诱导密度算子及其性质分析

Induced Density Operator and Its Properties

对密度算子进行拓展研究,提出了诱导密度算子的概念并对其进行了性质分析。对诱导变量进行了界定,给出了一种以诱导变量为基准的元素聚类方法;在此基础上,基于分组后各组的群组特征,给出了密度加权向量的确定方法;将诱导密度中间算子与已知的信息集结算子合成,得到了诱导密度算子,并对诱导密度算子的性质进行了分析。最后,通过一个算例对诱导密度算子的应用进行了说明。

Based on the traditional density operator,this paper presents an induced density operator,and analyzes its properties.First,we introduce the notion of induced variable and provide one clustering method by induced variables.then,we provide a density weighting vector determining method according to the clustering group feature.Secondly,the induced density operator is defined by combining the induced density middle operator and the known information aggregation operators.Finally,the properties of the induced density operator are analyzed.A numeric case is provided to illustrate the application of the induced density operator.