(语言)Heronian平均算子及其决策应用

doi:10.16381/j.cnki.issn1003-207x.2017.04.021

摘要/Abstract

摘要： 多属性决策中的许多集成算子假设属性相互独立，从而导致信息集成和决策结果出现不合理的情况。Heronian平均算子是一种体现属性间相互作用的集成算子，因此研究和推广Heronian平均算子具有重要的理论和现实意义。首先，针对相关文献中的加权Heronian平均算子不具有还原性，定义了一种具有还原性的广义加权Heronian平均算子（GWHM），随后定义了三参量Heronian平均算子（TPHM）和三参量加权Heronian平均算子（TPWHM），并分别研究了它们的幂等性、单调性和有界性等性质。然后，将GWHM算子、TPHM算子和TPWHM算子分别推广到语言决策中，给出了语言加权Heronian平均算子（LWHM）以及三参量语言Heronian平均算子（TPLHM）和三参量语言加权Heronian平均算子（TPLWHM），并对它们的性质进行了探讨。最后，给出了利用（语言）Heronian平均算子进行决策的方法，并通过两个实例说明了方法的可行性。

关键词: 集成算子, Heronian平均算子, 语言Heronian平均算子, 决策

Abstract: In information aggregation of multiple attribute decision making, some aggregation operators are defined based on the hypothesis in which all the attributes are mutually indenpent, resulting in unreasonable information aggregation and decision result. Heronian mean operator is an aggregation opeator in which can deal with the situation of interrelationshiop between attributes, and from the theoretical and and practical points of view, it is worth to study and generalize Heronian mean operator. Firstly, aiming at weighted Heronian mean operator without reducibility in related reference, the generalized weighted Heronian mean operator(GWHM) with reducibility is introduced. And then, the three parameters Heronian mean operator(TPHM) and the three parameters weighted Heronian mean operator(TPWHM) are defined, and their basic properties such as idempotency, monotonicity and boundness are studied. Further, in order to fulfill applications of Heronian mean operator in linguistic multiple attribute decision making, linguistic weighted Heronian mean operator(LWHM), three parameters linguisitic Heronian mean operator(TPLWHM) and three parameters linguisitic weighted Heronian mean operator(TPLHM) are dedined, and their properties such as idempotency, monotonicity and boundness are also discussed. Finally, an approach to multiple attribute decision making based on the (linguisitic) Heronian mean operators is proposed, and two practical examples are given to illustrate our results.

Key words: aggregation operator, Heronian mean operator, linguistic Heronian mean operator, decision making

中图分类号:

C934

刘卫锋, 常娟, 杜迎雪. (语言)Heronian平均算子及其决策应用[J]. 中国管理科学, 2017, 25(4): 174-183.

LIU Wei-feng, CHANG Juan, DU Ying-xue. (Linguistic) Heronian Mean Operators and Applications in Decision Making[J]. Chinese Journal of Management Science, 2017, 25(4): 174-183.

参考文献

[1] Harasnyi J C.Cardinal welfare,individualistic ethics,and interpersonal comparisons of utility[J]. Journal of Political Economy,1955,63(4):309-321.

[2] Aczel J, Alsina C. Synthesizing judgement:A functional equation approach[J]. Mathematical Modelling, 1987,9(3-5):311-320.

[3] 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.

[4] Herrera F, Herrera Viedma, Chiclana F. Multiperson decision-making based on multiplicative preference relations[J]. European Journal of Operational Research, 2001,129(2):372-385.

[5] 陈华友,刘春林,盛昭瀚. IOWHA算子及其在组合预测中的应用[J].中国管理科学,2004,12(5):35-40.

[6] Fodor J, Marichal J L, Roubens M. Characterization of the ordered weighted averaging operators[J]. IEEE Transactions on Fuzzy Systems, 1995, 3(2):236-240.

[7] Bonferroni C. Sulle medie multiple di potenze[J]. Bolletino Matematica Italiana,1950,5(3):267-270.

