Fuzzy概率空间的Fuzzy格刻划

本文研究了Fuzzy概率空间中Fuzzy事件及概率的代数性质.利用Fuzzy概率空间中的概率为集函数这一特征和Fuzzy格的相关理论，得到了Fuzzy概率空间中的概率是从一个Fuzzy格到某个区间的Fuzzy格模同态，并将概率分解成Fuzzy格同态与Fuzzy格模同态的乘积。     

Fuzzy集的基数

关于Fuzzy集的基数，[1]中曾对有限支集的Fuzzy集以及极苛刻条件下的无限Fuzzy集给出过一种定义。但是，正如本文将要指出的那样，该定义是不合理的。本文将从研究Fuzzy映射入手，给出Fuzzy集基数的一般性定义。基于这一定义，不但得到有关基数的大部分结论，而且有其自身的特殊性。     

布尔代数上的Fuzzy同余关系

引入了布尔代数上的Fuzzy同余关系的概念，讨论了布尔代数上的Fuzzy同余关系与布尔代数的Fuzzy理想之间的关系，给出了商布尔代数的同构定理。     

BCK-代数的模糊代数理想

在有界可换BCK-代数上引入了Fuzzy代数理想的概念，给出了Fuzzy代数理想的某些特征，讨论了Fuzzy理想与Fuzzy代数理想的关系。最后描述了全体Fuzzy集的BCK-代数特征。     

Fuzzy矩阵方程=■的解及性质

本文首先给出了矩阵方程Ax＝b的解的定义，然后对此解进行了深入的研究。给出了锥形Fuzzy集的概念，讨论了方程Ax－b与锥形Fuzzy集之间的关系。最后证明了一类锥形Fuzzy集全体构成完备的Fuzzy度量空间。     

模的Fuzzy同态性质

文[1]给出了Fuzzy子模、模的Fuzzy同态等概念，本文进一步讨论模的同态和模的Fuzzy同态性质，获得了Fuzzy子模的同态像和Fuzzy子模的模的Fuzzy同态像的基本定理。     

基于商空间和信息粒度的Fuzzy聚类分析

传统聚类分析主要从相似性度量的不同设计和判别函数的选择等方面进行研究。本从商空间理论和信息粒度原理角度出发，引入分层递阶结构，论述聚类分析的本质以及Fuzzy聚类分析这种软件统计方法。     

R0-代数上的Fuzzy同余关系

在R0-代数中引入Fuzzy同余关系的概念，讨论了Fuzzy同余关系的一些基本性质，并通过对R0-代数中的Fuzzy MP滤子，特别是生成Fuzzy MP滤子的讨论建立了Fuzzy MP滤子与Fuzzy同余关系之间的联系。     

布尔代数的Fuzzy子代数和Fuzzy理想

引入了布尔代数的Fuzzy子代数、Fuzzy理想和Fuzzy商布尔代数的概念,给出了布尔代数的Fuzzy集是Fuzzy子代数(Fuzzy理想)的充要条件,讨论了布尔代数的Fuzzy子代数(Fuzzy理想)在布尔代数同态下的像和逆像,得到了布尔代数的Fuzzy子代数的同态基本定理。     

Fuzzy线性映射

在基本Fuzzy点空间上提出了Fuzzy线性映射的概念,证明了Fuzzy线性映射的表示定理,讨论了Fuzzy线性映射的合成、可逆及保持Fuzzy集合的线性运算等相关性质。     

Evaluation of fuzzy linear regression models by comparing membership functions

Fuzzy linear regression models can provide an estimated fuzzy number that has a fuzzy membership function. If a point that has the highest membership value from the estimated fuzzy number is not within the support of the observed fuzzy membership function, a decision-maker can have high risk from the estimate. In this study a modification of fuzzy linear regression analysis based on a criterion of minimizing the difference of the fuzzy membership values between the observed and estimated fuzzy numbers is proposed. Two numerical examples are used to evaluate the fuzzy regression models.     

具有Fuzzy概率的Fuzzy可靠性问题的求解途径

本文提出了工程实践中常见的清晰事件－Ｆｕｚｚｙ概率的Ｆｕｚｚｙ可靠性分析问题的求解途径，首先讨论了Ｆｕｚｚｙ数的代数运算法则，然后在此基础上将Ｆｕｚｚｙ可靠性求解问题转换为Ｆｕｚｚｙ数的运算问题，从而使这类Ｆｕｚｚｙ可靠性分析问题在理论上得到解决，本文还给出了一个算例。     

基于结构元的复模糊数及其序列极限

复模糊数是模糊复分析中的基本概念,在模糊复分析中,它的运算是基于扩张原理的形式给出的,是对元素遍历某个条件所对应的结果进行运算,这种遍历过程给实际操作带来了很多的不便,因此,在一定程度上也阻碍了模糊复分析理论的应用.对此,本文基于模糊结构元的理论基础,探讨了复模糊数运算的另一种新的途径,这种方法简化了复模糊数的运算,也...     

