Abstract: With respect to multi-attribute group decision making problems, where the attribute values take the form of the interval grey uncertain linguistic variables, three kinds of geometric aggregation operators are given based on the definition and operation rules of interval grey uncertain linguistic variables. According to interval grey uncertain linguistic weighted geometric aggregation operator, evaluation matrices which are given by all decision makers are aggregated to the group evaluation matrix. In the case of known attribute weights information, attribute weights vectors which are given by every decision maker are aggregated to the group attribute weights vector; when the attribute weights are unknown completely, the attribute weights are determined based on information entropy method. All attribute values of alternatives are concentrated by interval grey uncertain linguistic hybrid weighted geometric aggregation operator, then comprehensive evaluation values of alternatives are received, the rank results of alternatives are obtained based on one comparison of the interval grey uncertain linguistic variables. Finally, an illustrative example analysis shows the effectiveness and feasibility of the proposed method.

Key words: multi-attribute group decision making, grey fuzzy number, information entropy, interval grey uncertain linguistic variables, geometric aggregation operator

摘要： 针对属性值为区间灰色不确定语言信息的多属性群决策问题，在定义区间灰色不确定语言变量及其运算规则的基础上，给出了3种几何加权集结算子，由区间灰色不确定语言几何加权算子集结各决策者给出的决策矩阵得到群体决策矩阵。在属性权重已知的情形下，基于该算子集结单个决策者给出的属性权重向量得到群体属性权重向量；在属性权重完全未知的情形下，采用信息熵法确定属性权重向量。采用区间灰色不确定语言混合几何加权算子集结各属性评价信息，得到各方案的综合评价值，基于区间灰色不确定语言变量大小比较的方法得到方案排序结果。算例分析表明了该方法的有效性与可行性。

关键词: 多属性群决策, 灰色模糊数, 信息熵, 区间灰色不确定语言变量, 几何集结算子