混合型广义犹豫模糊语言多准则群决策方法
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摘要
针对各专家决策矩阵中方案赋值为不同犹豫模糊语言集的多准则群决策问题,提出基于广义犹豫模糊语言集、得分函数与排序得分的新方法。运用新得分函数,将各专家的广义犹豫模糊语言决策矩阵转化为得分决策矩阵;根据各专家给出的准则权重向量的不同情况,计算各方案在准则集下的加权得分函数值或得分函数值;依据这些函数值的特征,得到各专家认为各方案的排序位置及其得分;按照专家权重向量的不同情况,求得各方案的综合排序得分,进而确定各方案的排序。以新能源汽车零配件小微企业的信用评估为例,验证了所提方法的可行性和有效性。
Aiming at the multi-criterion group decision-making problems with different hesitant fuzzy linguistic sets in expert decision matrices,a new method was proposed based on generalized hesitant fuzzy linguistic sets,score functions and ranking scores.By adopting some new score functions,the generalized hesitant fuzzy linguistic decision matrices of the experts were transformed into score decision matrices.According to the different situations of criterion weight vectors given by the experts,the weighted score function or score function evaluations of alternatives were gotten under the criterion set.With the consideration of these function evaluations'characteristics,the ranking positions and scores of the alternatives were attained on the experts'opinions.Based on the different situations of expert weight vector,the comprehensive ranking scores of the alternatives were computed.Accordingly,the ranking order of the alternatives was derived.For the micro and small enterprises in the new-energy auto-parts industry,a numeric example of the credit evaluation was offered to illustrate the feasibility and validity of the proposed method.
Aiming at the multi-criterion group decision-making problems with different hesitant fuzzy linguistic sets in expert decision matrices,a new method was proposed based on generalized hesitant fuzzy linguistic sets,score functions and ranking scores.By adopting some new score functions,the generalized hesitant fuzzy linguistic decision matrices of the experts were transformed into score decision matrices.According to the different situations of criterion weight vectors given by the experts,the weighted score function or score function evaluations of alternatives were gotten under the criterion set.With the consideration of these function evaluations'characteristics,the ranking positions and scores of the alternatives were attained on the experts'opinions.Based on the different situations of expert weight vector,the comprehensive ranking scores of the alternatives were computed.Accordingly,the ranking order of the alternatives was derived.For the micro and small enterprises in the new-energy auto-parts industry,a numeric example of the credit evaluation was offered to illustrate the feasibility and validity of the proposed method.
引文
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[2] XU Z S,XIA M M.Distance and similarity measures for hesitant fuzzy sets[J].Information Sciences,2011,181(11):2128-2138.
[3] RODRGUEZ R M,MARTNEZ L,HERRERA F.Hesitant fuzzy linguistic terms sets for decision making[J].IEEE Transactions on Fuzzy Systems,2012,20(1):109-119.
[4] LIN R,ZHAO X F,WEI G W.Models for selecting an ERP system with hesitant fuzzy linguistic information[J].Journal of Intelligent&Fuzzy Systems,2014,26(5):2155-2165.
[5] MENG F Y,CHEN X H,ZHANG Q.Multi-attribute decision analysis under a linguistic hesitant fuzzy environment[J].Information Sciences,2014,267(5):287-305.
[6] LIAO H C,XU Z S,ZENG X J.Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making[J].Information Sciences,2014,271(7):125-142.
[7] WANG J Q,WANG J,CHEN Q H,et al.An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets[J].Information Sciences,2014,280(10):338-351.
[8] WANG J Q,WU J T,WANG J,et al.Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems[J].Information Sciences,2014,288(12):55-72.
[9] LEE L W,CHEN S M.Fuzzy decision making based on likelihood-based comparison relations of hesitant fuzzy linguistic term sets and hesitant fuzzy linguistic operators[J].Information Sciences,2015,294(2):513-529.
[10] DONG Y C,CHEN X,HERRERA F.Minimizing adjusted simple terms in the consensus reaching process with hesitant linguistic assessments in group decision making[J].Information Sciences,2015,297(3):95-117.
[11] YAVUZ M,OZTAYSI B,ONAR S C,et al.Multi-criteria evaluation of alternative-fuel vehicles via a hierarchical hesitant fuzzy linguistic model[J].Expert Systems with Applications,2015,42(5):2835-2848.