[8] Beliakov G,Pradera A, Calvo T. Aggregation functions:A guide for practitioners[M]. Berlin:Springer,2007.

[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] Beliakov G, James S, Mordelva J,et al. Generalized Bonferroni mean operators in multi-criteria aggregation[J]. Fuzzy Sets and Systems,2010,161(17):2227-2242.

[11] Xia Meimei, Xu Zeshui, Zhu Bin. Generalized intuitionistic fuzzy Bonferroni means[J]. International Journal of Intelligent Systems,2012, 27(1):23-47.

[12] Zhou Wei, He Jianmin. Intuitionistic fuzzy geometric Bonferroni means and their application in multicriteria decision making[J]. International Journal of Intelligent Systems,2012,27(12):995-1019.

[13] Xia Meimei, Xu Zeshui, Zhu Bin. Geometric Bonferroni means with their application in multi-criteria decision making[J]. Knowledge-Based Systems, 2013,40:88-100.

[14] 刘焕章,裴道武.H-OWA算子及其在多属性决策中的应用[J].浙江理工大学学报.2012,29(1):138-142.

[15] Yu Dejian. Intuitionistic fuzzy geometric Heronian mean aggregation operators[J]. Applied Soft Computing, 2013,13(2):1235-1246.

[16] Xu Zeshui,Da Qingli.The uncertain OWA operator[J]. International Journal of Intelligent Systems,2002,17(6):569-575.

[17] Xu Zeshui,Da Qingli.An uncertain ordered weighted geometric(UOWG) operator and its application[J]. Information,2004,7(2):175-182.

[18] Yager R R. OWA aggregation over a continuous interval argument with applications to decision making[J].IEEE Transactions on Systems, Man, and Cybernetics,Part B:Cybernetics,2004,34(5):1952-1963.

[19] Yager R R, Xu Zeshui. The continuous ordered weighted geometric operator and its application to decision making[J].Fuzzy Sets and Systems,2006,157(10):1393-1402.

[20] 徐泽水.拓展的C-OWA算子及其在不确定多属性决策中的应用[J].系统工程理论与实践,2005,25(11):7-13.

[21] 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.

[22] 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.

[23] 王东晓,李自强,刘卫锋.区间数Heronian平均算子[J].数学的实践与认识,2015,45(21):274-281.

[24] Xu Zeshui. Uncertain Bonferroni mean operators[J]. International Journal of Computational Intelligence Systems,2010,3(6):761-769.

[25] Bellman R E,Zadeh L A.Decision-making in a fuzzy environment[J]. Management Science,1970,17(4):B141-B164.

[26] 徐泽水.基于FOWA算子的三角模糊数互补判断矩阵排序法[J].系统工程理论与实践,2003,23(10):86-89.

[27] 王欣荣,樊治平.一种有序加权(FOWA)算子及其应用[J].模糊系统与数学,2003,17(4):67-72.

[28] 徐泽水.一种FOWG算子及其在模糊AHP中的应用[J].系统工程与电子技术,2002,24(7):31-33.

[29] 许叶军,达庆利.TFOWA算子及其在决策中的应用[J].东南大学学报(自然科学版),2006,36(6):1034-1038.

[30] 刘金培,林盛,陈华友.模糊Bonferroni平均算子及在多准则群决策中的应用[J].系统工程与电子技术, 2012,34(1):115-119.

[31] Xu Zeshui. Intuitionistic preference realtions and their application in group decision making[J].Information Science,2007,177(11):2363-2379.

[32] Xu Zeshui. Intuitionistic fuzzy aggregation operator[J]. IEEE Transactios on Fuzzy Systems,2007,15(6):1179-1187.

[33] Xu Zeshui, Yager R R. Some geometric aggragation operators based on intuitionistic fuzzy sets[J]. International Journal of General System,2006,35(4):417-433.

