一种新的二型模糊熵在多属性决策中的应用

Application of a new type-2 fuzzy entropy in multi-attribute decision making

为了度量二型模糊集的不确定性信息并解决以二型模糊集为信息环境的多属性决策问题,该文首先基于二型模糊熵的公理化准则,利用余弦函数定义一个新的二型模糊熵公式。该公式不仅将二型模糊集的犹豫性和模糊性皆考虑在内,而且利用余弦函数的单调性与对称性容易比较两个二型模糊集之间熵的大小。其次在决策过程中考虑决策者的风险态度引入风险偏好函数,同时考虑主隶属度与次隶属度的交叉影响给出新的得分矩阵,并结合熵构建基于属性权重完全未知的非线性优化模型来观察风险偏好对属性权重的影响。最后通过一个实例分析证明了该决策模型的可行性与稳定性。

In order to measure the uncertainty information of type-2 fuzzy sets and solve the multi-attribute decision-making problem with type-2 fuzzy sets as the information environment,based on the axiomatization criterion of the type-2 fuzzy entropy,a new type-2 fuzzy entropy formula is defined by the cosine function.This formula not only takes into account the hesitability and ambiguity of type-2 fuzzy sets,but also more easily compares the size of entropy between two type-2 fuzzy sets based on the monotonicity and symmetry of cosine functions.Considering the risk attitude of decision makers in the decision-making process,the risk preference function is introduced,and the new scoring matrix is given by considering the cross-effect of the primary membership degree and the sub-degree membership.Combining with an entropy,a nonlinear optimization model based on completely unknown attribute weights is constructed to observe the influence of risk preference on attribute weights.An example analysis proves the feasibility and stability of the decision model.