[12] CHEN S M,TAN J M.Handling multicriteria fuzzy decision-making problems based on vague set theory[J].Fuzzy Sets and Systems,1994,67(2):163-172.
[13] LIU H W,WANG G J.Multi-criteria decision-making methods based on intuitionistic fuzzy sets[J].European Journal of Operational Research,2007,179(1):220-233.
[14] XU Zeshui.Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making[J].Control and Decision,2007,22(2):215-219(in Chinese).[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.]
[15] XU Zeshui.Approaches to multiple attribute decision making with intuitionistic fuzzy preference information[J].Systems Engineering—Theory&Practice,2007,27(11):62-71(in Chinese).[徐泽水.直觉模糊偏好信息下的多属性决策途径[J].系统工程理论与实践,2007,27(11):62-71.]
[16] CHEN T Y.An outcome-oriented approach to multicriteria decision analysis with intuitionistic fuzzy optimistic/pessimistic operators[J].Expert Systems with Applications,2010,37(12):7762-7774.
[17] WANG J Q,LI J J.Multi-criteria fuzzy decision-making method based on cross entropy and score functions[J].Expert Systems with Applications,2011,38(1):1032-1038.
[18] CHEN T Y,WANG H P,LU Y Y.A multicriteria group decision-making approach based on interval-valued intuitionistic fuzzy sets:a comparative perspective[J].Expert Systems with Applications,2011,38(6):7647-7658.
[19] CHEN T Y.A comparative analysis of score functions for multiple criteria decision making in intuitionistic fuzzy settings[J].Information Sciences,2011,181(17):3652-3676.
[20] PEI Z,ZHENG L.A novel approach to multi-attribute decision making based on intuitionistic fuzzy sets[J].Expert Systems with Applications,2012,39(3):2560-2566.
[21] WANG J Q,LI K J,ZHANG H Y.Interval-valued intuitionistic fuzzy multi-criteria decision-making approach based on prospect score function[J].Knowledge-Based Systems,2012,27(3):119-125.
[22] CHEN Z P,YANG W.A new multiple criteria decision making method based on intuitionistic fuzzy information[J].Expert Systems with Applications,2012,39(4):4328-4334.
[23] WU J,LIU Y J.An approach for multiple attribute group decision making problems with interval-valued intuitionistic trapezoidal fuzzy numbers[J].Computers&Industrial Engineering,2013,66(2):311-324.
[24] AGARWAL M,BISWAS K K,HANMANDLU M.Generalized intuitionistic fuzzy soft sets with applications in decision-making[J].Applied Soft Computing,2013,13(8):3552-3566.
[25] WANG Z X,NIU L L,WU R X,et al.Multicriteria decision-making method based on risk attitude under interval-valued intuitionistic fuzzy environment[J].Fuzzy Information and Engineering,2014,6(4):489-504.
[26] HU J H,XIAO K L,CHEN X H,et al.Interval type-2hesitant fuzzy set and its application in multi-criteria decision making[J].Computers&Industrial Engineering,2015,87(9):91-103.
[27] WANG J Q,PENG J J,ZHANG H Y,et al.An uncertain linguistic multi-criteria group decision-making method based on a cloud model[J].Group Decision and Negotiation,2015,24(1):171-192.
[28] MOU Q,XU Z S,LIAO H C.An intuitionistic fuzzy multiplicative best-worst method for multi-criteria group decision making[J].Information Sciences,2016,374(12):224-239.
[29] TIAN Z P,WANG J,WANG J Q,et al.Simplified neutrosophic linguistic multi-criteria group decision-making approach to green product development[J].Group Decision and Negotiation,2017,26(3):597-627.
[30] ZHONG L,YAO L M.An ELECTRE I-based multi-criteria group decision making method with interval type-2fuzzy numbers and its application to supplier selection[J].Applied Soft Computing,2017,57(8):556-576.
[31] MOHAGHEGHI V,MOUSAVI S M,VAHDANI B.Enhancing decision-making flexibility by introducing a new last aggregation evaluating approach based on multi-criteria group decision making and Pythagorean fuzzy sets[J].Applied Soft Computing,2017,61(12):527-535.
[32] WAN S P,QIN Y L,DONG J Y.A hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making with hesitant fuzzy truth degrees[J].Knowledge-Based Systems,2017,138(12):232-248.
[33] YU W Y,ZHANG Z,ZHONG Q Y,et al.Extended TODIM for multi-criteria group decision making based on unbalanced hesitant fuzzy linguistic term sets[J].Computers&Industrial Engineering,2017,114(12):316-328.
