方案有不确定偏好的区间数相对熵群决策方法

中国管理科学 ›› 2014, Vol. 22 ›› Issue (6): 134-140.

方案有不确定偏好的区间数相对熵群决策方法

刘小弟^1,2, 朱建军¹, 刘思峰¹

1. 南京航空航天大学经济与管理学院, 江苏南京 211106;
2. 安徽工业大学数理学院, 安徽马鞍山 243002

收稿日期:2012-10-26 修回日期:2013-03-25 出版日期:2014-06-20 发布日期:2014-06-26
作者简介:刘小弟（1981- ），男（汉族），安徽合肥人，南京航空航天大学经济与管理学院，讲师，博士，研究方向：多属性决策、复杂系统建模等.
基金资助:
国家自然科学基金资助项目（71171112）；江苏省高校哲学社会科学重点项目（2012ZDIXM007）；江苏省高校哲学社会科学重点研究基地重大项目（2012JDXM003）；中央高校基本科研业务费专项资金（NS2014086）；江苏省普通高校研究生科研创新计划项目（CXLX13_171）；广义虚拟经济研究专项（GX2013-1017CM）；安徽工业大学青年教师科研基金资助课题（QZ201321）

Group Decision-Making Method with Uncertain Preference Information on Alternatives by Interval Number Relative Entropy

LIU Xiao-di^1,2, ZHU Jian-jun¹, LIU Si-feng¹

1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;
2. School of Mathematics and Physics, Anhui University of Technology, Ma'anshan 243002, China

Received:2012-10-26 Revised:2013-03-25 Online:2014-06-20 Published:2014-06-26

摘要/Abstract

摘要： 研究了属性值是区间数并且已知方案偏好信息的多属性群决策问题。建立了每个方案客观偏好值与主观偏好值偏差的相对熵测度矩阵；基于客观信息和方案偏好信息的相对熵建立了属性权重模型；建立了一个新的区间数比较的可能度公式，基于可能度公式给出了方案排序方法，算例说明方法可行性。

关键词: 群决策, 区间数, 相对熵, 可能度

Abstract: The problem of multiple attribute group decision making with interval numbers and preference information on alternatives is studied in this paper. Firstly,he relative entropy matrix for the deviation between objective preference and subjective preference value on each alternative is obtained. Then a mathematical model based on the relative entropy of objective and preference information on alternatives is constructed to obtain the attribute weights. Furthermore,a new probability degree formula for the comparison between two interval numbers is presented. Based on the formula, a method for ranking alternatives is given. Finally, a numerical example is given to verify the proposed method and to demonstrate its feasibility.

Key words: group decision-making, interval number, relative entropy, probability degree

中图分类号:

C934

刘小弟, 朱建军, 刘思峰. 方案有不确定偏好的区间数相对熵群决策方法[J]. 中国管理科学, 2014, 22(6): 134-140.

LIU Xiao-di, ZHU Jian-jun, LIU Si-feng. Group Decision-Making Method with Uncertain Preference Information on Alternatives by Interval Number Relative Entropy[J]. Chinese Journal of Management Science, 2014, 22(6): 134-140.

参考文献

[1] 朱建军. 群决策信息分析及集结模型研究[M]. 北京:科学出版社, 2012.

[2] 卫贵武. 基于模糊信息的多属性决策理论与方法[M]. 北京:中国经济出版社, 2010.

[3] 徐泽水. 不确定多属性决策方法及应用[M]. 北京:清华大学出版社, 2004.

[4] 刘健, 刘思峰. 属性值为区间数的多属性决策对象排序研究[J]. 中国管理科学, 2010, 18(3): 90-94.

[5] Jiang C, Han X, Liu G R, et al. A nonlinear interval number programming method for uncertain optimization problems[J]. Europearn Journal of Operational Research, 2008, 188(1): 1-13.

[6] Sayadi M K, Heydari M, Shahanaghi K. Extention of VIKOR method for decision making problem with interval numbers[J]. Applied Mathematical Modelling, 2009, 33(5): 2257-2262.

[7] Chen S M,Sanguansat K. Analyzing fuzzy risk based on similarity measures between interval-valued fuzzy numbers[J]. Computers & Mathematics with Applications,2008,55(8):1670-1685.

[8] Kuo M S, Liang G S.A soft computing method of performance evaluation with MCDM based on interval-valued fuzzy numbers[J]. Applied soft computing, 2012, 12(1): 476-485.

