基于前景理论和区间二元语义MULTIMOORA的多属性决策方法
|
摘要
针对属性值为不确定语言,属性权重为部分已知或完全未知的多属性决策问题,提出一种新的决策方法。运用前景理论计算出每个属性的二元语义前景值,建立二元语义前景决策矩阵。在考虑主、客观影响因素的基础上,构建属性权重优化模型,得到属性的综合权重。基于区间二元语义对MULTIMOORA进行扩展,并对方案进行排序。在此基础上,运用占优理论得到方案的最终排序。最后,通过算例验证了该方法的可行性与有效性。
For the multi-attribute decision making problem in which the attribute values are uncertain language and the attribute weights are incomplete or completely unknown, a novel decision making method is proposed. At first, the prospect decision matrix is established according to the computation of the 2-tuple linguistic prospect value of each attribute. The attribute weights optimization model is constructed considering the objective and subjective influencing factors. The attribute weights can be computed using this model. Then, the MULTIMOORA is extended based on the interval 2-tuple linguistic terms, by which the alternatives are ranked, based on which, the final ranking of alternatives is obtained according to the dominance theory. Finally, a numerical example is presented to illustrate the feasiblity and effectiveness of the method proposed.
For the multi-attribute decision making problem in which the attribute values are uncertain language and the attribute weights are incomplete or completely unknown, a novel decision making method is proposed. At first, the prospect decision matrix is established according to the computation of the 2-tuple linguistic prospect value of each attribute. The attribute weights optimization model is constructed considering the objective and subjective influencing factors. The attribute weights can be computed using this model. Then, the MULTIMOORA is extended based on the interval 2-tuple linguistic terms, by which the alternatives are ranked, based on which, the final ranking of alternatives is obtained according to the dominance theory. Finally, a numerical example is presented to illustrate the feasiblity and effectiveness of the method proposed.
引文
[1] Kahneman D,Tversky A. Prospect theory: An analysis of decision under risk[J].Econometrica,1979, 47(2): 263-292.
[2] 高建伟,刘慧晖,谷云东,等. 基于前景理论的区间直觉模糊多准则决策方法[J]. 系统工程理论与实践, 2014, 34(12): 3175-3181.
[3] 江文奇. 基于前景理论和VIKOR的风险型模糊多准则决策方法[J]. 控制与决策, 2014, 29 (12): 2287-2291.
[4] 赵树平,梁昌勇,戚筱雯,等.城市突发事件的应急设施选址群决策方法[J].系统管理学报, 2014, 23(6): 810-818.
[5] 尤天慧,高美丽.一种基于误差分析的区间数多属性决策方法[J].系统管理学报, 2014, 23(2): 224-228.
[6] 巩在武,刘思峰.直觉模糊判断矩阵群决策中的逆判问题[J].系统管理学报, 2007, 16(5): 497-501.
[7] Liao H T, Xu Z B, Zeng X J. Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making[J]. IEEE Transactions on Fuzzy Systems, 2015, 23(5):1343-1355.
[8] Liao H C, Xu Z S, Zeng X J. Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets[J]. Knowledge-Based Systems, 2015,76:127-138, 2015.
[9] Herrera A F, Martinez L. A 2-tuple fuzzy linguistic representation model for computing with words [J]. IEEE Trans on Fuzzy Systems, 2000, 8 (6):746-752.
[10] Herrera A F, Martinez L. A model based on 2-tuples linguistic for dealing with multi-granularity hierarchical linguistic contexts in multi-expert decision-making [J]. IEEE Trans on Systems, Man and Cybernetics, Part B:Cybernetics, 2001, 31(2): 227-234.
[11] Jiang Y P, Fan Z P. An approach to group decision making problems based on 2-tuples linguistic symbol operation [J]. Systems Engineering and Electronics, 2003, 25(11): 1373-1376.
[12] Wei G W. A method for multiple attribute group decision making based on the ET-WG and ET-OWG operators with 2-tuple linguistic information [J]. Expert Systems with Applications, 2010, 37(12): 7895-7900.
[13] Wei G W. A method for multiple making based on the T-OWG attributes group decision and T-IOWG operators with 2-tuple linguistic information [J]. Statistics and Decision-making, 2008(10): 155-156.
[14] Wei G W, Lin R. Models for multiple attribute group decision making with 2-tuple linguistic assessment information [J]. International Journal of Computational Intelligence Systems, 2010, 3(3): 315-324.
[15] Zhang Z, Guo C H. Multiple attributes group decision making method based on 2-tuple linguistic information processing [J]. Control and Decision, 2011, 26(12): 1881-1887.
[16] Wei G W, Zhao X F. Some dependent aggregation operators with 2-tuple linguistic information and their application to multiple attribute group decision making [J]. Expert Systems with Applications, 2012, 39(5): 5881-5886.
