Abstract: For solving Multiple Attribute Group Decision-Making（MAGDM） problems where attribute values are in the form of interval-valued intuitionistic fuzzy numbers and attributes are associated with each other, an approach is proposed based on Interval-Valued Intuitionistic Fuzzy Geometric Weighted Bonferroni Means（IVIFGWBM） operator. The concepts of interval-valued intuitionistic fuzzy numbers are introduced, and Interval-Valued Intuitionistic Fuzzy Geometric Bonferroni Means（IVIFGBM） operator and IVIFGWBM operator are defined at the same time, which are based on operational laws and Bonferroni means operator. Meanwhile, the related properties are researched, and then a model of multi-attribute decision group making is constructed based on IVIFGWBM operator, which is for making decisions combining with sort methods. This approach is further applied in MAGDM, and the results show that the developed approach is feasible and effective.

Key words: interval-valued intuitionistic fuzzy number, interval-valued intuitionistic fuzzy geometric Bonferroni means operator, interval-valued intuitionistic fuzzy geometric weighted Bonferroni means operator, multi-attribute group decision making

摘要： 研究了决策信息为区间直觉模糊数（IVIFN）且属性间存在相互关联的多属性群决策（MAGDM）问题，提出一种基于区间直觉模糊几何加权Bonferroni平均（IVIFGWBM）算子的决策方法。介绍了IVIFN的概念和运算法则，基于这些运算法则和几何Bonferroni平均（GBM）算子，定义了区间直觉模糊几何Bonferroni平均（IVIFGBM）算子和IVIFGWBM算子。研究了这些算子的一些性质，建立基于IVIFGWBM算子的MAGDM模型，结合排序方法进行决策。将该方法应用在一个MAGDM问题中，结果表明了该方法的有效性与可行性。

关键词: 区间直觉模糊数, 区间直觉模糊几何Bonferroni平均算子, 区间直觉模糊几何加权Bonferroni平均算子, 多属性群决策