一种具有不确定偏好序信息的多指标群决策方法

中国管理科学 ›› 2013, Vol. 21 ›› Issue (5): 110-114.

一种具有不确定偏好序信息的多指标群决策方法

尤天慧¹, 李洪燕¹, 刘彩娜²

1. 东北大学工商管理学院, 辽宁沈阳 110819;
2. 石家庄工商职业学院, 河北石家庄 050091

收稿日期:2011-11-24 修回日期:2013-05-02 出版日期:2013-10-30 发布日期:2013-10-15
基金资助:
国家自然科学基金资助项目(71271049,71101021,71171043);教育部人文社会科学研究规划基金资助项目(11YJA630180)

A Method for Multiple Criteria Group Decision Making with Uncertain Preference Ordinals

YOU Tian-hui¹, LI Hong-yan¹, LIU Cai-na²

1. School of Business Administration, Northeastern University, Shenyang 110819, China;
2. Shijiazhuang Vocational College of Industry and Commerce, Shijiazhuang 050091, China

Received:2011-11-24 Revised:2013-05-02 Online:2013-10-30 Published:2013-10-15

摘要/Abstract

摘要： 针对具有不确定偏好序信息的多指标群决策问题,给出了一种决策分析方法。在本文中,首先对具有不确定偏好序信息的多指标群决策问题进行了描述;然后给出了将不确定偏好序转换为投票数的计算公式;进一步地,依据Bernardo方法的基本思想,根据每个专家给出的不确定偏好序信息,计算相应的投票数并构建群体投票矩阵,并基于群体投票矩阵构建0-1整数规划模型,通过求解模型可得到方案排序结果。最后,通过一个算例以及与已有方法的对比分析说明了本文给出的方法的可行性和有效性。

关键词: 多指标群决策, 不确定偏好序, Bernardo方法, 权重, 方案排序

Abstract: A method to solve the multiple criteria group decision making (MCGDM) problem with uncertain preference ordinals is proposed, in this paper. The MCGDM problem with uncertain preference ordinals is described first, and then the calculation formula for votes transformed from uncertain preference ordinals is given. Furthermore, according to the fundamental idea of Bernardo method, the corresponding votes are calculated and the group voting matrix is constructed based on the the uncertain preference ordinals given by expers. An 0-1 integer programming model is built based on the group voting matrix and the alternatives can be ranked by solving the model. At last, though a numerical study and comparatively analysis with previous method, the proposed method is proved to be feasible and effective.

Key words: multiple criteria group decision making (MCGDM), uncertain preference ordinal, Bernardo method, weight, ranking of alternative

中图分类号:

N945.25
C934

尤天慧, 李洪燕, 刘彩娜. 一种具有不确定偏好序信息的多指标群决策方法[J]. 中国管理科学, 2013, 21(5): 110-114.

YOU Tian-hui, LI Hong-yan, LIU Cai-na. A Method for Multiple Criteria Group Decision Making with Uncertain Preference Ordinals[J]. Chinese Journal of Management Science, 2013, 21(5): 110-114.

参考文献

[1] Hwang C L, Yoon K. Multiple attribute decision making: methods and applications [M]. New York: Springer-Verlag, 1981.
[2] Hwang C L, Lin M J. Group decision making under multiple criteria: methods and applications [M]. Berlin: Springer-Verlag, 1987.
[3] 相辉. 语言型时序多属性群决策方法及在服务创新中的应用 [J]. 运筹与管理, 2009, 18(4): 44-49.
[4] Chuu S J. Selecting the advanced manufacturing technology using fuzzy multiple attributes group decision making with multiple fuzzy information [J]. Computers & Industrial Engineering, 2009, 57(3): 1033-1042.
[5] 梁昌勇, 张恩桥, 戚筱雯, 等. 一种评价信息不完全的混合型多属性群决策方法[J]. 中国管理科学, 2009, 17(4): 126-132.
[6] Gonzále-Pachón J, Romero C. Aggregation of partial ordinal rankings: an interval goal programming approach [J]. Computers & Operations Research, 2001, 28(8): 827-834.
[7] González-Pachón J, Rodríguez-Galiano M I, Romero C. Transitive approximation to pairwise comparison matrices by using interval goal programming [J]. Journal of Operational Research Society, 2003, 54(5): 532-538.
[8] 尤天慧, 樊治平, 俞竹超. 一种具有序区间偏好信息的群决策方法[J]. 东北大学学报(自然科学版), 2007, 28(2): 286-288.
[9] 樊治平, 尤天慧. 求解序区间偏好信息群决策问题的理想点法[J]. 东北大学学报(自然科学版), 2007, 28(12): 1779-1781.
[10] 樊治平, 刘洋, 孙永洪. 一种具有序区间排序信息的多目标指派方法[J]. 工业工程与管理, 2008, 13(3): 42-45.
[11] Fan Zhiping, Liu Yang. An approach to solve group-decision-making problems with ordinal interval numbers [J]. IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics, 2010, 40(5): 1413-1423.
[12] Fan Zhiping, Yue Qi, Feng Bo, et al. An approach to group decision-making with uncertain preference ordinals [J]. Computers & Industrial Engineering, 2010, 58(1): 51-57.
[13] 陈侠, 樊治平. 一种基于序区间偏好信息的群决策分析方法[J]. 运筹与管理, 2010, 19(4): 63-67.
[14] 乐琦, 樊治平. 一种具有不确定偏好序评价信息的群决策方法[J]. 运筹与管理, 2010, 19(6): 39-44.
[15] You Tianhui, Fan Zhiping, Yu Zhuchao.An assignment method for group decision making with uncertain preference ordinals [J]. Journal of Systems Science and Systems Engineering, 2012, 21(2): 174-183.
[16] Bernardo J J. An assignment approach to choosing R&D experiments [J]. Decision Science, 1977, 8(2): 489-501.