Stability analysis of sampled-data fuzzy controller for nonlinear systems based on switching T–S fuzzy model

This paper investigates the system stability of a sampled-data fuzzy-model-based control system, formed by a nonlinear plant and a sampled-data fuzzy controller connected in a closed loop. The sampled-data fuzzy controller has an advantage that it can be implemented using a microcontroller or a digital computer to lower the implementation cost and time. However, discontinuity introduced by the sampling activity complicates the system dynamics and makes the stability analysis difficult compared with the pure continuous-time fuzzy control systems. Moreover, the favourable property of the continuous-time fuzzy control systems which is able to relax the stability analysis result vanishes in the sampled-data fuzzy control systems. A Lyapunov-based approach is employed to derive the LMI-based stability conditions to guarantee the system stability. To facilitate the stability analysis, a switching fuzzy model consisting of some local fuzzy models is employed to represent the nonlinear plant to be controlled. The comparatively less strong nonlinearity of each local fuzzy model eases the satisfaction of the stability conditions. Furthermore, membership functions of both fuzzy model and sampled-data fuzzy controller are considered to alleviate the conservativeness of the stability analysis result. A simulation example is given to illustrate the merits of the proposed approach.     

Possibilistic linear regression analysis for fuzzy data

Fuzzy data given by expert knowledge can be regarded as a possibility distribution by which possibilistic linear systems are defined. Recently, it has become important to deal with fuzzy data in connection with expert knowledge. Three formulations of possibilistic linear regression analysis are proposed here to deal with fuzzy data. Since our formulations can be reduced to linear programming problems, the merit of our formulations is to be able to obtain easily fuzzy parameters in possibilistic linear models and to add other constraint conditions which might be obtained from expert knowledge of fuzzy parameters. This approach can be regarded as a fuzzy interval analysis in a fuzzy environment.     

基于相对隶属度的织物风格模糊聚类分析

分析比较了统计数学、模糊数学和灰色数学在织物风格分析中的缺陷.特别针对模糊数学需人为确定隶属函数的缺陷提出采用基于相对隶属度的织物风格模糊聚类分析方法.以相对隶属度矩阵和模糊聚类中心矩阵的迭代求解为依据,对苎麻等十种织物的风格测试参数进行了聚类分析.通过聚类计算得到了织物相对类别特征值的聚类结果.经验证认为该结果符合客观实际和人们的感知经验.     

一个模糊凸性的新的证明

用一种新的更传统的方法证明了在下半连续的条件下模糊凸性的两个充分条件.证明充分利用了下半连续即有最小值这一引理,没有沿用讨论该类模糊凸性问题常用方法,将模糊凸性的研究与传统分析中的有关内容融合、统一起来,给该类模糊凸性的研究提供了一种新的思路.     

On the extent analysis method for fuzzy AHP and its applications

In a paper by Chang [D.Y. Chang, Applications of the extent analysis method on fuzzy AHP, European Journal of Operational Research 95 (1996) 649–655], an extent analysis method on fuzzy AHP was proposed to obtain a crisp priority vector from a triangular fuzzy comparison matrix. It is found that the extent analysis method cannot estimate the true weights from a fuzzy comparison matrix and has led to quite a number of misapplications in the literature. In this paper, we show by examples that the priority vectors determined by the extent analysis method do not represent the relative importance of decision criteria or alternatives and that the misapplication of the extent analysis method to fuzzy AHP problems may lead to a wrong decision to be made and some useful decision information such as decision criteria and fuzzy comparison matrices not to be considered. We show these problems to avoid any possible misapplications in the future.     

Fuzzy analytic hierarchy process: A logarithmic fuzzy preference programming methodology

Fuzzy analytic hierarchy process (AHP) proves to be a very useful methodology for multiple criteria decision-making in fuzzy environments, which has found substantial applications in recent years. The vast majority of the applications use a crisp point estimate method such as the extent analysis or the fuzzy preference programming (FPP) based nonlinear method for fuzzy AHP priority derivation. The extent analysis has been revealed to be invalid and the weights derived by this method do not represent the relative importance of decision criteria or alternatives. The FPP-based nonlinear priority method also turns out to be subject to significant drawbacks, one of which is that it may produce multiple, even conflict priority vectors for a fuzzy pairwise comparison matrix, leading to entirely different conclusions. To address these drawbacks and provide a valid yet practical priority method for fuzzy AHP, this paper proposes a logarithmic fuzzy preference programming (LFPP) based methodology for fuzzy AHP priority derivation, which formulates the priorities of a fuzzy pairwise comparison matrix as a logarithmic nonlinear programming and derives crisp priorities from fuzzy pairwise comparison matrices. Numerical examples are tested to show the advantages of the proposed methodology and its potential applications in fuzzy AHP decision-making.     

水环境质量评价的模糊聚类法

将模糊聚类最大矩阵元原理与基于数据迭代为基础的水质模糊评价理论模型相结合，形成模糊聚类迭代方法．并用该方法对甘肃金昌市地下水质进行了分类评价，得到了今人满意的结果．