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.     

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.     

模糊度量空间的强嵌入北大核心CSCD

本文定义了George和Veeramani意义下的模糊度量空间的强嵌入,证明了可强嵌入的模糊度量空间能够粗嵌入到Hilbert空间.另外还证明了强嵌入在模糊度量空间的粗范畴下是不变的,并给出了模糊度量空间强嵌入的一些等价刻画.     

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.     

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     

A fixed point theorem for a family of mappings in a fuzzy metric space

In this paper we give a common fixed point theorem for a family of mappings of a G-complete fuzzy metric space (X, M, *) into itself. From this result we deduce a common fixed point theorem for a family of mappings of a complete metric space (X, d) into itself. Supported by University of Palermo.     

Similarities in Fuzzy Regression Models

The solutions of a fuzzy regression model are obtained by converting the problem into a linear programming problem. For each level h, h[0, 1), there exists a solution. In this paper, we study the set of all the solutions to the fuzzy regression model that comes from a set of data as a metric space with an appropriate metric on it. We define a similarity ratio that allows us to compare the spaces of solutions of a fuzzy regression model that come from different sets of data. We also give an application using data sets concerning the GNP–money relationship.     

n维模糊度量空间及其完备性

定义了n维模糊向量的模糊距离、n维模糊度量空间及其完备性的概念,实现了用R上的模糊数度量模糊向量间距离的目的,不仅使得模糊距离的度量更加合理、更加贴切,也创立一套独立于实数的模糊数学分析理论打下了基础。     

Analog of <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> with a subadditive measure

For a subadditive fuzzy measure (not assumed finite), a Minkowski type triangle inequality, with Choquet integrals in place of Lebesgue integrals, is shown to hold. It is immediate that the set of functions for which a certain positive power of the absolute values have finite Choquet integrals is closed under addition, leading to a linear space analogous to the Lebesgue space L ^p , with a metric related to the integral of that power. Under the additional condition that the subadditive fuzzy measure is inner continuous (Sugeno), the space is shown to be complete. Consequences of the Minkowski type inequality are illustrated in two specific instances.      

模糊粒度空间的性质研究

在文献[16]基础上,进一步将模糊粒度空间推广到更一般地模糊等价关系上,研究了模糊粒度空间的性质,主要获得了3个结论.首先,引入了有序的等价关系集的概念,给出了下列的四个命题是等价的:(1) 给定一个模糊等价关系;(2) 给定一个等腰归一化伪距离;(3) 给定一个有序的粒度空间;(4) 给定一个有序的等价关系集.第二,通过模糊等价关系诱导的等腰归一化伪距离的投影距离和扩展距离,建立了模糊粒度空间上的距离,即是等腰归一化距离,并且给出了模糊粒度空间上距离度量的动态性质研究.最后,给出了模糊粒度空间与模糊等价关系之间的序关系,即它们的序是一致的.这些研究工作进一步完善了模糊粒度空间的理论,为模糊粒度计算提供了更为直观的数学理论和工具.     

Fuzzy度量空间中Fuzzy映象的重合定理与Ekeland‘s变分原理

本文给出了Ｆｕｚｚｙ度量空间中Ｆｕｚｚｙ映射的重合定理，推广了文（３）（５）中主要的结果。     

Fuzzy度量空间中的单值映射的Caristi型不动点定理

本文采用Ｋａｌａｖａ和Ｓｅｉｋｋａｌａ的模糊度量空间定义，利用文（７）中建立的亚度量簇生成空间理论，研究了Ｆｕｚｚｙ度量空间中的单值映射的Ｃａｒｉｓｔｉ型不动点定理以及它在Ｍｅｎｇｅｒ概率度量空间中的应用。     

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.     

Controlled fuzzy metric spaces and some related fixed point results

In this paper, we introduce a new extension in the subject of fuzzy metric, called controlled fuzzy metric space. This notion is a generalization of fuzzy b‐metric space. Also, we prove a Banach‐type fixed point theorem and a new fixed point theorem for some self‐mappings satisfying fuzzy ψ ‐contraction condition that is more general than existing theorems. Furthermore, we establish some examples about our main results.     

Some remarks on distances between fuzzy numbers

In this paper we consider different approaches to assigning distances between fuzzy numbers. A pseudo-metric on the set of fuzzy numbers arising from the idea of the value of a fuzzy number is described, and some of its topological properties are noted. Reducing functions are used to define a family of metrics on the space of fuzzy numbers; some convergent properties for these metrics are illustrated. Finally, a fuzzy distance between fuzzy numbers is introduced and its basic properties are studied.     

Fixed point theorems in fuzzy metric spaces

In this paper, we state and prove some common fixed point theorems in fuzzy metric spaces. These theorems generalize and improve known results (see [1]).     

Compact supported endographs and fuzzy sets

A metric is defined on a space of functions from a locally compact metric space X into the unit interval I in terms of the Hausdorff metric distance between their compact supported endographs in X × I. Convergence in this metric is shown to be equivalent to the conjunction of the Hausdorff metric convergence of supports in X and two conditions involving numerical values of the functions. The space of nonempty compact subsets of X with the Hausdorff metric is imbedded in the above function space by the characteristic function on subsets of X. Applications of these results to fuzzy subsets of X and fuzzy dynamical systems on X are indicated.     

Common fixed point theorems for hybrid pairs of maps in fuzzy metric spaces

The purpose of this paper is to introduce the notion of common limit range property (CLR property) for two hybrid pairs of mappings in fuzzy metric spaces, and we prove common fixed point theorems using (CLR) property for these mappings with implicit relation. Our results extend some known results to multi-valued arena. Also, we prove common fixed point theorem in fuzzy metric spaces satisfying an integral type.     

关于模糊预度量空间中的三角不等式

在L，R为一般三角模时，给出在模糊预一度量空间中三角不等式成立的一个必要条件，并用其给出模糊度量空间的一个不动点定理。     

概率度量空间中Fuzzy映象的不动点定理

本文在概率度量空间的框架下,得到了Fuzzy映象的几个公共不动点和不动度定理。本文结果包含和改进了某些最新结果。