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[1] Sun Lu,. A min-max optimization approachfor weight determination in analytic hierarchy process [J]. Journal of Southeast University (English Edition), 2012, 28 (2): 245-250. [doi:10.3969/j.issn.1003-7985.2012.02.020]
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A min-max optimization approachfor weight determination in analytic hierarchy process()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
28
Issue:
2012 2
Page:
245-250
Research Field:
Traffic and Transportation Engineering
Publishing date:
2012-06-30

Info

Title:
A min-max optimization approachfor weight determination in analytic hierarchy process
Author(s):
Sun Lu
School of Transportation, Southeast University, Nanjing 210096, China
Department of Civil Engineering, Catholic University of America, Washington DC 20064, USA
Keywords:
analytic hierarchy process min-max optimization weight linear programming
PACS:
U491
DOI:
10.3969/j.issn.1003-7985.2012.02.020
Abstract:
A min-max optimization method is proposed as a new approach to deal with the weight determination problem in the context of the analytic hierarchy process. The priority is obtained through minimizing the maximal absolute difference between the weight vector obtained from each column and the ideal weight vector. By transformation, the constrained min-max optimization problem is converted to a linear programming problem, which can be solved using either the simplex method or the interior method. The Karush-Kuhn-Tucker condition is also analytically provided. These control thresholds provide a straightforward indication of inconsistency of the pairwise comparison matrix. Numerical computations for several case studies are conducted to compare the performance of the proposed method with three existing methods. This observation illustrates that the min-max method controls maximum deviation and gives more weight to non-dominate factors.

References:

[1] Saaty T L. The analytical hierarchy process [M]. New York: McGraw-Hill, 1980.
[2] Genest C, M’Lan C E. Deriving priorities from the Bradley-Terry model [J].Mathematical and Computer Modelling, 1999, 29(4):87-102.
[3] Sun L, Greenberg B S. Multicriteria group decision making: optimal priority synthesis from pairwise comparisons [J].Journal of Optimization Theory and Applications, 2006, 130(2): 317-339.
[4] Pedrycz W, Gomide F. An introduction to fuzzy sets: analysis and design [M]. Cambridge, MA: The MIT Press, 1998.
[5] Pak P S, Tsuji K, Suzuki Y. Comprehensive evaluation of new urban transportation systems by AHP [J]. International Journal of Systems Science, 1987, 18(6): 1179-1190.
[6] Cheng C H, Mon D L. Evaluating weapon system by analytical hierarchy process based on fuzzy scales [J].Fuzzy Sets and Systems, 1994, 63(1):1-10.
[7] Mon D L, Cheng C H, Lin J C, Evaluating weapon system using fuzzy analytical hierarchy process based on entropy weight [J]. Fuzzy Sets and Systems, 1994, 62(2):127-134.
[8] Chen S M. Evaluating weapon systems using fuzzy arithmetic operations [J].Fuzzy Sets and Systems, 1996, 77(3): 265-276.
[9] Cheng C H. Evaluating naval tactical missile systems by fuzzy AHP based on the grade value of membership function [J]. European Journal of Operations Research, 1996, 96(2):343-350.
[10] Cheng C H, Yang K L, Hwang C L. Evaluating attack helicopters by AHP based on linguistic variable weight [J]. European Journal of Operations Research, 1999, 116(2):423-435.
[11] Deng X J, Sun L. The Euclid norm weight model and application in pavement evaluation [J].China Journal of Highway and Transport, 1996, 9(1):21-29.(in Chinese)
[12] Forman E, Peniwati K. Aggregate individual judgments and priorities with the analytic hierarchy process [J]. European Journal of Operations Research, 1998, 108(1):165-169.
[13] Takeda E, Yu P L. Assessing priority weights from subsets of pairwise comparisons in multiple criteria optimization problems [J]. European Journal of Operations Research, 1995, 86(2): 315-331.
[14] Triantaphyllou E, Mann S H. An examination of the effectiveness of multi-dimensional decision-making methods: a decision-making paradox [J]. Decision Making Systems, 1989, 5(3):303-312.
[15] Triantaphyllou E. Multi-criteria decision making methods: a comparative study [M]. Kluwer Academic Publishers, 2002.
[16] Mikhailov L. A fuzzy programming method for deriving priorities in the analytic hierarchy process [J].Journal of Operations Research Society, 2000, 51(3):341-349.
[17] Chu A, Kalaba R, Springarn K. A comparison of two methods for determining the weights of belonging to fuzzy sets [J].Journal of Optimization Theory and Applications, 1979, 27(4):531-541.
[18] Saaty T L. A scaling method for priorities in hierarchical structures [J]. Journal of Mathematical Psychology, 1977, 15(3):234-281.
[19] Sun L, Deng X J. Weight analysis in evaluation systems [J]. Journal of Systems Science and Systems Engineering, 1997, 6(2):137-147.
[20] Crawford G, Williams C. A note on the analysis of subjective judgment matrices [J]. Journal of Mathematical Psychology, 1985, 29(4):387-405.
[21] Golany B, Kress M. A multicriteria evaluation of methods for obtaining weights from ratio-scale matrices [J].European Journal of Operations Research, 1993, 69(2):210-220.
[22] Bertsimas D, Tsitsiklis J N. Introduction to linear programming [M]. Belmont, MA: Athena Scientific, 1997.

Memo

Memo:
Biography: Sun Lu(1972—), male, doctor, professor, sunl@cua.edu.
Foundation items: The US National Science Foundation(No.CMMI-0408390, CMMI-0644552, BCS-0527508), the National Natural Science Foundation of China(No.51010044, U1134206), the Fok Ying-Tong Education Foundation(No.114024), the Natural Science Foundation of Jiangsu Province(No.BK2009015), the Postdoctoral Science Foundation of Jiangsu Province(No.0901005C).
Citation: Sun Lu.A min-max optimization approach for weight determination in analytic hierarchy process[J].Journal of Southeast University(English Edition), 2012, 28(2):245-250.[doi:10.3969/j.issn.1003-7985.2012.02.020]
Last Update: 2012-06-20