Twotuple Iinguistic Bonferroni Aggregation Operators and Their Applications to Multi-attribute Group Decision-making

Operations Research and Management Science ›› 2013, Vol. 22 ›› Issue (5): 122-127.

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Twotuple Iinguistic Bonferroni Aggregation Operators and Their Applications to Multi-attribute Group Decision-making

LIU Jin-pei^1,2, LIN Sheng², CHEN Hua-you³

1. School of Business, Anhui University, Hefei 230601, China;
2. College of Management and Economics, Tianjin University, Tianjin 300072, China;
3. School of Mathematical Science, Anhui University, Hefei 230601, China

Received:2012-08-27 Online:2013-10-25

二元语义Bonferroni集成算子及其在多属性群决策中的应用

刘金培¹, 林盛², 陈华友³

1.安徽大学商学院, 安徽合肥 230601;
2.天津大学管理与经济学部, 天津 300072;
3.安徽大学数学科学学院, 安徽合肥 230601

作者简介:刘金培 (1984-),男,山东滨州人,博士,讲师,研究方向:预测与决策分析;林盛(1964-),男,天津市人,博士,教授,博士生导师,研究方向:预测与决策分析。
基金资助:
国家自然科学基金资助项目(71371011,71301001);教育部人文社会科学研究青年基金资助项目(13YJC630092);教育部高等学校博士点基金基金资助项目(20123401110001);留学回国人员科研启动项目,安徽省自然科学基金资助项目(1308085QG127);安徽省高校省级自然科学研究重点项目(KJ2012A026);安徽省教育厅人文社科项目(SK2013B041)

Abstract

Abstract: The advantage of the Bonferroni mean operator is its capability to capture the interrelationship between input arguments. In this paper, we extend the Bonferroni mean operators to the situation where the inputs are linguistic arguments and proposed 2-tuple linguistic Bonferroni averaging(2TLBA)operator, weighted 2TLBA(W2TLBA)operator and combined W2TLBA(C-W2TLBA)operator. Moreover, some desirable properties and special cases of these aggregation operators are investigated. According to the multi-attribute group decision-making with the decision information being linguistic arguments, a decision-making approach is presented based on W2TLBA operator and C-W2TLBA operator. At last, a numerical experiment is given to prove the feasibility of the developed approach.

Key words: multi-attribute group decision-making, 2-tuple linguistic Bonferroni averaging(2TLBA)operator, weighted 2TLBA(W2TLBA)operator, combined W2TLBA(C-W2TLBA)operator

摘要： Bonferroni平均算子的优点是在进行信息集成的过程中能够考虑到输入变量之间的相互影响。本文首先将其推广到语言环境中,提出了二元语义Bonferroni平均(2TLBA)算子、加权2TLBA(W2TLBA)算子和组合W2TLBA(C-W2TLBA)算子的概念,研究它们的相关性质。然后针对决策信息以语言变量给出的多属性群决策问题,提出一种基于W2TLBA算子和C-W2TLBA算子的群决策方法。最后应用实例说明了该方法是切实可行的。

关键词: 多属性群决策, 二元语义Bonferroni平均(2TLBA)算子, 加权2TLBA(W2TLBA)算子, 组合W2TLBA(C-W2TLBA)算子

CLC Number:

C934

LIU Jin-pei, LIN Sheng, CHEN Hua-you. Twotuple Iinguistic Bonferroni Aggregation Operators and Their Applications to Multi-attribute Group Decision-making[J]. Operations Research and Management Science, 2013, 22(5): 122-127.

刘金培, 林盛, 陈华友. 二元语义Bonferroni集成算子及其在多属性群决策中的应用[J]. 运筹与管理, 2013, 22(5): 122-127.

References

[1] 徐泽水.不确定多属性决策方法与应用[M].北京:清华大学出版社,2005.
[2] Herrera F, Martinez L. A 2-Tuple fuzzy linguistic representation model for computing with words[J]. IEEE Transactions on Fuzzy Systems, 2000, 8(6): 746-752.
[3] Xu Y J, Wang H M. Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment[J]. Applied Soft Computing, 2011, 11(5): 3988-3997.
[4] Herrera F, Herrera-Viedma E. Aggregation operators for linguistic weighted information[J]. IEEE Transactions on Systems, Man, and Cybernetics-part A: Systems and Humans, 1997, 20(5): 646-656.
[5] Torra V. The weighted OWA operator[J]. International Journal of Intelligent Systems, 1997, 12(2): 153-166.
[6] Xu Z S. A method based on linguistic aggregation operators for group decision making with linguistic preference relations[J]. Information Sciences, 2004, 166(1): 19-30.
[7] Xu Z S. Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment[J]. Information Sciences, 2004, 168(1): 171-184.
[8] 姜艳萍,樊治平.基于不同粒度语言判断矩阵的群决策方法[J].系统工程学报,2006,21(3):249-253.
[9] Yager R R. On generalized Bonferroni mean operators for multi-criteria aggregation[J]. International Journal of Approximate Reasoning, 2009, 50(8): 1279-1286.
[10] Xu Z S. Uncertain Bonferroni mean operators[J]. International Journal of Computational Intelligence Systems, 2010, 3(6): 761-769.
[11] Xu Z S. Intuitionistic fuzzy bonferroni means[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 2011, 41(2): 568-578.
[12] Yager R R. On ordered weighted averaging aggregation operators in multicriteria decision making[J]. IEEE Transactions on Systems, Man, and Cybernetics, 1988, 18(1): 183-190.
[13] Beliakov G, James S, Modelová J, Rückschlossová T, Yager R R. Generalized bonferroni mean operators in multi-criteria aggregation[J]. Fuzzy Sets and Systems, 2010, 161(17): 2227-2242.

Twotuple Iinguistic Bonferroni Aggregation Operators and Their Applications to Multi-attribute Group Decision-making

二元语义Bonferroni集成算子及其在多属性群决策中的应用

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