# [1]孔松泉,达庆利,徐泽水.互补判断矩阵排序的广义χ2法[J].东南大学学报(自然科学版),2002,32(4):659-662.[doi:10.3969/j.issn.1001-0505.2002.04.028] 　Kong Songquan,Da Qingli,Xu Zeshui.Generalized chi square method for priorities of complementary judgement matrices[J].Journal of Southeast University (Natural Science Edition),2002,32(4):659-662.[doi:10.3969/j.issn.1001-0505.2002.04.028] 点击复制 互补判断矩阵排序的广义χ2法() 分享到： var jiathis_config = { data_track_clickback: true };

32

2002年第4期

659-662

2002-07-20

## 文章信息/Info

Title:
Generalized chi square method for priorities of complementary judgement matrices

Author(s):
College of Economics and Management, Southeast University, Nanjing 210096, China

Keywords:

C934
DOI:
10.3969/j.issn.1001-0505.2002.04.028

Abstract:
Based on the definition of perfectly consistent complementary judgement matrix and a formula for transferring the definitions of perfect consistency of reciprocal judgement matrix and complementary judgement matrix, some theorems were proven, and generalized chi square method for priorities of complementary judgement matrices is proposed. Some properties, such as rank preservation under strong condition etc., were studied. A simple convergent iterative algorithm is given. These results are extended to accommodate group decision making. In practical applications, people can make rational decisions by taking proper values of α in the algorithm according to different decision-making problems. Finally, a numerical example is given.

## 参考文献/References:

[1] Saaty T L.The analytic hierarchy process [M].New York:McGraw-Hill,1980.10-90.
[2] 徐泽水.关于层次分析中几种标度的模拟评估[J].系统工程理论与实践,2000,20(7):58-62.
Xu Zeshui.A simulation-based evaluation of several scales in the analytic hierarchy process[J]. Systems Engineering-Theory & Practice,2000,20(7):58-62.(in Chinese)
[3] 徐泽水.AHP中两类标度的关系研究[J].系统工程理论与实践,1999,19(7):97-101.
Xu Zeshui.Study on the relation between two classes of scales in AHP[J]. Systems Engineering-Theory & Practice,1999,19(7):97-101.(in Chinese)
[4] Orlovsky S A.Decision-making with a fuzzy preference relation[J].Fuzzy Sets and Systems,1978,1:155-167.
[5] Tanino T.Fuzzy preference orderings in group decision making[J].Fuzzy Sets and Systems,1984,12:117-131.
[6] 徐泽水.一种改进的模糊一致性判断矩阵构造方法[J].应用数学与计算数学学报,1997,11(2):63-67.
Xu Zeshui.An improved method for constructing judgement matrix with fuzzy consistency[J]. Comm on Appl Math and Comput,1997,11(2):63-67.(in Chinese)
[7] Chiclana F,Herrera F,Herrera Viedma E.Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations[J]. Fuzzy Sets and Systems,1998,97:33-48.
[8] 王应明.判断矩阵排序方法综述[J].决策与决策支持系统,1995,5(3):101-114.
Wang Yingming.An overview of priority methods of comparison matrix[J]. Journal of Decision Making and Decision Support Systems,1995,5(3):101-114.(in Chinese)
[9] Xu Z S,Lu J J.A new method for calculating priorities in AHP [J]. Journal of Systems Science and Systems Engineering, 1999,8(2):179-188.
[10] Xu Z S.Generalized chi square method for the estimation of weights [J].Journal of Optimization Theory and Applications, 2000,107:183-192.
[11] 徐泽水.广义模糊一致性矩阵及其排序方法[J].解放军理工大学学报,2000,1(6):97-99.
Xu Zeshui.Generalized fuzzy consistent matrix and its priority method[J]. Journal of PLA University of Science and Technology, 2000,1(6):97-99.(in Chinese)
[12] 樊治平,胡国奋.模糊判断矩阵一致性逼近及排序方法[J].运筹与管理,2000,9(3):21-25.
Fan Zhiping,Hu Guofen.The consistency approximation and ranking method for fuzzy judgement matrix[J]. Operations Research and Management Science, 2000,9(3):21-25.(in Chinese)

## 相似文献/References:

[1]徐泽水,达庆利.3种基于互反判断矩阵的互补判断矩阵排序法[J].东南大学学报(自然科学版),2001,31(5):106.[doi:10.3969/j.issn.1001-0505.2001.05.023]
Xu Zeshui,Da Qingli.Three Reciprocal Judgement Matrices-Based Methods for Priorities of Complementary Judgement Matrices[J].Journal of Southeast University (Natural Science Edition),2001,31(4):106.[doi:10.3969/j.issn.1001-0505.2001.05.023]