定义在复数上的复模糊值函数

把所有的关于y轴对称的模糊数都定义为零模糊数,则两个相同的模糊数的差为零,利用~ar-+~ar+这样一个数值来描述模糊数的序关系,就可以得到关于纵向对称的模糊数都是等同的.在此基础之上对实模糊数的模糊距离及极限进行了研究.并研究了复模糊数的距离与复模糊数列的极限以及复模糊值函数的极限.将研究的复模糊值函数是定义在复数集C上取值于F(C)(所有的复模糊数的集合)中的复模糊数的函数.在新的序关系意义下讨论复模糊值函数的极限,并讨论复模糊值函数的收敛性质及Cauchy收敛判别法等.     

复模糊值函数级数的收敛性

在新的模糊数序关系意义下,介绍了复模糊数的概念及运算性质,复模糊数列收敛的定义及复模糊级数收敛性的判别法.并以此为基础,定义了复模糊值函数级数的收敛性及一致收敛性,讨论了复模糊值函数级数的收敛判别法及其基本性质,以及一致收敛的判别法.     

复模糊值函数的收敛性

复模糊值函数是定义在实数集R上取值于F(C)(所有的复模糊数的集合)中的复模糊数的函数.将在新的序关系意义下,定义复模糊值函数的极限,并讨论复模糊值函数的收敛性质及Cauchy收敛判别法等.     

模糊数的运算性质及模糊数的距离与极限

通过对零模糊数以及模糊数的序关系的重新定义,使得模糊数与实数有了更相似的运算性质。定义了模糊数的距离,讨论了模数列的极限及性质。     

一种新的模糊数的距离定义

指出模糊数的Hausdorff距离定义的不足和模糊距离定义在模糊数的数列应用上的缺陷,给出一种新的定义，并在此定义的基础上给出相关的几个定理．     

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...     

复模糊函数与模糊复函数的微分及其性质

已有的复模糊函数的微分是由复区间值函数的微分和扩张原理给出的,本文利用模糊结构元理论及模糊数的广义限定运算给出与已有的复模糊函数微分等价的定义,同时给出模糊复函数微分的定义,并讨论其解析性质,给出模糊复函数解析的充要条件.     

基于结构元的复模糊数四则运算

运用模糊数的模糊结构元表述理论,引入了区间[-1,1]上单调函数的某些同序单调变换,将复模糊数的加、减、乘、除运算转换为同序单调函数之间的相应运算.解决了以往基于扩张原理运算中的遍历过程带来的极大不便.同时,讨论了模糊结构元线性生成的复模糊数及其运算.     

模糊数无穷乘积

在定义了区间无穷乘积、模糊数无穷乘积及其收敛的基础上 ,利用 [3]中得到的关于模糊级数收敛的某些结论 ,得出模糊数无穷乘积与实数无穷乘积理论类似的结果 ,从而说明本文定义的模糊数无穷乘积确为实数无穷乘积的推广。     

广义模糊数及其序列的极限

重新定义了广义模糊数,引入了"序"、"运算"及"度量",得到了一些基本性质,并研究了广义模糊数序列的极限及性质,给出了单调收敛、闭区间套等重要定理,使模糊数对应理论得以拓广.     

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 .     

The Convergence of Fuzzy Complex Valued Series

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基于TOPSIS的模糊群体多属性决策方法

针对模糊群体多属性决策问题,给出一种基于理想点法(TOPSIS)的多属性决策方法.方法先用三角模糊数的形式表示专家评价值的模糊性和不确定性,而后考虑了专家在不同评价属性中的重要程度和意见的相似度,并将专家意见进行集结得到专家群体关于方案集的模糊决策矩阵,最后定义了三角模糊数形式的正负理想方案,通过计算各方案与正负理想方案的距离以及各方案与理想点的相对接近度,最终确定最优方案.通过实例分析说明了该方法的可行性和有效性.     

Ranking generalized fuzzy numbers in fuzzy decision making based on the left and right transfer coefficients and areas

Although a number of recent studies have proposed ranking fuzzy numbers based on the deviation degree, most of them have exhibited several shortcomings associated with non-discriminative and counter-intuitive problems. In fact, none of the existing deviation degree methods has guaranteed consistencies between the ranking of fuzzy numbers and that of their images under all situations. They have also ignored decision maker’s attitude toward risk, which significantly influences final ranking result. To overcome the above-mentioned drawbacks, this study proposes a new approach for ranking fuzzy numbers that ensures full consideration for all information of fuzzy numbers. Accordingly, an overall ranking index is obtained by the integration of the information from the left and the right (LR) areas between fuzzy numbers, the centroid points of fuzzy numbers and the decision maker’s attitude toward risk. This new method is efficient for evaluating generalized fuzzy numbers and distinguishing symmetric fuzzy numbers. It also overcomes the shortcomings of the existing approaches based on deviation degree. Several numerical examples are provided to illustrate the superiority of the proposed approach. Lastly, a new fuzzy MCDM approach for generalized fuzzy numbers is proposed based on the proposed ranking approach and the concept of generalized fuzzy numbers. The proposed fuzzy MCDM approach does not require the normalization process and thus avoids the loss of information results from transforming generalized fuzzy numbers to normal form.     

Duality Theory in Fuzzy Linear Programming Problems with Fuzzy Coefficients

The concept of fuzzy scalar (inner) product that will be used in the fuzzy objective and inequality constraints of the fuzzy primal and dual linear programming problems with fuzzy coefficients is proposed in this paper. We also introduce a solution concept that is essentially similar to the notion of Pareto optimal solution in the multiobjective programming problems by imposing a partial ordering on the set of all fuzzy numbers. We then prove the weak and strong duality theorems for fuzzy linear programming problems with fuzzy coefficients.     

一种新的梯形模糊数间距离及在投资组合模型选择中的应用

给出一种新的模糊数间的距离公式.用新定义的距离公式来度量给定优先资产的条件下投资组合的分散度.用可能性均值度量投资组合的收益,可能性半方差度量投资组合的风险,在收益和风险满足一定的条件下构造分散度模型.通过实例分析,给出的方法不仅分散度更好,而且资产分配多元化程度更高,计算也更简单.     

Shortest Path Problem on a Network with Imprecise Edge Weight

A network with its arc lengths as imprecise number, instead of a real number, namely, interval number and triangular fuzzy number is considered here. Existing ideas on addition and comparison between two imprecise numbers of same type are introduced. To obtain a fuzzy shortest path from a source vertex to all other vertices, a common algorithm is developed which works well on both types of imprecise numbers under consideration. In the proposed algorithm, a decision-maker is to negotiate with the obtained fuzzy shortest paths according to his/her view only when the means are same but the widths are different of the obtained paths. Otherwise, a fuzzy optimal path is obtained to which the decision-maker always satisfies with different grades of satisfaction. All pairs fuzzy shortest paths can be found by repeated use of the proposed algorithm.     

单源模糊数及其运算

本文首先指出模糊数的运算存在模糊源问题，然后定义了单源模糊数的一些基本概念，并建立了单源模糊数的运算方法，最后给出了单源模糊数线性方程组的求解方法。