三参数区间灰数信息下风险型多准则决策方法

李存斌; 赵坤; 祁之强

doi:10.16383/j.aas.2015.c140157

三参数区间灰数信息下风险型多准则决策方法

doi: 10.16383/j.aas.2015.c140157

1.
华北电力大学经济与管理学院北京 102206

基金项目:

国家自然科学基金(71071054, 71271084)资助

详细信息

作者简介:
李存斌华北电力大学经济与管理学院教授. 主要研究方向为信息管理与风险型决策分析.E-mail: Lcb999@263.net

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出版历程
- 收稿日期: 2014-03-14
- 修回日期: 2015-03-20
- 刊出日期: 2015-07-20

A Risky Multi-criteria Decision-making Method with Three-parameter Interval Grey Number

1.
School of Economics and Management, North China Electronic Power University, Beijing 102206

Funds:

Supported by National Natural Science Foundation of China (71071054, 71271084)

摘要

摘要: 针对概率和准则值均为三参数区间灰数的多准则决策问题,本文提出了一种基于前景理论的决策方法. 该方法首先定义了三参数区间灰数的距离和精确记分函数,并通过讨论其性质给出了比较大小的方法; 其次,通过给出三参数区间灰数前景价值和概率权重函数的定义,以多参考点为思路,构建前景决策矩阵, 并通过提出参考点集结算子,集结出综合前景决策矩阵. 进而,由优化模型求得的最优准则权系数加权得出方案的综合前景值及排序; 最后,通过算例对比说明了该方法的合理性和可靠性.
- 风险型决策 /
- 前景理论 /
- 三参数区间灰数 /
- 参考点
Abstract: In view of the multi-criteria decision-making problem that probabilities and the criteria values of alternatives are both three-parameter interval grey number, a risky decision-making approach based on prospect theory is proposed. In this method, firstly, the distance and the exact function of three-parameter interval grey number are defined, and on the basis of the analysis and discussion of its properties, a three-parameter interval grey number comparison method is defined. Secondly, we give the definition of the prospect value function and the probabilities weighting function of three-parameter interval grey number. Then, the prospect value of each alternative is calculated based on multi-reference point, and the integrated prospect decision matrix is constructed by giving the reference point aggregating operator. Moreover, the integrated prospect value of each alternative is aggregated by the integrated prospect decision matrix and the optimal criteria weights given by the optimization model. After that we can order these alternatives by comparing their integrated prospect values. Finally, an example is presented to examine the effectiveness of our method.
- Risky decision-making /
- prospect theory /
- three-parameter interval number /
- reference point

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参考文献(20)

[1]	Basar O. A decision model for information technology selection using AHP integrated TOPSIS-Grey: the case of content management systems. Knowledge-Based Systems, 2014, 70: 44-54
[2]	Wang P, Meng P, Zhai J Y, Zhu Z Q. A hybrid method using experiment design and grey relational analysis for multiple criteria decision making problems. Knowledge-Based Systems, 2013, 53: 100-107
[3]	Wang J Q, Zhang H Y, Ren S C. Grey stochastic multi-criteria decision-making approach based on expected probability degree. Scientia Iranica, 2013, 20(3): 873-878
[4]	Lin Y H, Lee P C, Ting H I. Dynamic multi-attribute decision making model with grey number evaluations. Expert Systems with Applications, 2008, 35(4): 1638-1644
[5]	Luo D, Wang X. The multi-attribute grey target decision method for attribute value within three-parameter interval grey number. Applied Mathematical Modelling, 2012, 36(5): 1957-1963
[6]	Kahneman D, Tversky A. Prospect theory: an analysis of decision under risk. Econometrica, 1979, 47(2): 263-291
[7]	Fan Z P, Zhang X, Chen F D, Liu Y. Multiple attribute decision making considering aspiration-levels: a method based on prospect theory. Computers & Industrial Engineering, 2013, 65(2): 341-350
[8]	Liu P D, Jin F, Zhang X, Su Y, Wang M H. Research on the multi-attribute decision-making under risk with interval probability based on prospect theory and the uncertain linguistic variables. Knowledge-Based Systems, 2011, 24(4): 554-561
[9]	Wang J Q, Li K J, Zhang H Y. Interval-valued intuitionistic fuzzy multi-criteria decision-making approach based on prospect score function. Knowledge-Based Systems, 2012, 27: 119-125
[10]	Luo Dang. Decision-making methods with three-parameter interval grey number. Systems Engineering---Theory & Practice, 2009, 29(1): 124-130(罗党. 三参数区间灰数信息下的决策方法. 系统工程理论与实践, 2009, 29(1): 124-130)
[11]	Bu Guang-Zhi, Zhang Yu-Wen. Grey fuzzy comprehensive evaluation method based on interval numbers of three parameters. Systems Engineering and Electronics, 2001, 23(9): 43-45 (卜广志, 张宇文. 基于三参数区间数的灰色模糊综合评判. 系统工程与电子技术, 2001, 23(9): 43-45)
[12]	Hu Qi-Zhou, Zhang Wei-Hua, Yu Li. The research and application in of interval numbers of three parameters. Engineering Science, 2007, 9(3): 47-51(胡启洲, 张卫华, 于莉. 三参数区间数研究及其在决策分析中的应用. 中国工程科学, 2007, 9(3): 47-51)
[13]	Yan Shu-Li, Liu Si-Feng, Zhu Jian-Jun, Fang Zhi-Geng, Liu Jian. TOPSIS decision-making method with three-parameter interval number based on entropy measure. Chinese Journal of Management Science, 2013, 21(6): 145-151(闫书丽, 刘思峰, 朱建军, 方志耕, 刘健. 基于熵测度的三参数区间数信息下的TOPSIS决策方法. 中国管理科学, 2013, 21(6): 145-151)
[14]	Wu G, Gonzalez R. Curvature of the probability weighting function. Management Science, 1996, 42(12): 1676-1690
[15]	Yang Bao-Hua, Fang Zhi-Geng, Zhou Wei, Liu Jian. Incidence decision model of multi-attribute interval grey number based on information reduction operator. Control and Decision, 2012, 27(2): 182-186 (杨保华, 方志耕, 周伟, 刘健. 基于信息还原算子的多指标区间灰数关联决策模型. 控制与决策, 2012, 27(2): 182-186)
[16]	Wang Jian-Qiang, Zhou Ling. Grey-stochastic multi-criteria decision-making approach based on prospect theory. Systems Engineering ---Theory & Practice, 2010, 30(9): 1658-1664 (王坚强, 周玲. 基于前景理论的灰色随机多准则决策方法. 系统工程理论与实践, 2010, 30(9): 1658-1664)
[17]	Tversky A, Kahneman D. Advances in prospect theory: cumulative representation of uncertainly. Journal of Risk and Uncertainty, 1992, 5(4): 297-323
[18]	Liu Pei-De. Method for multi-attribute decision-making under risk with the uncertain linguistic variables based on prospect theory. Control and Decision, 2011, 26(6): 893-897 (刘培德. 一种基于前景理论的不确定语言变量风险型多属性决策方法. 控制与决策, 2011, 26(6): 893-897)
[19]	Eirik B A, Frank A. On how access to an insurance market affects investments in safety measures, based on the expected utility theory. Reliability Engineering & System Safety, 2011, 96(3): 361-364
[20]	Park C, Ahn S, Lee S. A Bayesian decision model based on expected utility and uncertainty risk. Applied Mathematics and Computation, 2014, 242: 643-648