基于最大熵原则的2-可加模糊测度确定方法

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。

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

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, Mobius 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 Mobius 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.