基于前景理论和三角模糊MULTIMOORA的多阶段决策方法

doi:10.12005/orms.2018.0062

摘要/Abstract

摘要： 针对时间权重与属性权重完全未知的三角模糊多属性决策问题,基于前景理论和MULTIMOORA提出一种新的决策方法。首先,建立备选方案在不同时段的三角模糊前景决策矩阵,根据时间度及不同时段内备选方案前景值的差异构建时间权重优化模型,并运用最大偏差法的基本思想获得属性权重。其次,基于三角模糊数提出一种新的MULTIMOORA扩展形式,并结合占优理论对备选方案进行比选。最后,通过实例证明了所提方法是可行的,也是有效的。

关键词: 前景理论, 三角模糊数, MLTIMOORA, 占优理论

Abstract: For the triangular fuzzy multi-attribute decision making problem, in which period weights and attribute weights are completely unknown, a new decisiong making method based on the prospect theory and MULTIMOORA was presented. Firstly, the triangular fuzzy prospect decision matrices in different periods are built and the period weight optimization model was established on the basis of the time degree and differences of prospect values of alternatives in different periods. According to the maximise deviation, attribute weights were determined. Then, a novel extension form of MULTIMOORA was proposed based on the triangular fuzzy number. Alternatives are ranked and selected by the triangular fuzzy MULTIMOORA and the dominance theory. Finally, the feasibility and validity of the proposed method are verified with an example.

Key words: prospect theory, triangular fuzzy number, MULTIMOORA, dominance theory

中图分类号:

C934

代文锋, 仲秋雁, 齐春泽. 基于前景理论和三角模糊MULTIMOORA的多阶段决策方法[J]. 运筹与管理, 2018, 27(3): 74-81.

DAI Wen-feng, ZHONG Qiu-yan, QI Chun-ze. Multi-stage Decision Making Method Based on Prospect Theory and MULTIMOORA in the Triangular Fuzzy Environment[J]. Operations Research and Management Science, 2018, 27(3): 74-81.

参考文献

[1] Cao Q W, Wu J. The extended COWG operators and their application to multiple attributive group decision making problems with interval numbers[J]. Applied Mathematical Modelling, 2011, (35): 2075-2086.
[2] Baležentis T, Zeng S. Group multi-criteria decision making based upon interval-valued fuzzy numbers: an extension of the MULTIMOORA method[J]. Expert Systems with Applications, 2013, (40): 543-550.
[3] Stanujkic D, Magdalinovic N, Jovanovic R, Stojanovic R. An objective multi-criteria approach to optimization using MOORA method and interval grey numbers[J]. Technological & Economic Development of Economy, 2012, (18): 331-363.
[4] 赵萌,任嵘嵘,李刚.基于模糊熵-熵权法的混合多属性决策方法[J].运筹与管理,2013,22(06):78-83.
[5] 梁昌勇,戚筱雯,丁勇等.一种基于TOPSIS的混合型多属性群决策方法[J].中国管理科学,2012,20(4):109-117.
[6] Liu Y, Jeffrey Forrest, Liu S F. Dynamic grey incidence group decision making methodology based on interval 2-tuple linguistic information processing[J]. Systems Engineering and Electronics, 2013, 35 (9): 1915-1922.
[7] Qin J D, Liu X W. An extended VIKOR method based on prospect theory for multiple attribute decision making under interval type-2 fuzzy environment[J]. Knowledge-Based Systems, 2015, (86): 116-130.
[8] 刘勇,王成军,等.基于犹豫模糊语言信息的权重信息部分可知TOPSIS方法[J].工程数学学报,2015,32(04):497-506.
[9] Dong M, Li S. Approaches to group decision making with incomplete information based on power geometric operators and triangular fuzzy AHP[J]. Expert Systems with Applications, 2015, (42): 7846-7857.
[10] Ö Aydin. Bulanik AHP ile Ankara icin hastane yer secimi[J]. Journal of Dokuz Eylul University Faculty of Economics and Administrative Sciences, 2009, 24(2): 87-104.
[11] Liu W S. Research on preferred method of connection mining village based on AHP-TOPSIS of triangular fuzzy numbers[J]. Application Research of Computers, 2016, 33(2): 458-462.
[12] Jiang W Q. Extension of VIKOR method for multi-criteria group decision making problems with triangular fuzzy numbers[J]. Control and Decision, 2015, 30(6): 1059-1064.
[13] Brauers W K M, Zavadskas E K. The MOORA method and its application to privatization in a transition economy[J]. Control Cybern, 2006, (35): 445-469.
[14] Brauers W K M, Zavadskas E K. MULTIMOORA optimization used to decide on a bank loan to buy property[J]. Technological & Economic Development of Economy, 2011, (17): 174-188.
[15] Brauers W K M, Baležentis A, Baležentis T. MULTIMOORA for the EU Member States updated with fuzzy number theory[J]. Technological & Economic Development of Economy, 2011, (17): 259-290.
[16] Liu H C, Fan X J, Li P, Chen Y Z. Evaluating the risk of failure modes with extended MULTIMOORA method under fuzzy environment[J]. Engineering Applications of Artificial Intelligence, 2014, (34): 168-177.
[17] Kahneman D, Tversky A. Prospect theory: an analysis of decision under risk[J]. Econometrica, 1979, 47(2): 263-292.
[18] Tversky A, Kahneman D. Advances in prospect theory: cumulative representation of uncertainty[J]. Journal of Risk and Uncertainty, 1992, 5(4): 297-323.
[19] Brauers W K M, Zavadskas E K. Project management by MULTIMOORA as an instrument for transition economies[J]. Technological & Economic Development of Economy, 2010, (16): 5-24.
[20] Datta S, Sahu N, Mahapatra S. Robot selection based on grey-MULTIMOORA approach[J]. Grey Systems Theory & Application, 2013, (3): 201-232.
[21] Brauers W K M, Zavadskas E K. Robustness of MULTIMOORA: a method for multi-objective optimization[J]. Informatica, 2012, (23): 1-25.
[22] Yager R R. On order weighted averaging aggregation operators in multi-criteria decision making[J]. IEEE Transactions on Systems, Man, and Cybernetics, 1988, 18(1): 183-190.
[23] Chatterjee P, Chakraborty S. Material selection using preferential ranking methods[J]. Materials & Design, 2012, (35): 384-393.
[24] Spearman C. The proof and measurement of association between two things[J]. American Journal of Psychology, 1904, (15): 72-101.