基于结构元理论的模糊多属性群决策

Fuzzy Multi-attribute Group Decision Making Based on Structured Element Theory

将结构元理论引入到模糊多属性决策中,利用同序标准单调函数类与有界实模糊数同胚的性质,将模糊数的复杂运算转化为同序单调函数的运算,通过单调函数间的序关系描述模糊数之间的序关系,简化传统决策的复杂运算。将模糊结构元理论同经典的ELECTRE方法结合,用来解决模糊多属性群决策问题,克服了以往应用ELECTRE方法遇到模糊数难以排序或直接转化为确定系统的缺点,这种方法以结构元理伦为基础,运算简便,易于理解,对于进一步研究模糊多属性群决策问题有很好的参考作用。给出的实例验证了该方法的有效性和可行性。

In this paper, the structured element theory is introduced into the fuzzy multi-attribute decision making. The fuzzy number space and the family of standard bounded monotone functions have the homeomorphic property. Based on this feature, complex operations of fuzzy numbers are put into monotone functions with the same monotonic format. The order relation of monotone functions is used to describe that of fuzzy numbers. The aim is to simplify the complex operations of the traditional fuzzy decision making. The classic ELECTRE method is extended into the fuzzy environment and is combined with the fuzzy structured element. The fuzzy multi-attribute decision making problem is thus solved. It overcomes some shortcomings. For example, the classic ELECTRE method is diffcult to rank fuzzy numbers and has to be turned into a deterministic system. This new method is based on the fuzzy structured element, is simple to operate and easy to understand. It can be used for further study of fuzzy multi-attribute group decision making. An example shows the effectiveness and feasibility of this method.