基于后悔理论和证据理论的犹豫模糊决策方法

doi:10.11772/j.issn.1001-9081.2017.02.0540

计算机应用 ›› 2017, Vol. 37 ›› Issue (2): 540-545.DOI: 10.11772/j.issn.1001-9081.2017.02.0540

基于后悔理论和证据理论的犹豫模糊决策方法

朱轮

常州大学信息科学与工程学院, 江苏常州 213016

收稿日期:2016-07-11 修回日期:2016-09-08 出版日期:2017-02-10 发布日期:2017-02-11
通讯作者: 朱轮,3278191370@qq.com
作者简介:朱轮(1974-),男,江苏常州人,高级工程师,硕士,主要研究方向:电子信息技术、智能决策。
基金资助:
江苏省科技支撑计划（工业）重点项目（BE2013005-3）。

Hesitant fuzzy decision-making method based on regret theory and evidence theory

ZHU Lun

School of Information Science and Engineering, Changzhou University, Changzhou Jiangsu 213016, China

Received:2016-07-11 Revised:2016-09-08 Online:2017-02-10 Published:2017-02-11
Supported by:
This work is partially supported by the Jiangsu Province Science and Technology Support Program (Industrial) Key Project (BE2013005-3).

摘要/Abstract

摘要： 针对属性值为犹豫模糊信息、属性权重和自然状态发生概率完全未知的多属性群决策问题，考虑决策者心理行为，提出一种基于后悔理论和证据理论的多属性群决策方法。首先，运用证据理论计算各自然状态发生的概率；然后，基于区间模糊矩阵、t-分布估计以及得分函数矩阵确定属性信息的效用值，进而依据后悔理论得到每个自然状态下的感知效用矩阵；通过加权算术平均得到综合感知效用矩阵，并依据方案综合感知效用的大小确定方案优劣排序；最后，将所提方法运用于对投资公司的选择实例中。实验结果表明，虽然所提方法与现有方法得到的决策结果相同，但是所提方法在决策过程中只需考虑较少数量的参数。对比分析实验表明，所提方法得到的决策结果合理、可靠，且能反映实际决策情况。

关键词: 犹豫模糊集, 后悔理论, 证据理论, 综合感知效用, 多属性群决策

Abstract: Under the hesitant fuzzy environment, considering the decision makers' psychological behavior, a method based on regret theory and evidence theory was proposed to cope with Multi-Attribute Group Decision Making (MAGDM) problems that the attribute value is hesitant fuzzy information, the attribute weights and probability information of situation are completely unknown. First, evidence theory was utilized to calculate the probability information of the states. Then, based on the interval fuzzy matrices, the estimation of t-distribution and the score function matrices, the utility values of attribute values were determined. Moreover, by using regret theory, the decision makers' perceived utility values were obtained. The overall perceived utility of each alternative was acquired on the basis of the weighted arithmetic mean. After that, all the alternatives were ordered. Finally, the proposed approach was applied to a numerical example about the selection of enterprise. The experimental results show that the proposed method can get the same results as the existing methods, but only a small number of parameters needed to be considersed in the decision process. The results of comparative analysis domonstrate that the decision making results obtained by the proposed method are reasonable and reliable, which can reflect the actual situation.

Key words: Hesitant Fuzzy Set (HFS), regret theory, evidence theory, overall perceived utility, multi-attribute group decision making

中图分类号:

TP273.4
O159

朱轮. 基于后悔理论和证据理论的犹豫模糊决策方法[J]. 计算机应用, 2017, 37(2): 540-545.

ZHU Lun. Hesitant fuzzy decision-making method based on regret theory and evidence theory[J]. Journal of Computer Applications, 2017, 37(2): 540-545.

