基于最大熵原则的2-可加模糊测度确定方法

2-order additive fuzzy measures identification method based on maximum entropy principle

2-可加模糊测度以适量的参数,灵活有效地描述和处理了普遍存在于决策准则间的各种交互作用。对模糊测度、默比乌斯变换形式及交互作用系数间的转化关系进行了说明,论证了交互作用系数与2-可加模糊测度之间的唯一确定条件,并给出了模糊测度熵的默比乌斯变换及交互作用系数表现形式。依据决策者的经验和主观判断,利用最大模糊测度熵原则,构造出了一种新的2-可加模糊测度确定方法。最后,数值算例说明了该方法的可行性和有效性。

With an appropriate number of parameters,the 2-order additive fuzzy measure can flexibly describe and effectively deal with the different interaction among decision criteria.The transformation among the fuzzy measure,Mbius representation and interaction index is introduced.The condition for interaction indexes to uniquely identify a 2-order additive fuzzy measure is given.The representations of fuzzy measure entropy in terms of Mbius representation and interaction index are also presented.Based on the experience and judgment of the decision maker,a new identification method of 2-order additive fuzzy measure is proposed according to the maximum fuzzy measure entropy principle.Finally,an illustrative example shows the feasibility and validity of the proposed method.