Abstract: A decision-making method with a modified interval number density aggregation operator is proposed to solve the group weights problems with index data known and weights unknown. First, the several concepts of interval number and interval number density aggregation operator are introduced, the method of interval number clustering is improved, the direct algorithm is applied to cluster the one-dimensional data, and fuzzy statistics variables are defined to make sure which is the best way to clustering. Then based on a modified interval number density aggregation operator the group weights problems with index data known and weights unknown are solved. Finally it is shown that the method is feasible and effective with an example.

Key words: group decision-making, interval number, modified interval number density aggregation operator, fuzzy clustering, group weight

摘要： 针对指标数据已知,而权重数据未知的群组赋权问题,给出了一种基于改进的区间数密度集结算子来进行指标群组赋权的决策方法。首先给出了区间数和区间数密度集结算子(IDM)的定义及性质,改进了以前区间数聚类的方法,应用直接法对一维区间数据组进行聚类,并定义了模糊统计量,以确定最为合理的一种聚类方式。然后基于改进的区间数密度集结算子这种数学模型,来解决指标值数据已知,而权重未知的群组赋权问题。最后举例说明该方法的可行性和实用性。

关键词: 群决策, 区间数, 改进的区间数密度集结算子, 模糊聚类, 群组权重