[9] Facchinetti G, Ricci R G, Muzzioli S. Note on ranking fuzzy triangular numbers [J]. International Journal of Intelligent Systems, 1998, 13(7): 613-622.

[10] 达庆利, 刘新旺. 区间数线性规划及其满意解[J]. 系统工程理论与实践, 1999, 19(4): 3-7.

[11] 徐泽水, 达庆利. 区间数排序的可能度法及其应用[J]. 系统工程学报, 2003, 18(1): 67-70.

[12] 张全, 樊治平, 潘德惠. 不确定多属性决策中区间数的一种排序方法[J].系统工程理论与实践, 1999, 19(5): 129-133.

[13] Kunda S. Min-transitivity of fuzzy leftness relationship and its application to decision making[J]. Fuzzy Sets and Systems, 1997, 86(3): 357-367.

[14] Sengupta A, Pal TK. On comparing interval numbers[J]. European Journal of Operational Research, 2000, 127(1): 28-43.

[15] Wang Yingming, Yang Jianbo, Xu Dongling. A preference aggregation method through the estimation of utility intervals [J]. Computers & operations research, 2005, 32(8): 2027-2049.

[16] Fan Zhiping, Ma Jian, Zhang Quan. An approach to multiple attribute decision making based on fuzzy preference information on alternatives[J]. Fuzzy Sets and Systems,2002, 131(1): 101-106.

[17] Xu Zeshui,Da Q L. Prejection method for uncertain multi-attribute decision making with preference information on alternatives[J]. International Journal of Information Technology & Decision Making,2004, 3(3): 429-434.

[18] 徐泽水. 求解不确定型多属性决策问题的一种新方法[J]. 系统工程学报, 2002, 17(2): 177-181.

[19] 徐泽水. 部分权重信息下对方案有偏好的多属性决策法[J]. 控制与决策, 2004, 19(1): 85-88.

[20] 徐泽水. 对方案有偏好的三角模糊数型多属性决策方法研究[J]. 系统工程与电子技术, 2002, 24(8): 9-12.

[21] 徐泽水. 权重信息完全未知且对方案有偏好的多属性决策法[J]. 系统工程理论与实践, 2003, 23(12): 100-103.

[22] 刘树林, 汪寿阳. 一个已知方案偏好信息的多属性决策新方法[J].系统工程理论与实践, 1999, 19(4): 12-15.

[23] 卫贵武, 魏宇. 对方案有偏好的区间数多属性灰色关联决策模型[J]. 中国管理科学, 2008, 16(1): 158-162.

[24] 刘於勋, 沈轶, 谢妞妞. 基于梯形模糊数期望值的多维偏好群决策模型[J]. 控制与决策, 2009, 24(9): 1377-1340.

[25] Xu Zheshui. Multiple attribute group decision making with different formats of preference information on attributes[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B, 2007, 37(6):1500-1511.

[26] Xu Zheshui, Chen Jian. MAGDM linear programming models with distinct uncertain preference structures[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B, 2008, 38(5):1356-1370.

[27] 邱菀华. 管理决策与应用熵学[M]. 北京: 机械工业出版社, 2001.

[28] Andrew E B, Lim J, Shanthikumar G. Relative entropy, exponential utility, and robust dynamic pricing[J].Operations Research,2007, 55(2), 198-214.

[29] Chen Huayou, Zhou Ligang. A relative entropy approach to group decision making with interval reciprocal relations based on COWA operator[J].Group Decision and Negotiation, 2012, 21(4): 585-599.

[30] Lai J, Ford J. Relative entropy rate based multiple hidden markov model approximation[J].IEEE Transactions on signal process, 2010, 58(1): 165-174.

[31] 吕跃进, 程宏涛, 覃菊莹. 基于相对熵的互补判断矩阵排序方法[J]. 系统工程理论与实践, 2011, 31(7): 1328-1333.

[32] 赵萌, 邱菀华, 刘北上. 基于相对熵的多属性决策排序方法[J]. 控制与决策, 2010, 25(7): 1098-1011.

[33] 赵萌, 邱菀华, 何大义. 区间型多属性决策的相对熵排序法[J].系统工程,2010, 28(8): 70-74.

[34] Xu Ruoning, Zhai Xiaoyan. Extensions of the analytic hierarchy process in fuzzy environment[J]. Fuzzy Sets and Systems, 1992. 52(3): 251-257.

[35] Xu Zeshui, Chen Jian. Some models for deriving the priority weights from interval fuzzy preference relations[J]. European Journal of Operational Research, 2008, 184(1): 266-280.