[17] Xu Y, Wang H. Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment [J]. Applied Soft Computing Journal, 2011, 11(5):3988-3997.
[18] Dong Y, Hong W C. Selecting the individual numerical scale and prioritization method in the analytic hierarchy process: A 2-tuple fuzzy linguistic approach [J].IEEE Trans on Fuzzy Sets, 2011, 19(1): 13-25.
[19] Bao G Y, Lian X L. Improved 2-tuple linguistic representation model based on new linguistic evaluation scale [J]. Control and Decision, 2010, 25(5): 780-785.
[20] Yi P T, Li W W, Guo Y J. 2-tuple linguistic density attributes operator and its application in multi-attribute decision making [J]. Control and Decision, 2012, 27(5): 757-760.
[21] Wei G W. Project method for multiple attribute group decision making in 2-tuple linguistic setting[J]. Operations Research and Management Science, 2009, 18(5): 59-63.
[22] Wei G W, Lin Y. Method of grey relational analysis for multiple attribute group decision making in 2-tuple linguistic setting[J]. Systems Engineering and Electronics, 2008, 30(9): 1686-1689.
[23] Liu Y, Forrest J, 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.
[24] Qin J D, Liu X W. An extended VIKOR method based on prospect theory for multiple attribute decision making under interval 2-tuple fuzzy environment[J]. Knowledge-Based Systems, 2015, (86): 116-130.
[25] 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.
[26] 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.
[27] Brauers W K M, Bale?entis A, Bale?entis T. MULTIMOORA for the EU Member States updated with fuzzy number theory[J]. Technological & Economic Development of Economy, 2011 (17): 259-290.
[28] Liu H C, Fan X J. Evaluating the risk of failure modes with extended MULTIMOORA method under fuzzy environment[J]. Engineering Applications of Artificial Intelligence, 2014 (34): 168-177.
[29] You X Y, You J X, Liu H C. Group multi-criteria supplier selection using an extended VIKOR method with interval 2-tuple linguistic information[J]. Expert Systems with Applications, 2015, 42(4): 1906-1016.
[30] Kahneman D, Tversky A. Prospect theory: An analysis of decision under risk [J]. Econometrica, 1979, 47(2): 263-292.
[31] Tversky A, Kahneman D. Advances in prospect theory: Cumulative representation of uncertainty [J]. Journal of Risk and Uncertainty, 1992, 5(4): 297-323.
[32] Qi X W, Liang C Y. Approach to interval-valued intuitionistic fuzzy multiple attributes group decision-making based on maximum entropy [J]. Systems Engineering-Theory & Practice, 2011, 31(10): 1940-1948.
[33] Wang J Q, Sun T. Multi-criteria fuzzy decision-making method based on prospect theory with incomplete information [J]. Control and Decision, 2009, 24(8): 1198-1202.
[34] Li P, Liu S F. Intuitionistic fuzzy stochastic multi-criteria decision-making methods based on prospect theory [J]. Control and Decision, 2012, 27(11): 1601-1606.
[35] Tversky A, Kahneman D. Advances in prospect theory: Cumulative representation of uncertaint[J]. Journal Risk Uncert, 1992 (5): 297-323.
[36] Liu H C, Ren M L. An interval 2-tuple linguistic MCDM method for robot evaluation and selection [J]. International Journal of Production Research, 2014, 52(10): 2867-2880.
[37] Kahneman D, Tversky A. Prospect theory: An analysis of decision under risk [J]. Econometric, 1979, 47(2): 263-291.
[2] 高建伟,刘慧晖,谷云东,等. 基于前景理论的区间直觉模糊多准则决策方法[J]. 系统工程理论与实践, 2014, 34(12): 3175-3181.
[3] 江文奇. 基于前景理论和VIKOR的风险型模糊多准则决策方法[J]. 控制与决策, 2014, 29 (12): 2287-2291.
[4] 赵树平,梁昌勇,戚筱雯,等.城市突发事件的应急设施选址群决策方法[J].系统管理学报, 2014, 23(6): 810-818.
[5] 尤天慧,高美丽.一种基于误差分析的区间数多属性决策方法[J].系统管理学报, 2014, 23(2): 224-228.
[6] 巩在武,刘思峰.直觉模糊判断矩阵群决策中的逆判问题[J].系统管理学报, 2007, 16(5): 497-501.
[7] Liao H T, Xu Z B, Zeng X J. Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making[J]. IEEE Transactions on Fuzzy Systems, 2015, 23(5):1343-1355.
[8] Liao H C, Xu Z S, Zeng X J. Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets[J]. Knowledge-Based Systems, 2015,76:127-138, 2015.
[9] Herrera A F, Martinez L. A 2-tuple fuzzy linguistic representation model for computing with words [J]. IEEE Trans on Fuzzy Systems, 2000, 8 (6):746-752.
