Abstract:

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.