【作者】 岳立柱；

【导师】 仲维清；

【作者基本信息】 辽宁工程技术大学 ， 管理科学与工程， 2011， 博士

【摘要】 由于现代决策日趋复杂,模糊不确定性更加突出,模糊决策理论具有重要的应用价值。目前,模糊运算大多是建立Zadeh模糊扩张原理之上的,不过这种运算方法存在运算困难与繁杂的问题。为了解决该问题,郭嗣琮教授提出了模糊结构元理论,该理论思想是将模糊数的运算转换成函数的运算。不过,该理论对一些决策模型,存在无法应用的问题。因此,对结构元理论进行拓展,得到了若干模糊决策模型。首先,研究了模糊数非单调变换条件下的结构元表示方法。结构元理论主要思想:将任意的有界闭模糊数A用结构元E (即一类特殊的模糊数)和一单调函数来表示,即A = f ( E),进而将模糊数的运算转换成单调函数的运算。本文将变换函数f的限制条件由单调拓展为连续,即A = f ( E)中,若f连续,则A为模糊数。同时,给出了由连续变换函数转换成单调函数的方法。解决了一类模糊值函数无法微积分的问题。研究了模糊限定运算的结构元表示方法。限定运算主要是体现集合间元素的对应关系,不同的限定算子体现了不同的关系。本文利用函数的运算来表示这种关系,得到了模糊限定运算更为一般的表述形式。解决了结构元理论中,由于引人限定算子而导致的应用局限和运算困难。其次,在以上研究的基础上,进一步对结构元理论进行研究。一是对模糊数加减乘除四则运算进行拓展。拓展后的结果表明,模糊数运算时仅要求单调变换单调就可以运算,将多个运算法则统一成一个基本的运算定理。二是给出了无界模糊数的单调变换函数与其隶属函数之间的转换定理,证明了无界模糊数的加减乘除运算法则。三是给出了含零模糊数运算的机构元表示。在拓展后结构元理论的基础上,重点研究了模糊数的矩阵应用问题和运筹学中的模糊优化问题。给出了模糊数权重、模糊排队论、模糊最大流与最短路等模型的求解方法。在模糊最短路模型中提出了组合序,在模糊博弈模型总提出了元序,这两个序具有不仅具有良好的数学性质,还能反映决策者的偏好。更多还原

【Abstract】 As the modern decision is more complicated, fuzzy uncertainty is more prominent, and the fuzzy decision theory is important for application. At present, most fuzzy operation is based on the principle of fuzzy expansion that Zadeh put forward, but this kind of operation method are difficult and complex. In order to solve the problem, the professor GuoSiCong put forward the theory of fuzzy structure element, it converted the operations of fuzzy Numbers into the function operation. However, the theory can’t be applied in decision-making model. Therefore, the structure theory is developed, some fuzzy decision model are reached.First of all, it is researched that how to express the fuzzy number in structure element when it is non-monotone transformation. In the theory of Structure element ,any major thought is : for any bounded closed fuzzy number Aand structured element E (namely : a kind of special fuzzy number), there is always the only monotonic increase (or decrease) function (called the transformed-function), make A = f ( E).and the operations of fuzzy number is converted the operations of monotonic function. in this article, restriction condition of transform function is developed from monotonic to continuous, namely, in A = f ( E),if f is continuous, then A is fuzzy number. And at the same time, the method is gave that the continuous transformation function is converted into monotonic function. Solve the calculus of fuzzy value function. it is researched how to express fuzzy limit operation in structure element .Limit operation mainly reflect the corresponding relationship between collection elements, different limit operator reflects different relationship. In this paper, by using the function operations this relationship is expressed, the more general expression form of the fuzzy limit operation is researched. It is Solved the problem of difficult operation and the application limit as a result of limit operator in structure element theory.Secondly, on basis of the research in this article, there is further study for the theory of structure element .one : the arithmetic of fuzzy number are developed, and The results showed that after developing, only fuzzy number is monotone and transformed ,the operation can be carried out ,so several algorithms are unified into a basic computing theorems. The other is that The transformation-theorem between monotonic transformed-function of unbounded fuzzy number and membership function is put forward, and the computed-algorithm of unbounded fuzzy number is proved .the last is the operations that the fuzzy number that contain zero are given.on basis of the theory of structure element that has been developed, application of fuzzy matrix and fuzzy optimization are researched. The model of fuzzy number weight, fuzzy queuing theory and fuzzy maximum flow and the most short circuit of fuzzy number are solved.. In the fuzzy shortest path model, combination sequence is proposed, and the element order in the fuzzy shortest path, the two orders not only have good mathematical property, but also reflect the preferences of decision makers. Therefore, they are more practical.更多还原