相应的结论：离散型精确事件模糊概率随机变量及其分布函数、分布列、模糊数学期望和模糊方差的定义。连续型第二类模糊随机问题是指由于概率密度函数的模糊性而引起的模糊概率随机问题,在区间密度函数的基础上建立了具有模糊密度的连续型精确事件模糊概率随机变量及其分布函数的定义和基本性质,并给出了相

8、应随机变量的模糊数学期望、模糊方差的定义和计算方法。其次本文对一些在文献中未给出证明的性质给出了合理的证明；最后本文将有关的结论运用到对第三类模糊概率的研究中,并初步得到了一些结论：包括离散型和连续型。在离散型中给出了模糊事件模糊概率随机变量及其分布函数、分布列、模糊数学期望和模糊方差的定义；在连续型中给出了具有模糊密度的模糊事件模糊概率随机变量及其分布函数的定义和基本性质,并给出了相应随机变量的模糊数学期望、模糊方差的定义。在对第三类模糊概率问题的研究中,有些结论还不成熟,有待进一步的研究探索。  【Abstract】 Fuzzy probability falls into th

9、ree categories according to fuzzy situation:fuzzy events-accurate probability; clear events-fuzzy probability; fuzzy events-fuzzy probability. In recent years, many scholars               have made many achievements about the firs

10、t kind of fuzzy probability. Some scholars have also made some progress about the second kind of fuzzy probability, but are not in-depth study, mainly because that the calculation methods of fuzzy probability are not yet ripe.In 1998, Wang Baisheng presented the idea about fuzzy number origin, the i

11、dea has great inspirational for exploring the fuzzy numbers reasonable computing. Based on this idea, random variable of interval probability and its digital features have been relatively detailed studied. On this basis, the second kind of fuzzy probability has been study in some of the literature,

12、mainly on the discrete fuzzy random problems. In continuous random problems, the random variable has been fully described by the probability density function, but it is not an easy task to get the accurate probability density function. So it will be of practical significance to describe the fuzzy pr

13、obability density function using fuzzy-valued function if the data is not complete and the probability density function can not be fully defined. The fuzzy-valued function is said to be fuzzy probability density function, and the corresponding random variables is said to be fuzzy random variables. O

14、n this basis, the problem of the second kind of continuous fuzzy probability random variables has been studied.In this paper, the knowledge of interval probability and its random problem has been first introduced, and then conclusions about the second type of fuzzy probability and its random problem

15、 have been detailed and specific summarized, including discrete fuzzy random problems and continuous fuzzy random problems. Based on the idea of fuzzy number origin, an interval probability space of the finite origin is established by the operation of fuzzy probability. Definitions of interval proba

16、bility random variable (random vecter) and its distribution function, distribution sequence, math expectation, variance and so on are given, and the specific nature and operational law have been studied too. The discrete random question of the second kind of fuzzy probability is based on the discret

17、e random problem of interval probability and then gets a series of corresponding conclusions:definitions of fuzzy probability random variable (random vecter) and its distribution function, distribution sequence, fuzzy math expectation, fuzzy variance and so on are given, and the specific nature and

18、operational law have been studied too. The problem of the second kind of continuous fuzzy probability random variables is the problem of fuzzy probability random because of the fuzziness of probability density function, the definition and basic nature of the fuzzy random variable with fuzzy density and its distribution function on