参考文献

[1] 金飞飞,倪志伟.基于犹豫模糊偏好关系的雾霾影响因素评价[J].模式识别与人工智能,2015,28(9):839-847.(JIN F F, NI Z W. Factors evaluation of fog-haze weather based on hesitant fuzzy preference relations[J]. Pattern Recognition and Artificial Intelligence, 2015, 28(9):839-847.).
[2] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8(3):338-356.
[3] KACPRZYK J, ORLOVSKI S A. Optimization Models Using Fuzzy Sets and Possibility Theory[M]. Berlin:Springer, 1987:226-235.
[4] 汪峰,毛军军,黄超.基于熵和协相关度的直觉模糊多属性决策方法[J].计算机应用,2015,35(12):3456-3460. (WANG F, MAO J J, HUANG C. Multi-attribute decision-making method of intuitionistic fuzziness based on entropy and co-correlation degree[J]. Journal of Computer Applications, 2015, 35(12):3456-3460.).
[5] DUBOIS D J. Readings in Fuzzy Sets for Intelligent Systems[M]. San Francisco, CA:Morgan Kaufmann, 1993:137-143.
[6] TURKSEN I B. Interval valued fuzzy sets based on normal forms[J]. Fuzzy Sets and Systems, 1986, 20(2):191-210.
[7] ATANASSOV K T. Intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1986, 20(1):87-96.
[8] ATANASSOV K T, GARGOV G. Interval-valued intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1989, 31(3):343-349.
[9] TORRA V. Hesitant fuzzy sets[J]. International Journal of Intelligent Systems, 2010, 25(6):529-539.
[10] 朱丽,朱传喜,张小芝.基于前景理论的犹豫模糊风险型多属性决策方法[J].统计与决策,2014(17):68-71. (ZHU L, ZHU C X, ZHANG X Z. Hesitant fuzzy risky multi-attribute decision making method based on prospect theory[J]. Statistics & Decision, 2014(17):68-71.).
[11] 刘云志,樊治平.基于前景理论的具有指标期望的多指标决策方法[J].控制与决策,2015,30(1):91-97. (LIU Y Z, FAN Z P. Multiple attribute decision making considering attribute aspirations:a method based on prospect theory[J]. Control and Decision, 2015, 30(1):91-97.).
[12] LIU P, JIN F, ZHANG X, et al. Research on the multi-attribute decision-making under risk with interval probability based on prospect theory and the uncertain linguistic variables[J]. Knowledge-Based Systems, 2011, 24(4):554-561.
[13] 高建伟,刘慧晖,谷云东.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.(GAO W J, LIU H H, GU Y D. Interval-valued intuitionistic fuzzy multi-criteria decision-making method based on prospect theory[J]. Systems Engineering-Theory & Practice, 2014, 34(12):3175-3181.).
[14] 闫书丽,刘思峰,吴利丰.一种基于前景理论的三参数区间灰数型群体灰靶决策方法[J].控制与决策,2015,30(1):105-109. (YAN S L, LIU S F, WU L F. A group grey target decision making method with three parameter interval grey number based on prospect theory[J]. Control and Decision, 2015, 30(1):105-109.).
[15] BELL D E. Regret in decision making under uncertainty[J]. Operations Research, 1982, 30(5):961-981.
[16] LOOMES G, SUGDEN R. Regret theory:an alternative theory of rational choice under uncertainty[J]. The Economic Journal, 1982, 92(368):805-824.
[17] 张晓,樊治平,陈发动.基于后悔理论的风险型多属性决策方法[J].系统工程理论与实践,2013,33(9):2313-2320.(ZHANG X, FAN Z P, CHEN F D. Method for risky multiple attribute decision making based on regret theory[J]. Systems Engineering-Theory & Practice, 2013, 33(9):2313-2320.).
[18] 张晓,樊治平,陈发动.考虑后悔规避的风险型多属性决策方法[J].系统管理学报,2014,23(1):111-117. (ZHANG X, FAN Z P, CHEN F D. Risky multiple attribute decision making with regret aversion[J]. Journal of Systems & Engineering, 2014, 23(1):111-117.).
[19] 张世涛,朱建军,刘小弟.方案对多维偏好信息下基于后悔理论的群决策方法[J].中国管理科学,2014,22(Supp.):33-41. (ZHANG S T, ZHU J J, LIU X D. Group decision-making method based on regret theory under multidimensional preference information of pair-wise alternatives[J]. Chinese Journal of Management Science, 2014, 22(Supp.):33-41.).
[20] ZHOU H, WANG J-Q, ZHANG H-Y. Grey stochastic multi-criteria decision-making based on regret theory and TOPSIS[J]. International Journal of Machine Learning and Cybernetics, 2015, 7(33):1-14.
[21] 郭三党,刘思峰,方志耕.基于后悔理论的多目标灰靶决策方法[J].控制与决策,2015,30(9):1635-1640. (GUO S D, LIU S F, FAN Z G. Multi-objective grey target decision model based on regret theory[J]. Control and Decision, 2015, 30(9):1635-1640.).
[22] 袁媛,刘洋,樊治平.考虑后悔规避的突发事件应急响应的风险决策方法[J].系统工程理论与实践,2015,35(10):2630-2636.(YUAN Y, LIU Y, FAN Z P. Risk decision making method for emergency response considering regret aversion[J]. Systems Engineering-Theory & Practice, 2015, 35(10):2630-2636.).
[23] 马庆功.基于前景理论的犹豫模糊多属性群决策方法[J].计算机工程与应用,2015,51(24):249-253. (MA Q G. Hesitant fuzzy multi-attribute group decision-making method based on prospect theory[J]. Computer Engineering and Applications, 2015, 51(24):249-253.).
[24] XIA M M, XU Z S. Hesitant fuzzy information aggregation in decision making[J]. International Journal of Approximate Reasoning, 2011, 52(3):395-407.
[25] QUIGGIN J. Regret theory with general choice sets[J]. Journal of Risk and Uncertainty, 1994, 8(2):153-165.
[26] 杜元伟,石方园,杨娜.基于证据理论/层次分析法的贝叶斯网络建模方法[J].计算机应用,2015,35(1):140-146.(DU Y W, SHI F Y, YANG N. Construction method for Bayesian network based on Dempster-Shafer/analytic hierarchy process[J]. Journal of Computer Applications, 2015, 35(1):140-146.).
[27] 阮闪闪,王小平,薛小平.基于证据理论信任模型的众包质量监控[J].计算机应用,2015,35(8):2380-2385.(RUAN S S, WANG X P, XUE X P. Crowdsourcing quality control based on reputation model of Dempster-Shafer theory[J]. Journal of Computer Applications, 2015, 35(8):2380-2385.).
[28] SMETS P, KENNES R. The transferable belief model[J]. Artificial Intelligence, 1994, 66(2):191-234.

基于后悔理论和证据理论的犹豫模糊决策方法

Hesitant fuzzy decision-making method based on regret theory and evidence theory

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