具有二次函数的多准则层次分类方法

Hierarchical discrimination approach of multi-criteria classification with quadratic function

提出了一种集成函数是二次函数且有训练集的多准则层次分类决策方法。该方法利用决策者对训练集的分类结果(属于最高分类和不属于最高分类)构建非线性规划模型,然后采用一系列处理方法将非线性规划模型转换成线性规划模型,求解线性规划,得到训练集中各方案准则值的偏好值和相应参数,通过线性插值或样条插值得到方案在各准则下的偏好值,并计算方案集中方案的与该分类一致性指标值和与低于该分类一致性指标值的差,以确定方案是否属于该分类,然后对不属于最高分类的训练集中的方案进行分类,并构建模型。继续上述过程,直到方案集中所有方案均进行分类为止。最后实例说明该方法的有效性和可行性。

A hierarchical discrimination method of multi-criteria classification with quadratic aggregation function is proposed. First, a nonlinear programming model is constructed by using classification （inside top category and outside top category） for reference set. Then nonlinear programming is converted into linear programming. The preference values of alternative in the reference set and the relational coefficient are gained by solving the linear programming. The preference values of alternative under the criteria and the category are obtained by using linear interpolation or spline interpolation, the differences of concordance index of each alternative in the category and that lower than the category are computed, and the alternatives in the category or the lower category are acquired. Then the reference set, in which alternative belongs to the lower top category, is classified, and a programming model is constructed. The above process is repeated until all alternatives are classified. Finally, an example is given to show the feasibility and validity of this method.