基于κ-可加模糊测度的多属性决策分析

Multiple attributes decision making based on κ-additive fuzzy measures

基于κ-可加模糊测度和 Choquet 积分理论,讨论基于关联的多属性决策分析问题的建模和求解.首先通过构建属性间的直接关联矩阵确定κ值;然后依据 Marichal 熵理论求解属性和属性集的权重;利用 Choquet 积分计算方案的综合评价值并以此对方案进行排序;最后给出算例验证上述理论和方法的合理性.

In this paper the model and solution of multi-attribute decision making （MADM） with interaction among attributes are analyzed based on k-additive fuzzy measure and Choquet integral. The optimal value of k is identified on the basis of direct-relationship matrix of attribute; the weights of attribute and their combines are determined through Marichal entropy; the synthetical values of the alternatives are computed by Choquet integral; and the alternatives are ranked. Finally, an example is given to verify our theories and methods.