Abstract: With regard to the multi-objective decision-making problems, in which the preference information provided by the decision maker takes the form of interval numbers complementary judgment matrix. Firstly, the concept of relative preponderant degree and theorem of interval numbers additive consistent complementary judgment matrix are presented. Then, an objective programming model is established and the weighted vector of the interval numbers complementary judgment matrix is obtained by solving the model. The alternatives are ranked by using the total relative superiority of every weighted vector. A ranking method based on the least deviation and relative preponderant degree for interval numbers complementary judgment matrix is proposed. The core of this method is development of the ranking method of numerical complementary judgment matrix. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.

Key words: multi-objective decision-making, interval numbers additive consistent complement-ary judgment matrix, least deviation, preponderant degree, priority

摘要： 针对决策信息以区间数互补判断矩阵形式给出的多目标决策问题。首先,给出相对优势度的概念和区间数加性一致性互补判断矩阵的判定定理。其次,建立一个目标规划模型,通过求解该模型得到区间数互补判断矩阵的权重向量,并利用各权重向量的总体相对优势度对方案进行排序,提出了基于最小偏差和优势度的区间数互补判断矩阵排序法。方法的核心是对数值型互补判断矩阵排序方法的拓展。最后,通过实例说明方法的可行性和有效性。

关键词: 多目标决策, 区间数加性一致性互补判断矩阵, 最小偏差, 优势度, 排序