[34] GONG Xiaomin,GENG Xiuli,SUN Shaorong.Multi-criteria group decision making based on 2-tuple linguistic DEMATEL and DEA[J].Computer Integrated Manufacturing Systems,2016,22(8):1992-2000(in Chinese).[弓晓敏,耿秀丽,孙绍荣.基于二元语义DEMATEL和DEA的多属性群决策方法[J].计算机集成制造系统,2016,22(8):1992-2000.]
[35] MI Wangjun,DAI Yuewei.Risk mixed multi-criteria fuzzy group decision-making approach based on prospect theory[J].Control and Decision,2017,32(7):1279-1285(in Chinese).[糜万俊,戴跃伟.基于前景理论的风险型混合模糊多准则群决策[J].控制与决策,2017,32(7):1279-1285.]
[36] ZADEH L A.The concept of a linguistic variable and its application to approximate reasoning—I[J].Information Sciences,1975,8(3):199-249.
[37] XU Z S.Deviation measures of linguistic preference relations in group decision making[J].Omega,2005,33(3):249-254.
[38] RODRGUEZ R M,MARTNEZ L.An analysis of symbolic linguistic computing models in decision making[J].International Journal of General Systems,2013,42(1):121-136.
[39] XU Zeshui,DA Qingli.Possibility degree method for ranking interval numbers and its application[J].Journal of Systems Engineering,2003,18(1):67-70.[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.]
[40] ZHANG Yangming,CHEN Yunxiang,WANG Pan,et al.Intuitionistic fuzzy combination multi-attribute group decision-making method based on improved fuzzy Borda method[J].Control and Decision,2017,32(12):2219-2226(in Chinese).[张洋铭,陈云翔,王攀,等.基于改进模糊Borda法的直觉模糊组合多属性群决策方法[J].控制与决策,2017,32(12):2219-2226.]
[41] XU Linming,LIN Zhibing,LI Meijuan,et al.A dynamic combined evaluation method based on fuzzy Borda and its application[J].Chinese Journal of Management Science,2017,25(2):165-173(in Chinese).[徐林明,林志炳,李美娟,等.基于模糊Borda法的动态组合评价方法及其应用研究[J].中国管理科学,2017,25(2):165-173.]
[42] SACHDEVA N,SINGH O,KAPUR P K,et al.Multi-criteria intuitionistic fuzzy group decision analysis with TOPSIS method for selecting appropriate cloud solution to manage big data projects[J].International Journal of System Assurance Engineering&Management,2016,7(3):316-324.
[43] YE Yuexiang,MI Zhongchun,WANG Hongyu,et al.Setpair-analysis-based method for multiple attributes decisionmaking with intervals[J].Systems Engineering and Electronics,2006,28(9):1344-1347(in Chinese).[叶跃祥,糜仲春,王宏宇,等.一种基于集对分析的区间数多属性决策方法[J].系统工程与电子技术,2006,28(9):1344-1347.]
[44] AN Xianghua,NIU Chunliang,XUE Dongjuan,et al.Optimal selection method for product service system scheme based on variable granule weight and group decision-making[J].Computer Integrated Manufacturing Systems,2016,22(1):155-165(in Chinese).[安相华,牛春亮,薛冬娟,等.基于变粒度权重与群决策的产品服务系统方案优选方法[J].计算机集成制造系统,2016,22(1):155-165.]
[2] XU Z S,XIA M M.Distance and similarity measures for hesitant fuzzy sets[J].Information Sciences,2011,181(11):2128-2138.
[3] RODRGUEZ R M,MARTNEZ L,HERRERA F.Hesitant fuzzy linguistic terms sets for decision making[J].IEEE Transactions on Fuzzy Systems,2012,20(1):109-119.
[4] LIN R,ZHAO X F,WEI G W.Models for selecting an ERP system with hesitant fuzzy linguistic information[J].Journal of Intelligent&Fuzzy Systems,2014,26(5):2155-2165.
[5] MENG F Y,CHEN X H,ZHANG Q.Multi-attribute decision analysis under a linguistic hesitant fuzzy environment[J].Information Sciences,2014,267(5):287-305.
[6] LIAO H C,XU Z S,ZENG X J.Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making[J].Information Sciences,2014,271(7):125-142.
[7] WANG J Q,WANG J,CHEN Q H,et al.An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets[J].Information Sciences,2014,280(10):338-351.
