基于矩阵相似性的异构群体偏好信息集结方法

Heterogeneous Group Preference Information Aggregation Method Based on Matrix Similarity

在群体信息集结过程中,专家提供的评估信息可以通过各种偏好形式表示.为了集结异构偏好信息,文章提出一种基于矩阵相似性的异构群体偏好信息集结方法.首先,应用不同的转化函数将不同的异构偏好信息转换为模糊偏好关系矩阵,然后,提出一种改进的基于矩阵相似性的幂加权平均算子,并给出该算子的一些性质.在偏好信息集结过程中,基于矩阵相似性的幂加权平均算子不仅考虑了偏好信息之间的相似程度,还能反映不同偏好信息之间的支撑程度.最后,基于提出的改进幂加权平均算子,构建一种新的异构群体偏好信息集结方法,并使用基于互补判断矩阵的排序方法来选择最佳决策方案.两个数值例子说明了文章提出方法的有效性和可行性.

In the process of group information aggregation,the evaluation information provided by experts can be expressed in various preference formats.In order to aggregate heterogeneous preference information,this paper proposes a heterogeneous group preference information aggregation method based on matrix similarity.Firstly,different transformation functions are used to transform different heterogeneous preference information into fuzzy preference relation matrix.Then,an improved power-weighted averaging operator based on matrix similarity is proposed and some properties of the operator are given.In the process of preference information aggregation,the power-weighted averaging operator based on matrix similarity not only considers the degree of similarity between preference information,but also reflects the degree of support between different preference information.Finally,based on the improved power-weighted averaging opera tor,a new het erogeneous group preference information aggregation method is constructed.Two numerical examples illustrate the effectiveness and feasibility of the proposed method.