模糊多属性决策的折衷方法

在假设属性指标和权重都是模糊数的条件下,利用两个模糊矢量的分量期望值构成的向量的夹角作为这两个模糊矢量的夹角,提出了模糊矢量投影的概念,以权重矢量作为标准衡量各个方案尺度,将模糊多属性理想矢量与模糊多属性指标构成的模糊矢量之差和模糊负理想矢量与模糊多属性指标构成的模糊矢量之差在模糊权重上的投影系数组合大小作为衡量各个方案优劣的准则,投影系数越大,方案越优,并给出该准则的算法及说明该准则的一个例子。

Compromise method for fuzzy multiple attribute decision making

Under the circumstance that the values of attribute index and weight are fuzzy numbers, using an angle, which is made of expectation ponderance of two fuzzy vectors as the angle of the two fuzzy vectors, a conception of fuzzy vector projection is presented. The fuzzy weighted vector being as a scale to measure each alternative, the size of combination projection coefficient that difference between fuzzy ideal vector and alternative projects on the fuzzy weighted vector, and difference between fuzzy negative ideal vector and alternative projects on the fuzzy weighted vector is taken as a criterion to judge each alternative superior or inferior. The more the projection coefficient is, the superior the alternative is. Then an algorithm of the criterion is presented and an example explaining the criterion is given.