[8] WANG J Q,WU J T,WANG J,et al.Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems[J].Information Sciences,2014,288(12):55-72.
[9] LEE L W,CHEN S M.Fuzzy decision making based on likelihood-based comparison relations of hesitant fuzzy linguistic term sets and hesitant fuzzy linguistic operators[J].Information Sciences,2015,294(2):513-529.
[10] DONG Y C,CHEN X,HERRERA F.Minimizing adjusted simple terms in the consensus reaching process with hesitant linguistic assessments in group decision making[J].Information Sciences,2015,297(3):95-117.
[11] YAVUZ M,OZTAYSI B,ONAR S C,et al.Multi-criteria evaluation of alternative-fuel vehicles via a hierarchical hesitant fuzzy linguistic model[J].Expert Systems with Applications,2015,42(5):2835-2848.
[12] CHEN S M,TAN J M.Handling multicriteria fuzzy decision-making problems based on vague set theory[J].Fuzzy Sets and Systems,1994,67(2):163-172.
[13] LIU H W,WANG G J.Multi-criteria decision-making methods based on intuitionistic fuzzy sets[J].European Journal of Operational Research,2007,179(1):220-233.
[14] XU Zeshui.Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making[J].Control and Decision,2007,22(2):215-219(in Chinese).[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.]
[15] XU Zeshui.Approaches to multiple attribute decision making with intuitionistic fuzzy preference information[J].Systems Engineering—Theory&Practice,2007,27(11):62-71(in Chinese).[徐泽水.直觉模糊偏好信息下的多属性决策途径[J].系统工程理论与实践,2007,27(11):62-71.]
[16] CHEN T Y.An outcome-oriented approach to multicriteria decision analysis with intuitionistic fuzzy optimistic/pessimistic operators[J].Expert Systems with Applications,2010,37(12):7762-7774.
[17] WANG J Q,LI J J.Multi-criteria fuzzy decision-making method based on cross entropy and score functions[J].Expert Systems with Applications,2011,38(1):1032-1038.
[18] CHEN T Y,WANG H P,LU Y Y.A multicriteria group decision-making approach based on interval-valued intuitionistic fuzzy sets:a comparative perspective[J].Expert Systems with Applications,2011,38(6):7647-7658.
[19] CHEN T Y.A comparative analysis of score functions for multiple criteria decision making in intuitionistic fuzzy settings[J].Information Sciences,2011,181(17):3652-3676.
[20] PEI Z,ZHENG L.A novel approach to multi-attribute decision making based on intuitionistic fuzzy sets[J].Expert Systems with Applications,2012,39(3):2560-2566.
[21] WANG J Q,LI K J,ZHANG H Y.Interval-valued intuitionistic fuzzy multi-criteria decision-making approach based on prospect score function[J].Knowledge-Based Systems,2012,27(3):119-125.
[22] CHEN Z P,YANG W.A new multiple criteria decision making method based on intuitionistic fuzzy information[J].Expert Systems with Applications,2012,39(4):4328-4334.
[23] WU J,LIU Y J.An approach for multiple attribute group decision making problems with interval-valued intuitionistic trapezoidal fuzzy numbers[J].Computers&Industrial Engineering,2013,66(2):311-324.
[24] AGARWAL M,BISWAS K K,HANMANDLU M.Generalized intuitionistic fuzzy soft sets with applications in decision-making[J].Applied Soft Computing,2013,13(8):3552-3566.
[25] WANG Z X,NIU L L,WU R X,et al.Multicriteria decision-making method based on risk attitude under interval-valued intuitionistic fuzzy environment[J].Fuzzy Information and Engineering,2014,6(4):489-504.
[26] HU J H,XIAO K L,CHEN X H,et al.Interval type-2hesitant fuzzy set and its application in multi-criteria decision making[J].Computers&Industrial Engineering,2015,87(9):91-103.
[27] WANG J Q,PENG J J,ZHANG H Y,et al.An uncertain linguistic multi-criteria group decision-making method based on a cloud model[J].Group Decision and Negotiation,2015,24(1):171-192.
[28] MOU Q,XU Z S,LIAO H C.An intuitionistic fuzzy multiplicative best-worst method for multi-criteria group decision making[J].Information Sciences,2016,374(12):224-239.
