The Development Of Fuzzy Structured Element And Decision-making Application

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.