Cross-efficiency Evaluation based on Consensus Model
DOI:
https://doi.org/10.54691/mb3ye671Keywords:
CCR; Cross-efficiency; Consensus.Abstract
In this paper, three methods are proposed to determine the weight of decision makers, namely deviation maximization based on MPR, information entropy and Fermat point. The cross-efficiency matrix provided by multiple decision makers is converted into MHFPRs. Combined with the weight of decision makers, the consensus model was used to make MHFPR reach a group consensus, so as to evaluate the cross-efficiency of all DMUs. The empirical example shows that the cross-efficiency based on reaching consensus is related to the weight of decision-makers. Three aggregation methods proposed in this paper are different from the traditional methods. The result of information entropy is between deviation maximization based on MPR and Fermat-Torricelli point.
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[1] Charnes A, Cooper W W & Rhodes E. Measuring the efficiency of decision making units. European Journal of Operational Research, 2(1978), 6, 429–444.
[2] Sexton T R , Silkman R H , Hogan A J . Data envelopment analysis: Critique and extensions[J]. New Directions for Evaluation, 1986(2010), 32, 73-105.
[3] Wang Y M & Chin K S. A neutral DEA model for cross-efficiency evaluation and its extension. Expert Systems with Applications, 37(2010), 5, 3666–3675.
[4] Shi Hailiu, Wang Yingming, Chen Lei. Neutral cross-efficiency evaluation regarding an ideal frontier and anti-ideal frontier as evaluation criteria[J]. Computers & Industrial Engineering, 132(2019), 6, 385-394.
[5] Hai-Liu Shi, Sheng-Qun Chen, Lei Chen, Ying-Ming Wang. A neutral cross-efficiency evaluation method based on interval reference points in consideration of bounded rational behavior[J]. European Journal of Operational Research, 290(2021), 3, 1098-1110.
[6] Jie Wu, Liang Liang, Feng Yang. Determination of the weights for the ultimate cross efficiency using Shapley value in cooperative game[J]. Expert Systems with Applications, 36(2009), 1, 872-876.
[7] Ying-Ming Wang, Kwai-Sang Chin. The use of OWA operator weights for cross-efficiency aggregation[J]. Omega, 39(2011), 5, 493-503.
[8] Yuhong Wang, Dongdong Wu, Wuyong Qian, Hui Li,Cross-efficiency intervals integrated ranking approach based on the generalized Fermat-Torricelli point[J]. Computers & Industrial Engineering, 2021, 162,
[9] Jiang-Hong Zhu, Jian Chen, Guo-Fang Li, Bin Shuai. Using cross efficiency method integrating regret theory and WASPAS to evaluate road safety performance of Chinese provinces[J]. Accident Analysis & Prevention, 2021, 162:
[10] Saaty T L. The Analytic Hierarchy Process [M], McGraw-Hill, New York, 1980.
[11] Orlovsky S A. Decision-making with a fuzzy preference relation[J]. Fuzzy Sets and Sytems, 1(1978), 155- 167.
[12] Xu Z S. A practical method for priority of interval number comolementary judgment matrix[J]. Operations Research and Management Science, 10(2002), 1, 16- 19.
[13] Van Laarhoven, P. J., and Pedrycz, W. A fuzzy extension of Saaty's priority theory. Fuzzy sets and Systems, 11(1983), 1-3, 229-241.
[14] Xu Z S. Intuitionistic preference ralations and their application in group decision making[J]. Information Sciences, 177(2007), 11, 2363- 2379.
[15] Zhu, B., & Xu, Z. Analytic hierarchy process-hesitant group decision making[J]. European Journal of Operational Research, 239(2014), 3, 794–801.
[16] Zhiming Zhang, Chong Wu. A decision support model for group decision making with hesitant multiplicative preference relations[J]. Information Sciences, 282(2014), 136-166.
[17] Ma Yonghong, Zhou Rongxi, Li Zhenguang. Determination Method of Decision-maker Weights Based on Deviation Maximization [J]. Journal of Beijing University of Chemical Technology (Natural Science Edition),2007, 2, 177-180.
[18] Zhang Guiqing Research on Consensus Model of Group Decision-making [D]. Xi 'an Jiaotong University,2011.
[19] Jie Wu, Jiasen Sun, Liang Liang, Yingchun Zha. Determination of weights for ultimate cross efficiency using Shannon entropy[J]. Expert Systems with Applications, 38(2011), 5, 5162-5165.
[20] Cao Linjian, Liu Bingsheng, Wang Xueqing, Feng Tao. Research on the Bid Evaluation Method Improved by DEA and Information Entropy [J]. Journal of Chongqing University (Social Science Edition),17(2011), 2, 86-89.
[21] Hu Qinghong, Wang Yingming. Comprehensive Evaluation of DEA Cross-efficiency Based on Information Entropy [J]. Research of Science and Technology Management,34(2014), 6, 54-60.
[22] Fanyong Meng, Beibei Xiong. Logical efficiency decomposition for general two-stage systems in view of cross efficiency[J]. European Journal of Operational Research, 294(2021), 2, 622-632.
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