基于投影的区间中智犹豫模糊VIKOR决策方法及应用
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摘要
针对属性值为区间中智犹豫模糊元,属性权重未知的决策问题,提出一种基于投影的VIKOR多属性决策方法。首先,给出区间中智犹豫模糊信息的投影测度并对其进行规范化处理,其次,把基于投影的差异度量和VIKOR方法相结合,提出基于投影的区间中智犹豫模糊VIKOR方法。考虑到属性之间存在的优先关系,利用区间中智犹豫模糊优先集结算子获得属性权重。从理论方面与传统方法进行对比,从而说明所提方法的优势。
Aiming at the decision problem that the attribute value is the ambiguous fuzzy element in the interval and the attribute weight is unknown, a projection-based VIKOR multi-attribute decision making method is proposed. Firstly, a projection measure of INHFEs is defined and normalized.Then,a projection-based difference measure and VIKOR method are combined and a new method. Considering the priority relationship exist over attributes, the prioritized aggregation operator is employed to obtain weights for attribute. Then compared with theoretically and traditional methods to illustrate the advantages of the proposed method.
Aiming at the decision problem that the attribute value is the ambiguous fuzzy element in the interval and the attribute weight is unknown, a projection-based VIKOR multi-attribute decision making method is proposed. Firstly, a projection measure of INHFEs is defined and normalized.Then,a projection-based difference measure and VIKOR method are combined and a new method. Considering the priority relationship exist over attributes, the prioritized aggregation operator is employed to obtain weights for attribute. Then compared with theoretically and traditional methods to illustrate the advantages of the proposed method.
引文
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[15] Liu P D,Shi L L.The generalized hybird weighted average operator based on interval neutrosophic hesitant set and its application to multiple attribute decision making[J].Neutral Computing & Applications,2015,26(2):457～471.
[16] Qi X W,Liang C Y,Zhang J L.Multiple attribute group decision making based on generalized power aggregation operators under interval-valued dual hesitant fuzzy linguistic environment[J].International Journal of Machine learning&Cybernetics,2016,7:1147～1193.
[17] Yager R R.Prioritized aggregation[J].International Journal of Approximate Reasoning,2008,24:245～262.
[18] Yue Z,Jia Y.A direct projection-based group decision making methodology with crisp values and interval data[J].Soft Computing,2015,21(9):1～11.
[2] Smarandache F.A unifying field in logics neutrosophy:Neutrosophic probability,set and logic[J].Multiple-Valued Logic,1999,8(3):489～503.
[3] Wang H,Smarandache F,Zhang Y Q.Single valued neutrosophic sets[J].Multispace and Multistructure,2010,4:410～413.
[4] Torra V.Hesitant fuzzy sets[J].International Journal of Intelligent Systems,2010,25:529～539.
[5] Ye J.Multiple-attribute decision-making method under a sungle-valued neutrosophic hesitant fuzzy environment[J].Journal of Intelligent Systems,2015,14(1):23～36.
[6] Liu C F,Lou Y S.Correlation coefficient for the interval-valued neutrosophic hesitant fuzzy set and its use in multi-attribute decision making[C]//International Conference on Engineering Technology and Application,2016:222～227.
[7] Opricovic S,Tzeng G H.Compromise solution by MCDM method:A comparative analysis of VIKOR and TOPSIS[J].European J of Operational Reserch,2004,156(2):445～455.
[8] Opricovic S,Tzeng G H.Extend VIKOR method in comparison with outranking methods[J].European J of Operational Reserch,2007,178(2):514～529.
[9] Singh S,Olugu E U,Musa S N,Mahat A B,Wong K Y.Strategy selection for sustainable manufacturing with integrated AHP-VIKOR method under interval-valued fuzzy environment[J].International Journal of Advanced Manufacturing Technology,2016,84:547～563.
[10] Ren Z,Xu Z S,Wang H.Dual hesitant fuzzy VIKOR method for multi-criteria group decision making based on fuzzy measure and new comparison method[J].Information Sciences,2017:1～16.
[11] Dong J Y,Yuan F F,Wan S P.Extended VIKOR method for multiple criteria decision-making with linguistic hesitant fuzzy information[J].Computers & Industrial Engineering,2017,(112):205～319.
[12] Huang Y H,Wei G W,Wei C.VIKOR method for interval neutrosophic multiple attribute group decision making[J].Information,2018,8(4):144～153.
[13] Surapati P,Shyamal D,Shariful A,Tapan K R.VIKOR based MAGDM strategy under bipolar neutrospphic set environment[J].Neutrosophic Sets and Systems,2018,19:57～69.
[14] Xu Z S,Hu H.Projection models for intuitionstic fuzzy multiple attribute decision making[J].International Journal of Information Technology and Decision Making,2010,9(2):267～280.
[15] Liu P D,Shi L L.The generalized hybird weighted average operator based on interval neutrosophic hesitant set and its application to multiple attribute decision making[J].Neutral Computing & Applications,2015,26(2):457～471.
[16] Qi X W,Liang C Y,Zhang J L.Multiple attribute group decision making based on generalized power aggregation operators under interval-valued dual hesitant fuzzy linguistic environment[J].International Journal of Machine learning&Cybernetics,2016,7:1147～1193.
[17] Yager R R.Prioritized aggregation[J].International Journal of Approximate Reasoning,2008,24:245～262.
[18] Yue Z,Jia Y.A direct projection-based group decision making methodology with crisp values and interval data[J].Soft Computing,2015,21(9):1～11.