Robust Optimization of Best-worst Multi-criteria Decision-making Method
The Best-worst multi-criteria decision-making method can determine optimal weight value of each criteria. It uses two vectors for pairwise comparisons in multi-criteria decision-making problem. This paper improves the original method from the perspective of robust optimization. Four robust counterpart constraints instead of two linear constraints in original optimization model are proposed. The decision-making problem can divide into full consistent and non-full consistent problems by classifying parameter value. We can achieve a unique set of interval solution in full consistent decision-making problem. Non-full consistent problem can result in multiple sets of optimal interval solution. The result which we get from this method is more effective than the original method. Each criterion can achieve optimal weight interval value. Then we take quantile value of each interval as optimal weight. This is effectively illustrated in the numerical test at the end of the paper.
M.V. Kumar, M. Ramkumar, S. Digjoy. A Multi-Criteria Decision-Making Ap-proach for the Urban Renewal in Southern India. Sustainable Cities and Society, 42(2018), 471-481.
C.J. Li, M. Negnevitsky, X. Wang, W. Yue, X. Zou. Multi-criteria analysis of policies for implementing clean energy vehicles in China. Energy Policy, 34(2019), 826-840.
G. Tré, R. De Mol, A. Bronselaer. Handling veracity in multi-criteria decision-making: A multi-dimensional approach. Information Sciences, 65(2018), 541-554.
X. Gou, Z. Xu, H. Liao et al. Multiple Criteria Decision Making based on Distance and Similarity Measures under Double Hierarchy Hesitant Fuzzy Linguistic environment. Computers & Industrial Engineering, 35(2018), 516-530.
R. Jafer Best-Worst Multi-Criteria Decision-Making Method. Omega, 53(2015), 49-57.
Q. Mou, Z. Xu, H. Liao, et al. An intuitionistic fuzzy multiplicative best-worst method for multi-criteria group decision making. Information Sciences, 374(2016), 224-239.
S. Guo, H. Zhao. Fuzzy best-worst multi-criteria decision-making method and its applications. Knowledge-Based Systems, 32(2017), 23-31.
H. Martin, G. Marc, W. Michael. A largest empty hypersphere metaheuristic for robust optimization with implementation uncertainty. Computers & Operations Research, 65(2019), 64-80.
M. Kaedi, C. Ahn. Robust Optimization Using Bayesian Optimization Algorithm: Early Detection of Non-robust Solutions. Applied Soft Computing, 121(2017), 1125-1138.
L. Marla, V. Vaze, C. Barnhart. Robust Optimization: Lessons Learned from Aircraft Routing. Social Science Electronic Publishing, 55(2017), 165-184.
R. Jafar. Best-worst multi-criteria decision-making method: Some properties and a linear model. Omega, 44(2016), 126-130.