[29] TIAN Z P,WANG J,WANG J Q,et al.Simplified neutrosophic linguistic multi-criteria group decision-making approach to green product development[J].Group Decision and Negotiation,2017,26(3):597-627.
[30] ZHONG L,YAO L M.An ELECTRE I-based multi-criteria group decision making method with interval type-2fuzzy numbers and its application to supplier selection[J].Applied Soft Computing,2017,57(8):556-576.
[31] MOHAGHEGHI V,MOUSAVI S M,VAHDANI B.Enhancing decision-making flexibility by introducing a new last aggregation evaluating approach based on multi-criteria group decision making and Pythagorean fuzzy sets[J].Applied Soft Computing,2017,61(12):527-535.
[32] WAN S P,QIN Y L,DONG J Y.A hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making with hesitant fuzzy truth degrees[J].Knowledge-Based Systems,2017,138(12):232-248.
[33] YU W Y,ZHANG Z,ZHONG Q Y,et al.Extended TODIM for multi-criteria group decision making based on unbalanced hesitant fuzzy linguistic term sets[J].Computers&Industrial Engineering,2017,114(12):316-328.
[34] GONG Xiaomin,GENG Xiuli,SUN Shaorong.Multi-criteria group decision making based on 2-tuple linguistic DEMATEL and DEA[J].Computer Integrated Manufacturing Systems,2016,22(8):1992-2000(in Chinese).[弓晓敏,耿秀丽,孙绍荣.基于二元语义DEMATEL和DEA的多属性群决策方法[J].计算机集成制造系统,2016,22(8):1992-2000.]
[35] MI Wangjun,DAI Yuewei.Risk mixed multi-criteria fuzzy group decision-making approach based on prospect theory[J].Control and Decision,2017,32(7):1279-1285(in Chinese).[糜万俊,戴跃伟.基于前景理论的风险型混合模糊多准则群决策[J].控制与决策,2017,32(7):1279-1285.]
[36] ZADEH L A.The concept of a linguistic variable and its application to approximate reasoning—I[J].Information Sciences,1975,8(3):199-249.
[37] XU Z S.Deviation measures of linguistic preference relations in group decision making[J].Omega,2005,33(3):249-254.
[38] RODRGUEZ R M,MARTNEZ L.An analysis of symbolic linguistic computing models in decision making[J].International Journal of General Systems,2013,42(1):121-136.
[39] XU Zeshui,DA Qingli.Possibility degree method for ranking interval numbers and its application[J].Journal of Systems Engineering,2003,18(1):67-70.[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.]
[40] ZHANG Yangming,CHEN Yunxiang,WANG Pan,et al.Intuitionistic fuzzy combination multi-attribute group decision-making method based on improved fuzzy Borda method[J].Control and Decision,2017,32(12):2219-2226(in Chinese).[张洋铭,陈云翔,王攀,等.基于改进模糊Borda法的直觉模糊组合多属性群决策方法[J].控制与决策,2017,32(12):2219-2226.]
[41] XU Linming,LIN Zhibing,LI Meijuan,et al.A dynamic combined evaluation method based on fuzzy Borda and its application[J].Chinese Journal of Management Science,2017,25(2):165-173(in Chinese).[徐林明,林志炳,李美娟,等.基于模糊Borda法的动态组合评价方法及其应用研究[J].中国管理科学,2017,25(2):165-173.]
[42] SACHDEVA N,SINGH O,KAPUR P K,et al.Multi-criteria intuitionistic fuzzy group decision analysis with TOPSIS method for selecting appropriate cloud solution to manage big data projects[J].International Journal of System Assurance Engineering&Management,2016,7(3):316-324.
[43] YE Yuexiang,MI Zhongchun,WANG Hongyu,et al.Setpair-analysis-based method for multiple attributes decisionmaking with intervals[J].Systems Engineering and Electronics,2006,28(9):1344-1347(in Chinese).[叶跃祥,糜仲春,王宏宇,等.一种基于集对分析的区间数多属性决策方法[J].系统工程与电子技术,2006,28(9):1344-1347.]
[44] AN Xianghua,NIU Chunliang,XUE Dongjuan,et al.Optimal selection method for product service system scheme based on variable granule weight and group decision-making[J].Computer Integrated Manufacturing Systems,2016,22(1):155-165(in Chinese).[安相华,牛春亮,薛冬娟,等.基于变粒度权重与群决策的产品服务系统方案优选方法[J].计算机集成制造系统,2016,22(1):155-165.]