[10] Herrera A F, Martinez L. A model based on 2-tuples linguistic for dealing with multi-granularity hierarchical linguistic contexts in multi-expert decision-making [J]. IEEE Trans on Systems, Man and Cybernetics, Part B:Cybernetics, 2001, 31(2): 227-234.
[11] Jiang Y P, Fan Z P. An approach to group decision making problems based on 2-tuples linguistic symbol operation [J]. Systems Engineering and Electronics, 2003, 25(11): 1373-1376.
[12] Wei G W. A method for multiple attribute group decision making based on the ET-WG and ET-OWG operators with 2-tuple linguistic information [J]. Expert Systems with Applications, 2010, 37(12): 7895-7900.
[13] Wei G W. A method for multiple making based on the T-OWG attributes group decision and T-IOWG operators with 2-tuple linguistic information [J]. Statistics and Decision-making, 2008(10): 155-156.
[14] Wei G W, Lin R. Models for multiple attribute group decision making with 2-tuple linguistic assessment information [J]. International Journal of Computational Intelligence Systems, 2010, 3(3): 315-324.
[15] Zhang Z, Guo C H. Multiple attributes group decision making method based on 2-tuple linguistic information processing [J]. Control and Decision, 2011, 26(12): 1881-1887.
[16] Wei G W, Zhao X F. Some dependent aggregation operators with 2-tuple linguistic information and their application to multiple attribute group decision making [J]. Expert Systems with Applications, 2012, 39(5): 5881-5886.
[17] Xu Y, Wang H. Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment [J]. Applied Soft Computing Journal, 2011, 11(5):3988-3997.
[18] Dong Y, Hong W C. Selecting the individual numerical scale and prioritization method in the analytic hierarchy process: A 2-tuple fuzzy linguistic approach [J].IEEE Trans on Fuzzy Sets, 2011, 19(1): 13-25.
[19] Bao G Y, Lian X L. Improved 2-tuple linguistic representation model based on new linguistic evaluation scale [J]. Control and Decision, 2010, 25(5): 780-785.
[20] Yi P T, Li W W, Guo Y J. 2-tuple linguistic density attributes operator and its application in multi-attribute decision making [J]. Control and Decision, 2012, 27(5): 757-760.
[21] Wei G W. Project method for multiple attribute group decision making in 2-tuple linguistic setting[J]. Operations Research and Management Science, 2009, 18(5): 59-63.
[22] Wei G W, Lin Y. Method of grey relational analysis for multiple attribute group decision making in 2-tuple linguistic setting[J]. Systems Engineering and Electronics, 2008, 30(9): 1686-1689.
[23] Liu Y, Forrest J, 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.
[24] Qin J D, Liu X W. An extended VIKOR method based on prospect theory for multiple attribute decision making under interval 2-tuple fuzzy environment[J]. Knowledge-Based Systems, 2015, (86): 116-130.
[25] 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.
[26] 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.
[27] Brauers W K M, Bale?entis A, Bale?entis T. MULTIMOORA for the EU Member States updated with fuzzy number theory[J]. Technological & Economic Development of Economy, 2011 (17): 259-290.
[28] Liu H C, Fan X J. Evaluating the risk of failure modes with extended MULTIMOORA method under fuzzy environment[J]. Engineering Applications of Artificial Intelligence, 2014 (34): 168-177.
[29] You X Y, You J X, Liu H C. Group multi-criteria supplier selection using an extended VIKOR method with interval 2-tuple linguistic information[J]. Expert Systems with Applications, 2015, 42(4): 1906-1016.
[30] Kahneman D, Tversky A. Prospect theory: An analysis of decision under risk [J]. Econometrica, 1979, 47(2): 263-292.
[31] Tversky A, Kahneman D. Advances in prospect theory: Cumulative representation of uncertainty [J]. Journal of Risk and Uncertainty, 1992, 5(4): 297-323.
[32] Qi X W, Liang C Y. Approach to interval-valued intuitionistic fuzzy multiple attributes group decision-making based on maximum entropy [J]. Systems Engineering-Theory & Practice, 2011, 31(10): 1940-1948.
[33] Wang J Q, Sun T. Multi-criteria fuzzy decision-making method based on prospect theory with incomplete information [J]. Control and Decision, 2009, 24(8): 1198-1202.
[34] Li P, Liu S F. Intuitionistic fuzzy stochastic multi-criteria decision-making methods based on prospect theory [J]. Control and Decision, 2012, 27(11): 1601-1606.
[35] Tversky A, Kahneman D. Advances in prospect theory: Cumulative representation of uncertaint[J]. Journal Risk Uncert, 1992 (5): 297-323.
[36] Liu H C, Ren M L. An interval 2-tuple linguistic MCDM method for robot evaluation and selection [J]. International Journal of Production Research, 2014, 52(10): 2867-2880.
[37] Kahneman D, Tversky A. Prospect theory: An analysis of decision under risk [J]. Econometric, 1979, 47(2): 263-291.