Abstract: Interval-valued intuitionistic multiplicative set is presented, which is regarded as an extension to intuitionistic multiplicative set. Interval-valued intuitionistic multiplicative number is defined for convenience of expression, the operational laws of interval-valued intuitionistic multiplicative number are given. The score function and accuracy function of interval-valued intuitionistic multiplicative number are defined, and based on these two functions, a method for ranking interval-valued intuitionistic multiplicative numbers is presented. Some aggregation operators, including interval-valued intuitionistic multiplicative weighted averaging operator and interval-valued intuitionistic multiplicative weighted geometric operator, are proposed. Furthermore, a method to multiple attribute decision making with preference information in the form of interval-valued intuitionistic multiplicative number is proposed, and a numerical example is used to illustrate the proposed method.

Key words: interval valued intuitionistic multiplicative number, operational laws, aggregation operator, preference, decision making

摘要： 对直觉乘法集（intuitionistic multiplicative set）进行推广，提出了区间直觉乘法集的概念。为了表达方便，定义了区间直觉乘法数，给出了区间直觉乘法数的基本运算法则。定义了区间直觉乘法数的得分函数和精确函数，并给出了区间直觉乘法数的一种排序方法。定义了区间直觉乘法数的加权平均算子和加权几何算子，进而给出决策者对方案的偏好信息以区间直觉乘法数给出的决策方法，并进行实例分析。

关键词: 区间直觉乘法数, 运算法则, 集成算子, 偏好, 决策