A Modified TOPSIS Method for Obtaining the Associated Weights of the OWA-Type Operators
A Modified TOPSIS Method for Obtaining the Associated Weights of the OWA-Type Operators
复制标题
一种获取OWA型算子关联权重的改进TOPSIS法
DOI：
10.1002/int.21737
复制
发表时间：
2015
影响因子：
7
通讯作者：
Pan Li-Hua
中科院分区：
文献类型：
--
作者：
Liu Fang;Shang Yu-Fan;Pan Li-Hua
Yager提出的有序加权平均算子（OWA）及其扩展算子已被广泛用于群体决策中个体偏好关系的均值型聚合。OWA型算子理论中的一个重要问题是关联权值的确定。本文对理想解相似性排序偏好技术进行了改进，提出了一种在一组可加性互反矩阵环境下产生关联权值的新方法。首先，由每个加性倒易矩阵得到一个一致的加性倒易矩阵。进一步利用算术平均算子生成理想的加性倒易矩阵。然后，定义了每个可加倒数矩阵与理想矩阵的相似度。在相似度的基础上，利用指数函数确定关联权重，表明相似度越大的权重越重要。最后，通过数值算例说明了所给出的方法。
The ordered weighted averaging (OWA) operator proposed by Yager and its some extensions have been extensively utilized to perform the mean‐type aggregation of individual preference relations in group decision making. An important issue in the theory of the OWA‐type operators is the determination of the associated weights. In the present paper, the technique for order preference by similarity to ideal solution is modified to propose a new method for generating the associated weights under the environment of a group of additive reciprocal matrices. First, a consistent additive reciprocal matrix is obtained from each additive reciprocal matrix. It is further used to generate an ideal additive reciprocal matrix by using the arithmetic averaging operator. Then, a similarity degree between every additive reciprocal matrix and the ideal one is defined. Based on the similarity degree, the associated weights are determined by making use of an exponential function and they show that more importance is given to that with more similarity degree. Finally, a numerical example is carried out to illustrate the given method.