A group decision making model based on a generalized ordered weighted geometric average operator with interval preference matrices
A group decision making model based on a generalized ordered weighted geometric average operator with interval preference matrices
复制标题
基于区间偏好矩阵广义有序加权几何平均算子的群体决策模型
DOI：
10.1016/j.fss.2013.07.010
复制
发表时间：
2014-07-01
影响因子：
3.9
通讯作者：
Zhang, Li-Hua
中科院分区：
文献类型：
--
作者：
Liu, Fang;Zhang, Wei-Guo;Zhang, Li-Hua
本文提出了一种具有区间偏好矩阵的群决策模型。首先给出了具有乘性一致性的区间可加互反矩阵的一个新定义。提出了区间加性互反矩阵与区间乘性互反矩阵之间的转换方法，并将其应用于区间偏好矩阵的同质化。其次，利用区间乘互反矩阵的一致性，提出了一种广义有序加权几何平均算子，该算子允许区间乘互反矩阵的聚集，使得一致性较高的矩阵具有更重要的权重。为了避免解的误导，详细研究了集体区间乘互反矩阵的一致性和可接受一致性。最后，给出了求解区间偏好矩阵群决策问题的一种新算法。数值结果分别说明了所给的定义、方法和算法。(c)2013爱思唯尔有限公司版权所有。
This paper presents a model for a group decision-making problem with interval preference matrices. First, a new definition of interval additive reciprocal matrices with multiplicative consistency is given. Transformation methods between interval additive and multiplicative reciprocal matrices are proposed and applied to homogenize interval preference matrices. Second, the consistency of interval multiplicative reciprocal matrices is utilized to propose a generalized ordered weighted geometric averaging operator, which permits the aggregation of interval multiplicative reciprocal matrices in such a way that more important weight is given to that with more consistency. In order to avoid a misleading solution, the consistency and acceptable consistency of the collective interval multiplicative reciprocal matrix are studied in detail. Finally, a new algorithm is presented to solve the group decision-making problem with interval preference matrices. Numerical results are carried out to illustrate the given definitions, methods and algorithm, respectively. (c) 2013 Elsevier B.V. All rights reserved.