|Table of Contents|

[1] Xu Zeshui, Da Qingli, Chen Qi,. Priority approach based on quadratic programming modelto fuzzy preference relation [J]. Journal of Southeast University (English Edition), 2005, 21 (1): 108-110. [doi:10.3969/j.issn.1003-7985.2005.01.023]
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Priority approach based on quadratic programming modelto fuzzy preference relation()
一种基于二次规划模型的模糊偏好关系排序法
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
21
Issue:
2005 1
Page:
108-110
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2005-03-30

Info

Title:
Priority approach based on quadratic programming modelto fuzzy preference relation
一种基于二次规划模型的模糊偏好关系排序法
Author(s):
Xu Zeshui1;  Da Qingli1;  Chen Qi2
1College of Economics and Management, Southeast University, Nanjing 210096, China
2Institute of Sciences, PLA University of Science and Technology, Nanjing 210007, China
徐泽水1;  达庆利1;  陈琦2
1东南大学经济管理学院, 南京 210096; 2解放军理工大学理学院, 南京 210007
Keywords:
decision making;  fuzzy preference relation;  quadratic programming;  priority
决策;  模糊偏好关系;  二次规划;  排序
PACS:
O223
DOI:
10.3969/j.issn.1003-7985.2005.01.023
Abstract:
We investigate the decision-making problem with a finite set of alternatives, in which the decision information takes the form of a fuzzy preference relation.We develop a simple and practical approach to obtaining the priority vector of a fuzzy preference relation.The prominent characteristic of the developed approach is that the priority vector can generally be obtained by a simple formula, which is derived from a quadratic programming model.We utilize the consistency ratio to check the consistency of fuzzy preference relation.If the fuzzy preference relation is of unacceptable consistency, then we can return it to the decision maker to reconsider structuring a new fuzzy preference relation until the fuzzy preference relation with acceptable consistency is obtained.We finally illustrate the priority approach by two numerical examples.The numerical results show that the developed approach is straightforward, effective, and can easily be performed on a computer.
研究了决策信息以模糊偏好关系给出的有限方案决策问题, 提出了一种简洁且实用的模糊偏好关系排序方法.该方法首先建立一个二次规划模型, 然后基于该模型推导出求解模糊偏好关系排序向量的一个简洁公式.基于获得的排序向量, 利用一致性比例对模糊偏好关系进行一致性检验.对于一致性较差的模糊偏好关系, 则需反馈给决策者重新进行判断, 直至得到一个一致性可接受的模糊偏好关系为止.最后, 利用2个算例对该方法进行分析和说明, 数值结果表明该方法简洁、有效, 且易于在计算机上操作.

References:

[1] Saaty T L.The analytic hierarchy process [M].New York:McGraw-Hill, 1980.
[2] Xu Z S.Uncertain multiple attribute decision making:methods and applications [M].Beijing:Tsinghua University Press, 2004.(in Chinese)
[3] Tanino T.Fuzzy preference orderings in group decision-making [J].Fuzzy Sets and Systems, 1984, 12(2):117-131.
[4] Xu Z S. Two methods for priorities of complementary judgement matrices — weighted least-square method and eigenvector method [J].Systems Engineering — Theory & Practice, 2002, 22(7):71-75.(in Chinese)
[5] Lipovetsky S, Michael Conklin M.Robust estimation of priorities in the AHP [J].European Journal of Operational Research, 2002, 137(1):110-122.
[6] Xu Z S.Generalized chi square method for the estimation of weights [J].Journal of Optimization Theory and Applications, 2000, 107(1):183-192.
[7] Wang Y M, Xu N R.Application of optimization theory in analytical hierarchy process [J].Systems Engineering — Theory & Practice, 1991, 11(2):24-29.(in Chinese)
[8] Xu Z S, Da Q L.An approach to improving consistency of fuzzy preference matrix [J].Fuzzy Optimization and Decision Making, 2003, 2(1):3-12.

Memo

Memo:
Biography: Xu Zeshui(1968—), male, doctor, professor, xu-zeshui@263.net.
Last Update: 2005-03-20