一类模糊数系数矩阵的模糊线性方程组的迭代算法

讨论模糊线性方程组X=A~X U解的存在条件及其迭代算法(其中,A~是以模糊数为元素的n×n矩阵,未知量X和常量U都是以模糊数为元素的n维向量,并且其加法和乘法均由Zadeh的扩张原理定义)。首先研究解的存在条件,尔后探讨求解的迭代算法及误差估计。     

二维模糊向量可信性分布的联合熵及其性质

基于可信性测度, 定义了二维离散型模糊向量和二维连续型模糊向量的联合熵, 并研究了它们的极小性、极大性、单调性, 以及二维简单模糊向量的扩展性和严格凹性.     

广义直觉模糊信息粒度

直觉模糊信息粒度是度量直觉模糊粒结构不确定性的一种重要方法。本文针对直觉模糊信息粒度在度量直觉模糊粒结构上存在的不足进行分析。首先,介绍直觉模糊粒结构距离。其次,改进了基于偏序关系提出的直觉模糊信息粒度的公理化定义,从直觉模糊粒结构距离观点出发,以最细的直觉模糊粒结构为参照物,计算每个直觉模糊粒结构与最细的直觉模糊粒结构之间的距离,距离的值越大,这个直觉模糊粒结构的信息粒度越大。最后,通过例子验证结论的合理性。     

一类模糊线性方程组的迭代算法及其误差估计

讨论模糊线性方程组X=AX+U解的存在条件及其迭代算法(其中,A是区间数为元素的n阶矩阵,未知量X和常量U都是以模糊数为元素的n维向量,并且其加法和乘法均由Zadeh的扩张原理定义).首先研究解的存在条件,尔后探讨求解的迭代算法及误差估计.     

一类区间数系数矩阵模糊线性方程组的迭代算法

讨论模糊线性方程组X=A-X+U解的存在条件及其迭代算法(其中,A-是区间数为元素的n阶矩阵,未知量X和常量U都是以模糊数为元素的n维向量,并且其加法和乘法均由Zadeh的扩张原理定义).首先研究解的存在条件,尔后探讨求解的迭代算法及误差估计.     

基于Hausdorff测度直觉模糊数距离度量的直觉模糊数序列极限研究

为了更深入地研究直觉模糊理论,构建直觉模糊数序列极限分析模型,在直觉模糊数、直觉模糊距离度量研究探讨的基础上给出了基于Hausdorff测度直觉模糊数距离度量的直觉模糊数序列的定义并对其极限及性质进行了重点研究,对直觉模糊数序列分析理论的研究具有重要的理论意义.     

模糊向量空间的商空间

在史和黄重新定义的模糊向量空间的模糊基和模糊维数的基础上,讨论模糊向量空间的模糊线性映射及其性质,定义模糊向量空间(V,μ)的商空间(V/K,μK)并研究了它的性质,证明公式dim(μK)+dim (k(e)ff)=dim(μ)成立,其中k(e)ff是模糊向量空间(V,μ)关于模糊线性映射f的模糊核空间.     

一种基于模糊信息的距离测度及应用

通过借用Shannon信息理论中的相关概念,提出了基于模糊信息测度的模糊对称交互熵(FSCE)这一距离测度。接下来证明了它是度量空间中的度量,满足非负性、对称性、三角不等式三个条件。最后利用数值例子说明了在模糊模式识别中,FSCE与常见的模糊贴近度可以得到一致的识别结果,并有其优势和实际意义,为模糊模式识别提供了新的研究方法。     

基于Hausdauff度量的模糊TOPSIS方法研究

针对模糊多属性决策中的模糊 TOPSIS方法 ,提出了一种基于 Hausdauff度量的模糊 TOPSIS方法 .首先由模糊极大集与模糊极小集确定模糊多属性决策问题的理想解与负理想解 ,进而由 Hausdauff度量获得不同备选方案到理想解与负理想解的距离及其贴近度 ,根据贴近度指标对方案进行排序 ,为决策者提供决策支持 .最后以 L-R梯形模糊数为例进行了实例研究 .     

模糊向量空间中模糊基的判定方法及其维数的计算

本文在（１）的基础上给出了模糊基的另一种构造方法，由此得到了模糊基的判定方法。研究了基的μ值分布状况，最后给出了模糊向量空间维数的计算方法。     

On fuzzy metric spaces

In this paper we introduce the concept of a fuzzy metric space. The distance between two points in a fuzzy metric space is a non-negative, upper semicontinuous, normal and convex fuzzy number. Properties of fuzzy metric spaces are studied and some fixed point theorems are proved.     

