基于Choquet积分的区间灰数多属性决策方法

针对多属性决策中属性间的关联性对决策结果的影响，提出了基于区间灰数灰度和Choquet积分的区间灰数多属性决策方法。根据区间灰数灰度的定义，证明了区间灰数的灰度是一种灰测度，由此定义了关于区间灰数灰度的离散Choquet积分并证明其性质；依据各方案的综合属性值的方差最小的原则建立多目标优化模型，确定了各属性或属性集的权重，最后利用Choquet积分对各方案的效果评价向量进行集成。通过实例说明了该方法的有效性。

Approach for multiple attribute decision-making with interval grey number based on Choquet integral

With regard to the interaction between attributes which has influenced on decision results in multiple attribute decision making, a multiple attribute decision making method of interval grey number based on degree of greyness and Choquet integral is presented. Degree of greyness of interval grey number is proved as a grey measure according to its definition, then discrete Choquet integral of degree of greyness of interval grey number is defined, and some of its properties are investigated. The weight of each attribute or attribute set is determined by using a multi objective optimization model，which variance of comprehensive attribute values of each scheme is minimum; and the effect evaluation vector of each scheme are integrated based on Choquet integral. Finally, an example is also presented to illustrate the effectiveness of the proposed method.