文献类型：期刊文献

中文题名：粗糙集理论下的模糊随机结构强度分析方法

英文题名：NEW ANALYSIS METHOD OF THE FUZZY-RANDOM STRENGTH IN THE ROUGH SET THEORY

作者：刘长虹[1]

机构：[1]华东理工大学机械与动力工程学院,上海200237

年份：2007

卷号：29

期号：6

起止页码：960

中文期刊名：机械强度

外文期刊名：Journal of Mechanical Strength

收录：CSTPCD;;Scopus;北大核心:【北大核心2004】；CSCD:【CSCD2011_2012】；

基金：国家自然科学基金;中国工程物理研究院联合基金(10076014)资助项目~~

语种：中文

中文关键词：粗糙集;不确定;上(下)近似;结构分析

外文关键词：Rough set theory; Uncertahity; Upper （lower） approximation; Structural analyses

摘要：在分析工程中含有模糊、随机变量的结构强度问题中,如何处理模糊变量和随机变量是一个非常重要的问题。根据粗糙集理论,利用基于模糊变量在粗糙集的上、下近似集合的定义和随机变量在粗糙集的上、下近似集合的定义,可以分别把结构中模糊和随机不确定因素这两种定义在不同集合下的不确定性变量处理为在完全属于论域集合和部分属于论域的上、下近似集合意义下区间参数。再根据区间估计定理,将模糊变量和随机变量转化为在统一尺度下的区间变量。使得含有模糊、随机变量的工程结构转化为含有区间数变量的工程结构,这时模糊随机结构分析的结果也将是区间数。从而避免了判断模糊或随机参数下隶属函数或概率分布函数的难点,使模糊随机结构能够在粗糙集理论下进行统一的结构分析。算例表明,文中所提方法不但可以避免在工程实际问题中确定模糊和随机变量的难点,而且可以利用处理工程结构强度问题方法和软件来解决这类模糊随机问题。
When analysis of the fuzzy-random structures, in generally speaking, it is important that who to deal with the fuzzy variables and random variables respectively. According to the upper （lower） approximation in the tough set theory, the uncertain parameters in the engineering, such as the fuzzy parameter can be transferred into the interval numbers in the upper （lower） approximation, and the random parameter also can be transferred into the interval numbers in the upper （lower） approximation. Moreover with the interval algorithms, the rules, in a standard level, how to transfer a fuzzy variable and a random variable into interval number respectively are presented. In this way, a fuzzy-random structure can be transferring into a structural problem with the interval variables, this problem can be analyses by the interval operations, and the calculation results are the interval numbers. By this method, the fuzzy membership functions or the probabilistic distribution functions in the parameters can be not determined, and the fuzzy-random structures which contained variables defined in tow different fields, one in the fuzzy field and another in the stochastic field can be analyses by the rough set theory. Finally the example shows, with this method, it is not only can be avoid to treatment the difficult problems such as to determine the properties of the fuzzy variables and of the random variables, but also can solve those fuzzy-random structural strength problems by the general methods and the general finite element method （FEM） programs.