梯形模糊偏好关系的DEA交叉效率群决策方法研究
|
摘要
针对梯形模糊偏好关系信息环境下的群决策问题,设计了一种面向区间DEA交叉效率的群决策方法。首先,利用α-截集将梯形模糊偏好关系转化为区间模糊偏好关系,并证明其符合DEA的产出特征,进而建立区间模糊偏好关系对应的交叉效率DEA模型,将自评和他评相结合,得到每个方案的区间交叉效率值。将不同专家的区间交叉效率矩阵通过UOWA算子进行集结,然后计算出决策单元的最大后悔值,据此得到最终的方案排序结果。实证分析表明该方法不需要对偏好关系进行一致性调整,可以有效减少决策信息的损失,有着较好的适用性。
Aiming at the group decision making problem with trapezoidal fuzzy preferences, a new group decision making method based on interval DEA cross-efficiency is proposed. First, the trapezoidal fuzzy preference relation is transformed into interval fuzzy preference relation using cuts, which are proven to satisfy the output characteristics of DEA. Then, the DEA cross-efficiency model for any interval fuzzy preference relation is established. The cross-efficiency value of each alternative is obtained by combining self-evaluation and other-evaluation. The interval cross-efficiency matrix from each expert is aggregated by UOWA operator. The maximum regret value of the decision making unit is then calculated, based on which the final ranking results are obtained. The empirical analysis shows that this method does not need to adjust the consistency of each preference relationship and can effectively avoid the loss of decision information. Thus our method has good applicability.
Aiming at the group decision making problem with trapezoidal fuzzy preferences, a new group decision making method based on interval DEA cross-efficiency is proposed. First, the trapezoidal fuzzy preference relation is transformed into interval fuzzy preference relation using cuts, which are proven to satisfy the output characteristics of DEA. Then, the DEA cross-efficiency model for any interval fuzzy preference relation is established. The cross-efficiency value of each alternative is obtained by combining self-evaluation and other-evaluation. The interval cross-efficiency matrix from each expert is aggregated by UOWA operator. The maximum regret value of the decision making unit is then calculated, based on which the final ranking results are obtained. The empirical analysis shows that this method does not need to adjust the consistency of each preference relationship and can effectively avoid the loss of decision information. Thus our method has good applicability.
引文
[1] Yejun Xu,Lei Chen,Kevin W Li,et al.A Chi-square method for priority derivation in group decision making with incomplete reciprocal preference relations[J].Information Sciences,2015,306:166–179.
[2] 陈小红,刘金培,张娜娜,等.基于加权不平衡语言Bonferroni算子的多属性群决策[J].佳木斯大学学报:自然科学版,2018,36(02):291-295.
[3] Peng Wu,Ligang Zhou,Tong Zheng,et al.A Fuzzy group decision making and its application based on compatibility with multiplicative trapezoidal fuzzy preference relations[J].International Journal of Fuzzy Systems,2017,19(3):683–701.
[4] 陈华友,周礼刚,刘金培,陶志富.不确定信息环境下多属性决策方法的研究进展[J].安徽大学学报:自然科学版,2018,42(05):10-29.
[5] Huimin Zhang.Group decision making based on Multiplicative consistent reciprocal preference Relations[J].Fuzzy Sets and Systems,2016,282:31–46.
[6] 王洪波,罗贺,杨善林.基于流形学习的非一致性判断矩阵排序方法[J].中国管理科学,2015,23(10):147-155.
[7] Lei Chen,Ying-Ming Wang.Data Envelopment analysis cross-efficiency model in fuzzy environments[J].Journal of Intelligent & Fuzzy Systems,2016,30:2601–2609.
[8] Guozhong Zheng,Neng Zhu,Zhe Tian,et al.Application of a trapezoidal fuzzy AHP method for work safety evaluation and early warning rating of hot and humid environments[J].Safety Science,2012,50:228–239.
[9] Meimei Xia,Jian Chen.Consistency and Consensus improving methods for pairwise comparison matrices based on Abelian linearly ordered group[J].Fuzzy Sets Syst,2015,266(1):1–32.
[10] 韦纯福.基于语言型混合算子的模糊信息聚合方法[J].控制与决策,2017,32(08):1505-1510.
[2] 陈小红,刘金培,张娜娜,等.基于加权不平衡语言Bonferroni算子的多属性群决策[J].佳木斯大学学报:自然科学版,2018,36(02):291-295.
[3] Peng Wu,Ligang Zhou,Tong Zheng,et al.A Fuzzy group decision making and its application based on compatibility with multiplicative trapezoidal fuzzy preference relations[J].International Journal of Fuzzy Systems,2017,19(3):683–701.
[4] 陈华友,周礼刚,刘金培,陶志富.不确定信息环境下多属性决策方法的研究进展[J].安徽大学学报:自然科学版,2018,42(05):10-29.
[5] Huimin Zhang.Group decision making based on Multiplicative consistent reciprocal preference Relations[J].Fuzzy Sets and Systems,2016,282:31–46.
[6] 王洪波,罗贺,杨善林.基于流形学习的非一致性判断矩阵排序方法[J].中国管理科学,2015,23(10):147-155.
[7] Lei Chen,Ying-Ming Wang.Data Envelopment analysis cross-efficiency model in fuzzy environments[J].Journal of Intelligent & Fuzzy Systems,2016,30:2601–2609.
[8] Guozhong Zheng,Neng Zhu,Zhe Tian,et al.Application of a trapezoidal fuzzy AHP method for work safety evaluation and early warning rating of hot and humid environments[J].Safety Science,2012,50:228–239.
[9] Meimei Xia,Jian Chen.Consistency and Consensus improving methods for pairwise comparison matrices based on Abelian linearly ordered group[J].Fuzzy Sets Syst,2015,266(1):1–32.
[10] 韦纯福.基于语言型混合算子的模糊信息聚合方法[J].控制与决策,2017,32(08):1505-1510.