Examples of fuzzy metrics and applications

In this paper we present new examples of fuzzy metrics in the sense of George and Veeramani. The examples have been classified attending to their construction and most of the well-known fuzzy metrics are particular cases of those given here. In particular, novel fuzzy metrics, by means of fuzzy and classical metrics and certain special types of functions, are introduced. We also give an extension theorem for two fuzzy metrics that agree in its nonempty intersection. Finally, we give an application of this type of fuzzy metrics to color image processing. We propose a fuzzy metric that simultaneously takes into account two different distance criteria between color image pixels and we use this fuzzy metric to filter noisy images, obtaining promising results. This application is also illustrative of how fuzzy metrics can be used in other engineering problems.     

Selecting IS personnel use fuzzy GDSS based on metric distance method

In this paper we propose a new approach to rank fuzzy numbers by metric distance. For showing our method is a good ranking method, we give two examples to compare with other methods. The paper also developes a computer-based group decision support system, FMCGDSS, to increase the recruiting productivity and to easily compare our method with other fuzzy number ranking methods. The FMCGDSS includes three ranking methods: intuition ranking, Lee and Li's fuzzy mean/spread and our metric distance method to help manager make better decision under fuzzy circumstance. The result indicates that the new method is coincident with the intuition ranking and the Lee and Li's fuzzy mean/spread method on each type weight.     

基于Hausdorff距离的模糊数互补判断矩阵排序研究

基于Bonissone近似计算、Hausdorff距离和模糊折衷型决策方法，给出带有梯形模糊数互补判断矩阵的一种排序方法。同时给出精确值、三角模糊数的互补判断矩阵转化为梯形模糊数互补判断矩阵的方法，因此本文方法同样适合于处理精确值、三角模糊数的互补判断矩阵的排序问题。最后用算例说明了计算过程。     

On completion of fuzzy metric spaces

Completions of fuzzy metric spaces (in the sense of George and Veeramani) are discussed. A complete fuzzy metric space Y is said to be a˜fuzzy metric completion of a˜given fuzzy metric space X if X is isometric to a˜dense subspace of Y. We present an example of a˜fuzzy metric space that does not admit any fuzzy metric completion. However, we prove that every standard fuzzy metric space has an (up to isometry) unique fuzzy metric completion. We also show that for each fuzzy metric space there is an (up to uniform isomorphism) unique complete fuzzy metric space that contains a˜dense subspace uniformly isomorphic to it.     

模糊黎曼积分的拓广

给出了模糊黎曼积分的拓广定义,并证明了拓广的模糊黎曼积分在下方图度量和d1度量下可以通过有限个层次集逼近.     

Fuzzy n-cell numbers and the differential of fuzzy n-cell number value mappings

In this paper, we give the definition of a special kind of n-dimension fuzzy numbers, fuzzy n-cell numbers, discuss their operations and representation theorems, define a complete metric on the fuzzy n-cell number space and prove that the metric is equivalent to the supremum metric derived by the Hausdorff metric between the level sets of the n-dimension fuzzy numbers, and obtain an embedding theorem of the fuzzy n-cell number space (isometrically embeds it into a concrete Banach space). We also consider the differential of the fuzzy mappings from an interval into the fuzzy n-cell number space by using the embedding theorem.     

On some results of analysis for fuzzy metric spaces

A necessary and sufficient condition for a fuzzy metric space to be complete is given. We prove that a subspace of a separable fuzzy metric space is separable and every separable fuzzy metric space is second countable. Uniform limit theorem is generalized to fuzzy metric spaces.     

新的模糊数的模糊距离

文[1]中基于现有的模糊数的距离定义及模糊距离定义的缺陷进行分析并给出了改进的模糊数的距离定义。本文在此基础上给出新的模糊数的模糊距离定义，并给出相应的定理。     

On Fuzzy Metric Space

In this paper we prove a common fixed point theorem for three mappings in fuzzy metric space and then extend this result to fuzzy 2 and 3-metric spaces. Our theorem is an extension of result of Fisher [12], to fuzzy metric spaces.AMS Subject Classification (1990): 47H10, 54H25