中文摘要：

研究了属性值以区间数表示的群决策问题,提出了区间数决策向量转化为互反判断矩阵的公式,定义了区间数互反判断矩阵几何加权集成算子.在此基础上,提出了区间数多属性群决策的新方法.方法首先针对每一个属性,将各决策者、各方案对应此属性的区间数向量转换为互反判断矩阵,由新定义的集成算子进行集成.由集成区间数矩阵的上界、下界矩阵计算各方案关于此属性的排序向量.由属性权重、可能度和排序公式对方案进行排序.最后给出一个实例进行分析,结果表明了此方法的实用性和可行性.

英文摘要：

In this paper, the multi-attribute group decision making problem is studied , in which the attribute values were in the form of interval numbers . A transformation formula between interval numbers decision vector and reciprocal judgment matrix is proposed A def- inition of weighted geometric operator for aggregating interval numbers reciprocal judgment matrices is presented Based on these, the new method of group decision making with inter- val number is proposed. First, for each attribute, the interval numbers decision vectors are transformed to reciprocal judgment matrices The new operator is utilized to aggregate several decision maker reciprocal judgment matrices. Second, aggregation matrices are divided into the upper bound matrixes and lower matrixes to calculate the sorting vectors of the alter- natives. By the attribute weights, possible degree and priority formula, the alternatives are ranked. Finally, a numerical example is presented to solve the group decision making problem with interval number matrices. The results verify the method and demonstrate its practicality and feasibility.