基于投影的单值中智集MAGDM一致性合成方法
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摘要
针对投影测度下的属性值和属性权重均为单值中智集的多属性群决策问题,提出了一种基于投影的群决策一致性合成方法。该方法以群体评价均值矩阵和群体评价正、负理想值矩阵为群体评价的参考基准,根据投影测度,构建了衡量决策者个体评价与群体评价一致性程度的投影贴近度公式;进而以决策者的相对一致性程度和决策者重要性合成得到策者权重,并构造加权规范化的群体最终决策矩阵;然后以单值中智集得分函数求解各方案的最终得分并排序;并给出详细的决策步骤,最后通过算例同其他方法进行了对比分析,表明本文方法的可行、有效。
Aiming at the multiattribute group decision-making problem, in which attribute values and weights are single valued neutrosophic sets, a new projection method for single valued neutrosophic group decision making based on consistency degree is put forward. According to the basic idea of projection method, the positive and negative ideals of group decision matrixes as the basic references of group decision making. Considering the projection relationship between personal and group decision, a new closeness degree formula based on projection to measure the relative consistency degree between personal and group decision is constructed. Then the weights of decision makers are acquired by combining the relative consistency degree with importance of decision makers, and the final weighted standardized group decision matrix is build. Next, the scoring function of single valued neutrosophic sets is presented to calculate the final score of these schemes and rank them. Finally, a numerical example is given to illustrate the validity and feasibility of the proposed method. The detailed decision making steps are given. Finally, an application example is analyzed. At last, the method proposed and others are compared, which shows the effectiveness and feasibility of the method.
Aiming at the multiattribute group decision-making problem, in which attribute values and weights are single valued neutrosophic sets, a new projection method for single valued neutrosophic group decision making based on consistency degree is put forward. According to the basic idea of projection method, the positive and negative ideals of group decision matrixes as the basic references of group decision making. Considering the projection relationship between personal and group decision, a new closeness degree formula based on projection to measure the relative consistency degree between personal and group decision is constructed. Then the weights of decision makers are acquired by combining the relative consistency degree with importance of decision makers, and the final weighted standardized group decision matrix is build. Next, the scoring function of single valued neutrosophic sets is presented to calculate the final score of these schemes and rank them. Finally, a numerical example is given to illustrate the validity and feasibility of the proposed method. The detailed decision making steps are given. Finally, an application example is analyzed. At last, the method proposed and others are compared, which shows the effectiveness and feasibility of the method.
引文
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[13] Ye J.Multiple attribute group decision-making method with completely unknown weights based on similarity measures under single valued neutrosophic environment[J].Journal of Intelligent & Fuzzy Systems,2014,27(6):2927～2935.
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[16] 王应明.多指标决策与评价的新方法——投影法[J].系统工程与电子技术,1999,21(3):1～4.
[17] 卫贵武.基于投影的直觉模糊数多属性决策方法[J].管理学报,2009,6(9):1154～1156.
[18] Xu Z S,Hu H.Projection models for intuitionistic fuzzy multiple attribute decision making[J].International Journal of Information Technology & Decision Making,2010,9(2):267～280.
[19] Yue Z L.An intuitionistic fuzzy projection-based approach for partner selection[J].Applied Mathematical Modelling,2013,37(23):9538～9551.
[20] 刘小弟,朱建军,刘思峰.犹豫模糊信息下的双向投影决策方法[J].系统工程理论与实践,2014,34(10):2637～2644.
[2] Atanassow K.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20(1):87～96.
[3] Chen Z,Yang W.A new multiple attribute group decision making method in intuitionistic fuzzy setting[J].Applied Mathematical Modelling,2011,35(9):4424～4437.
[4] Xu Y,Wang H.The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making[J].Applied Soft Computing,2012,12(3):1168～1179.
[5] Smarandache F.A unifying field in logics neutrosophiclogic:Neutrosophy,neutrosophic set,neutrosophic probability[M].Rehoboth:American Research Press,1999:111～114.
[6] Wang H,et al.Single valued neutrosophic sets[J].Multispace and Multistruct,2010,(4):410～413.
[7] Ye J.Multicriteria Decision-making method using the correlation coefficient under single-value neutrosophic environment[J].International Journal of General Systems,2013,42(4):386～394.
[8] Ye J.A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets[J].Journal of Intelligent & Fuzzy Systems,2014,26(5):2459～2466.
[9] Ye J.Single valued neutrosophic cross-entropy for multicriteria decision making problems[J].Applied Mathematical Modeling,2014,38(3):1170～1175.
[10] Peng J J,et al.An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets[J].Applied Soft Computing,2014,25:336～346.
[11] Ye J.An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers[J].Journal of Intelligent & Fuzzy Systems,2015,28(1):247～255.
[12] Yue Z L.Deriving decision maker’s weights based on distance measure for interval-valued intuitionistic fuzzy group decision making[J].Expert Systems with Applications,2011,38(9):11665～11670.
[13] Ye J.Multiple attribute group decision-making method with completely unknown weights based on similarity measures under single valued neutrosophic environment[J].Journal of Intelligent & Fuzzy Systems,2014,27(6):2927～2935.
[14] Wu J,et al.The induced continuous ordered weighted geometric operators and their application in group decision making[J].Computers & Industrial Engineering,2009,56(4):1545～1552.
[15] Yue Z L.A method for group decision-making based on determining weights of decision makers using TOPSIS[J].Applied Mathematical Modelling,2011,35(4):1926～1936.
[16] 王应明.多指标决策与评价的新方法——投影法[J].系统工程与电子技术,1999,21(3):1～4.
[17] 卫贵武.基于投影的直觉模糊数多属性决策方法[J].管理学报,2009,6(9):1154～1156.
[18] Xu Z S,Hu H.Projection models for intuitionistic fuzzy multiple attribute decision making[J].International Journal of Information Technology & Decision Making,2010,9(2):267～280.
[19] Yue Z L.An intuitionistic fuzzy projection-based approach for partner selection[J].Applied Mathematical Modelling,2013,37(23):9538～9551.
[20] 刘小弟,朱建军,刘思峰.犹豫模糊信息下的双向投影决策方法[J].系统工程理论与实践,2014,34(10):2637～2644.