摘要
A method of minimizing rankings inconsistency is proposed for a decision-making problem with rankings of alternatives given by multiple decision makers according to multiple criteria. For each criteria, at first, the total inconsistency between the rankings of all alternatives for the group and the ones for every decision maker is defined after the decision maker weights in respect to the criteria are considered. Similarly, the total inconsistency between their final rankings for the group and the ones under every criteria is determined after the criteria weights are taken into account. Then two nonlinear integer programming models minimizing respectively the two total inconsistencies above are developed and then transformed to two dynamic programming models to obtain separately the rankings of all alternatives for the group with respect to each criteria and their final rankings. A supplier selection case illustrated the proposed method, and some discussions on the results verified its effectiveness. This work develops a new measurement of ordinal preferences’ inconsistency in multi-criteria group decision-making （MCGDM） and extends the cook-seiford social selection function to MCGDM considering weights of criteria and decision makers and can obtain unique ranking result.
A method of minimizing rankings inconsistency is proposed for a decision-making problem with rankings of alternatives given by multiple decision makers according to multiple criteria. For each criteria, at first, the total inconsistency between the rankings of all alternatives for the group and the ones for every decision maker is defined after the decision maker weights in respect to the criteria are considered. Similarly, the total inconsistency between their final rankings for the group and the ones under every criteria is determined after the criteria weights are taken into account. Then two nonlinear integer programming models minimizing respectively the two total inconsistencies above are developed and then transformed to two dynamic programming models to obtain separately the rankings of all alternatives for the group with respect to each criteria and their final rankings. A supplier selection case illustrated the proposed method, and some discussions on the results verified its effectiveness. This work develops a new measurement of ordinal preferences’ inconsistency in multi-criteria group decision-making （MCGDM） and extends the cook-seiford social selection function to MCGDM considering weights of criteria and decision makers and can obtain unique ranking result.
基金
supported by the National Natural Science Foundation of China (60904059
60975049)
the Philosophy and Social Science Foundation of Hunan Province (2010YBA104)
the National High Technology Research and Development Program of China (863 Program)(2009AA04Z107)
作者简介
Corresponding author.Wu Li was born in 1977. He is a Ph.D. and an associate professor in Hunan Institute of Science and Technology. His research interests are decision analysis and supply chain manage- ment. E-mail： liwu0817@ 163.comGuanqi Guo was born in 1963. He is a Ph.D. and a professor in Hunan Institute of Science and Technology. His research interests are computational intelligence and multiobjective optimization.Chaoyuan Yue was born in 1944. He is a professor and doctoral advisor in Huazhong University of Science and Technology. His research interests are group decision-making and social selection.Yong Zhao was born in 1967. He is a professor and doctoral advisor in Huazhong University of Science and Technology. His research interests are decision analysis and auction.
