[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()

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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

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

Keywords:

decision making;  fuzzy preference relation;  quadratic programming;  priority

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.

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.

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