Fuzzy Entropy： Axiomatic Definition and Neural Networks Model

The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, firstly, the axiomatic definition of fuzzy entropy is discussed. Then, neural networks model of fuzzy entropy is proposed, based on the computing capability of neural networks. In the end, two examples are discussed to show the efficiency of the model.     

A New View on Fuzzy Hypermodules

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy     

Fuzzy幂群与Fuzzy商群的相互关系

In this paper,we extend the concept of fuzzy quotient groups.The structures of fuzzy power groups and fuzzy quotient groups are discussed.The relationship between fuzzy power groups and fuzzy quotient groups are considered.     

Fuzzy数的Fuzzy距离与Fuzzy极限

本文引入了两个重要概念,即Fuzzy数的Fuzzy距离和Fuzzy数序列的Fuzzy极限,并得到它们的一些完全类似实数绝对值与实数序列极限的性质。     

On the Space bvp（F） of Sequences of p-bounded Variation of Fuzzy Numbers

Recently, the space bvp of real or complex numbers consisting of all sequences whose differences are in the space lp has been studied by Basar, Altay [Ukrainian Math. J. 55（1）（2003）, 136-147], where 1 ≤ p ≤ ∞. The main purpose of the present paper is to introduce the space bvp（F） of sequences of p-bounded variation of fuzzy numbers. Moreover, it is proved that the space bvp（F） includes the space lp（F） and also shown that the spaces bvp（F） and lp（F） axe isomorphic for 1 ≤ p ≤∞. Furthermore, some inclusion relations have been given.     

L—Fuzzy集上的Fuzzy数值Fuzzy测度和Fuzzy数值Fuzzy积分

本文在L-FuZzy σ-代数上引入了Fuzzy数值Fuzzy测度和Fuzzy数值Fuzzy测度的自连续和零可加,以及L-Fuzzy集上的关于Fuzzy数值Fuzzy测度的Fuzzy数值Fuzzy积分等重要概念,并讨论了一些类似于[1]中给出的重要性质,特別给出了依测度收敛的情况下,自连续性与积分序列收敛的等价性定理。     

Well—posed Fuzzy Extensions of Ill—posed Linear Equality Systems

Linear equality systems With fuzzy parameters and crisp variables defined by the Zadeh's extension principle are called possibilistic linear equality systems. This study focuses on the problem of stability (with respect to small changes in the membership function of fuzzy parameters) of the solution in these systems.     

L—Fuzzy集上的Fuzzy值函数的Fuzzy积分的收敛

本文引入了L-Fuzzy集合上的Fuzzy值函数关于Fuzzy值Fuzzy测度的Fuzzy值Fuzzy积分的概念,给出上述概念的几个等价定义,讨论其基本性质,得到一系列积分序列的收敛定理。     

The Entropy and Amount of Information of Fuzzy Events

In this paper,the entropy of random experiments with results of fuzzy events and the mutualinformation between two experiments of such kind are defined,therefore,the Shannon entropy andinformation are extended to the fuzzy situations.The principal properties of entropy and informationof fuzzy events are discussed.Among other things,we find that the entropy of a random experimentwith fuzzy outcomes is the sum of random entropy and fuzzy entropy.The connection betweenShannon entropy and De Luca Entropy is established.     

Fuzzy值Fuzzy测度的完备化

引入Fuzzy值Fuzzy测度的完备化定义,证明Fuzzy值Fuzzy测度的完备化定理,讨论完备化Fuzzy值Fuzzy测度的某些重要性质。     

模糊事件贝叶斯公式

讨论了模糊事件的概率及其基本性质 ,并通过对经典贝叶斯公式的推广 ,提出了模糊事件的贝叶斯公式 .     

Fuzzy关系方程干解在模糊在线控制系统中的应用研究

讨论了怎样快速求出Fuzzy关系方程干解的方法.探讨了该方法在模糊在线控制系统中的应用,同时给出了如何快速构建经济适用的动态模糊控制器的设计方法.     

模糊数学在数学建模中的应用

主要讨论模糊数学在数学建模课程和数学建模竞赛中的应用问题.在数学建模中应当引进模糊数学方法,可以得到一些计算较为简单,更符合实际情况的数学模型.     

Fuzzy HX环的推广

为改进Fuzzy HX环的结果,使之包含Fuzzy商环,提出了弱Fuzzy HX环的概念,研究了它的性质与结构,并重新讨论了拟Fuzzy商环,证明了在正则条件下拟Fuzzy商环与弱Fuzzy HX环的统一性：同时也得到了一致弱Fuzzy HX环与普通Fuzzy商环的关系。     

关于模糊综合评判标准的一点注记

从应用角度出发,分析了常用三角范算子之间的内在联系,给出了各种不同类型的算子之间的隶属关系,解决了在使用不同类型的算子进行模糊综合评判时明显存在盲目性与随意性的问题,给出了模糊综合评判的统一评判标准及方法,同时给出了应用实例.     

运输问题的模糊聚类分析求解

通过对传统模糊聚类经验公式的改进和对最后两类排序的确定,提出了一种基 于模糊聚类分析的运输问题简单快速的求解方法．编出了通用程序,并给除了实例和计算 结果．该算法既是模糊聚类分析应用的扩展,又是对运筹学知识的补充和完善．     

Fuzzy矩阵的加权Moore-Penrose逆

给出了Fuzzy矩阵加权Moore-Penrose逆AM+N的定义,研究了Fuzzy矩阵加权Moore-Penrose逆AM+N的存在性问题,证明了当权矩阵M,N满足一定条件时,AM+N存在且A+MN=AT的充要条件是ANATMA≤A,推广了Fuzzy矩阵和Boolean矩阵的相应结果.     

区间模糊ISODATA动态聚类算法

目前模糊技术已经应用于许多智能系统,如模糊关系与模糊聚类.聚类是数据挖掘的重要任务,它将数据对像分成多个聚类,在同一个聚类中,对象的属性特征之间具有较高的相似度,有很大研究及应用价值.结合数据库中的挖掘技术,对属性特征为区间数的多属性决策问题,提出了一种基于区间数隶属度的区间模糊ISODATA动态聚类方法.     

通用系统模糊可靠度计算模型

对系统组成单元的含义作了新的定义,建立了单元模糊可靠度及其置信区间的估计模型;建立了常见通用系统的模糊可靠度估计模型;通过对单元模糊可靠度的直接估计,利用所建立的估计模型可以快速方便地预测出系统的模糊可靠度.实例分析给出了估计模型的使用方法,并显示了模型的有效性.     

基于因果聚类的模糊预测的择近选择

本文给出了对称三角模糊数的 Hausdauff度量的简明表示形式 ,从而解决了基于因果聚类的模糊预测的择近选择问题 .