[34] 徐泽水.区间直觉模糊信息的集成方法及其在决策中的应用[J].控制与决策,2007,22(2):215-219.

[35] Xu Zeshui, Yager R R. Intuitionistic fuzzy Bonferroni means[J].IEEE Transactions on Systems,Man and, Cybernetics-Part B:Cybernetics,2011,41(2):568-578.

[36] Xu Zeshui, Chen Qi. A multi-criteria decision making procedure based on interval-valued intuitionistic fuzzy Bonferroni means[J].Journal of Systems Science and Systmes Engineering,2011,20(2):217-228.

[37] Yu Dejian, Wu Yingyu. Interval-valued intuitionistic fuzzy Heronian mean operators and their application in multi-criteria decision making[J].African Journal of Business Management. 2012,6(11):4158-4168.

[38] Torra V. Hesitant fuzzy sets[J]. International Journal of Intelligent Systems,2012,25(6):529-539.

[39] Zhang Zhiming. Hesitant fuzzy power aggregaton operators and their application to multiple group decision making[J]. Information Science,2013,234:150-181.

[40] Wang Weize, Liu Xinwang. Some hesitant fuzzy geometric operators and their application to multiple attribute group decision making[J]. Technological and Economic Development of Economy,2014,20(3):371-390.

[41] Zhu Bin,Xu Zeshui, Xia Meimei. Hesitant fuzzy geometric Bonferroni means[J]. Information Sciences,2012,205:72-85.

[42] Yu Dejian, Wu Yingyu, Zhou Wei. Generalized hesitant fuzzy Bonferroni mean and its application in multi-criteria group decision making[J]. Journal of Information and Computational Science,2012,9(2):267-274.

[43] Zhu Bin,Xu Zeshui. Hesitant fuzzy Bonferroni means for multi-criteria decision making[J]. Journal of the Operational Research Society,2013,64(12):1831-1840.

[44] Bedregal B, Reiser R, Bustince H, et al. Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms[J]. Information Sciences, 2014,255:82-99.

[45] Bordogna G, Fedrizzi M, Passi G. A linguistic modeling of consensus in group decision making on OWA operator[J]. IEEE Transactions on Systems, Man, and Cybernetics,Part A:Systems and Humans,1997,27(1):126-132.

[46] 戴跃强,徐泽水,李琰,等.语言信息评估新标度及其应用[J].中国管理科学,2008,16(2):145-149.

[47] Xu Zeshui. EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations[J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,2004,12(6):791-810.

[48] Torra V. The weighted OWA operator[J]. International Journal of Intelligent Systems, 1997, 12(2):153-166.

[49] Xu Zeshui. On generalized induced linguistic aggregation operators[J]. International Journal of General Systems, 2006,35(1):17-28.

[50] Xu Zeshui. Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment[J]. Information Sciences,2004,168(1-4):171-184.

[51] Xu Zeshui. Induced uncertain linguistic OWA operators applied to group decision making[J]. Information Fusion,2006,7(2):231-238.

[52] Liu Xiaodi, Zhu Jianjun,Liu Guoding, et al. A multiple attribute decision making method based on uncertain linguistic Heronian mean[J]. Mathematics Problems in Engineering, 2013,2013:1-11.

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

[54] 彭勃,叶春明.基于不确定纯语言混合调和平均算子的多属性群决策方法[J]. 中国管理科学,2015,23(2):131-138.

[55] 王坚强,吴建文.基于区间灰色不确定语言的多准则决策方法[J].中国管理科学,2010,18(3):107-111.

[56] Liu Peide, Liu Zhengmin, Zhang Xin. Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making[J]. Applied Mathematics and Computation,2014,230:570-586.

[57] 刘家学.带有方案偏好信息的多指标决策法[J].系统工程与电子技术,1999,21(1):4-7.

[58] 徐泽水.语言多属性决策的目标规划模型[J].管理科学学报,2006,9(2):9-17.