An Aggregation Algorithm for Group AHP Judgment Matrices Based on the Collective Operator of Spanning Trees

LU Zhi-yong; AN Cheng-jin; JIAO Bo; BI Jian-quan; PANG Xun-long

doi:10.3969/j.issn.0372-2112.2015.12.015

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An Aggregation Algorithm for Group AHP Judgment Matrices Based on the Collective Operator of Spanning Trees

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- An Aggregation Algorithm for Group AHP Judgment Matrices Based on the Collective Operator of Spanning Trees
- Acta Electronica Sinica Vol. 43, Issue 12, Pages: 2449-2454(2015)
- 作者机构：
  
  1. 中国洛阳电子装备试验中心,河南,洛阳,471003
  2. 国防科技大学电子科学与工程学院,湖南,长沙,410073
  3. 中国洛阳电子装备试验中心,河南,洛阳,471003
  4. 国防科技大学电子科学与工程学院,湖南,长沙,410073
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61101073, No.61301236, No.61303061)
- DOI：10.3969/j.issn.0372-2112.2015.12.015
  CLC： TP309
- Published：2015
- 稿件说明：
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LU Zhi-yong, AN Cheng-jin, JIAO Bo, et al. An Aggregation Algorithm for Group AHP Judgment Matrices Based on the Collective Operator of Spanning Trees[J]. Acta Electronica Sinica, 2015, 43(12): 2449-2454.
DOI：

LU Zhi-yong, AN Cheng-jin, JIAO Bo, et al. An Aggregation Algorithm for Group AHP Judgment Matrices Based on the Collective Operator of Spanning Trees[J]. Acta Electronica Sinica, 2015, 43(12): 2449-2454. DOI： 10.3969/j.issn.0372-2112.2015.12.015.

摘要

针对现有群组AHP(Analytic Hierarchy Process)判断矩阵集结算法

偏重于专家权重的选择

而忽略判断矩阵元素之间联系的不足

提出一种基于生成树集结算子的群组AHP判断矩阵集结算法.该算法依据判断矩阵与简单无向图生成树之间的关系

采用生成树集结算子获取完全一致集结矩阵

并利用完全一致集结矩阵和群组关联集结矩阵

综合考虑判断矩阵元素之间的个体一致性和群组关联性

计算获得满足一致性约束和最优相似性的群组集结结果.通过算例分析

说明该算法的可行性与有效性.

Abstract

The existing group aggregation algorithms based on AHP(Analytic Hierarchy Process) judgment matrices pay more attentions on the determination of the weights of experts

and neglect the relationships among the values of judgment matrices.Therefore

a new aggregation algorithm based on the collective operator of spanning trees is proposed in this paper.The algorithm obtains complete consistency collective matrix using collective operator of spanning trees and the relationship between a judgment matrix and a spanning tree of a simple undirected graph.In the algorithm

a complete consistency collective matrix and a group incidence matrix

which represent the individual consistency and group incidence of the values of judgment matrices

are used to compute group collective result under the restraints of consistency and similarity.Finally

a numerical example shows that the method is feasible and effective.

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