考虑边际效用的二元语言术语集新算法及其应用
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摘要
二元语言术语集是表达不确定环境下决策信息的重要工具,然而,已有的二元语言术语集的运算法则往往不能保证计算结果仍在语言范围之内。本文通过定义新的转换函数并结合Einstein运算,提出了二元语言术语集的新算法。新算法有效解决了以往运算法则中计算结果超出语言范围的问题,新算法同时也考虑了决策者的决策评判心理边际效用递减现象。在此基础上提出了二元语言术语集的多属性信息聚合算子和相应的多属性决策方法,并通过供应商选择案例验证了该算法的有效性。
2-tuple language term sets are important tools for expressing decision information in uncertain environments.However,the existing algorithms for 2-tuple language term sets often cannot ensure that the calculation results are still within the language range.This paper proposes a new algorithm by defining a new transformation function and combining Einstein operations.The new algorithm effectively solves the problem that the calculation result exceeds the linguistic range in the previous algorithm.The new algorithm also considers the phenomenon of decision-making maker's decision-making psychological marginal utility decreases.On this basis,the multi-attribute information aggregation operators and the corresponding multi-attribute decision-making method of binary language term set are proposed,and the effectiveness of the algorithm is verified by the supplier selection case.
2-tuple language term sets are important tools for expressing decision information in uncertain environments.However,the existing algorithms for 2-tuple language term sets often cannot ensure that the calculation results are still within the language range.This paper proposes a new algorithm by defining a new transformation function and combining Einstein operations.The new algorithm effectively solves the problem that the calculation result exceeds the linguistic range in the previous algorithm.The new algorithm also considers the phenomenon of decision-making maker's decision-making psychological marginal utility decreases.On this basis,the multi-attribute information aggregation operators and the corresponding multi-attribute decision-making method of binary language term set are proposed,and the effectiveness of the algorithm is verified by the supplier selection case.
引文
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[12] NIE R X,WANG J Q,LI L.A shareholder voting method for proxy advisory firm selection based on 2-tuple linguistic picture preference relation[J].Appl Soft Comput,2017,60:520-539.
[13] LIU P,CHEN S M.Multiattribute group decision making based on intuitionistic 2-tuple linguistic information[J].Informa Sciences,2018,430:599-619.
[14] XU Z.Uncertain Multi-attribute decision making methods and applications[M].Lodon:Springer,2015.
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[16] GOU X,XU Z.Novel basic operational laws for linguistic terms,hesitant fuzzy linguistic term sets and probabilistic linguistic term sets[J].Informa Sciences,2016,372:407-427.
[17] 张慧,焦志敏,李伯权.区间直觉二元语言集成算子及其群决策方法[J].计算机工程与应用,2016,52(24):43-49.
[18] CHERNEY D,LATINI E,WALDRON A.Generalized Einstein operator generating functions [J].Physics Letters B,2010,682(4–5):472-475.
[19] WANG W,LIU X.Intuitionistic fuzzy geometric aggregation operators based on Einstein operations[J].Int J Intell Syst,2011,26(11):1049–1075.
[20] WANG W,LIU X.Intuitionistic fuzzy information aggregation using Einstein operations[J].IEEE T Fuzzy Syst,2012,20(5):923-938.
[21] ZHAO X,WEI G.Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making[J].Knowl-Based Syst,2013,37(2):472-479.
[2] TORRA V.Hesitant fuzzy sets[J].Int J Intell Syst,2010,25(6):529-539.
[3] ATANASSOV K T.Intuitionistic fuzzy sets[J].Fuzzy Set Syst,2012,20(1):87-96.
[4] 黄先玖,朱传喜,陈春芳.概率OWG算子及其在多属性决策中的应用[J].南昌大学学报(理科版),2010,34(1):12-15.
[5] 陈春芳,朱传喜,余克弟.WC-OWA算子的拓展及其在风险型多属性决策中的应用[J].南昌大学学报(理科版),2011,35(4):318-322.
[6] HERRERA F,HERRERA-VIEDMA E,MARTINEZ L.A fusion approach for managing multi-granularity linguistic term sets in decision making[J].Fuzzy Set Syst,2000,114(1):43-58.
[7] 顾亚琼,陈春芳,李广津.语言信息下基于占优关联系数的群决策模型[J].南昌大学学报(理科版),2017,41(3):205-210.
[8] XU Z.Deviation measures of linguistic preference relations in group decision making[J].Omega,2005,33(3):249-254.
[9] MARTINEZ L,HERRARE F.An overview on the 2-tuple linguistic model for computing with words in decision making:Extensions,applications and challenges[J].Informa Sciences,2012,207(1):1-18.
[10] HERRERA F,MARTINEZ L.A 2-tuple fuzzy linguistic representation model for computing with words[J].IEEE T Fuzzy Syst,2000,8(6):746-752.
[11] MERIGO J M,GILl-LAFUENTE A M.Induced 2-tuple linguistic generalized aggregation operators and their application in decision-making[J].Informa Sciences,2013,236:1-16.
[12] NIE R X,WANG J Q,LI L.A shareholder voting method for proxy advisory firm selection based on 2-tuple linguistic picture preference relation[J].Appl Soft Comput,2017,60:520-539.
[13] LIU P,CHEN S M.Multiattribute group decision making based on intuitionistic 2-tuple linguistic information[J].Informa Sciences,2018,430:599-619.
[14] XU Z.Uncertain Multi-attribute decision making methods and applications[M].Lodon:Springer,2015.
[15] ZHANG J L,QI X W.Research on multiple attribute decision making under hesitant fuzzy-linguistic environment with application to production strategy decision making[C].Advanced Materials Research,Switzerland:Trans Tech Publications,2013,753:2829-2836.
[16] GOU X,XU Z.Novel basic operational laws for linguistic terms,hesitant fuzzy linguistic term sets and probabilistic linguistic term sets[J].Informa Sciences,2016,372:407-427.
[17] 张慧,焦志敏,李伯权.区间直觉二元语言集成算子及其群决策方法[J].计算机工程与应用,2016,52(24):43-49.
[18] CHERNEY D,LATINI E,WALDRON A.Generalized Einstein operator generating functions [J].Physics Letters B,2010,682(4–5):472-475.
[19] WANG W,LIU X.Intuitionistic fuzzy geometric aggregation operators based on Einstein operations[J].Int J Intell Syst,2011,26(11):1049–1075.
[20] WANG W,LIU X.Intuitionistic fuzzy information aggregation using Einstein operations[J].IEEE T Fuzzy Syst,2012,20(5):923-938.
[21] ZHAO X,WEI G.Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making[J].Knowl-Based Syst,2013,37(2):472-479.