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Keywords = minimax regret approach

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14 pages, 577 KiB  
Article
Linguistic Multiple-Attribute Decision Making Based on Regret Theory and Minimax-DEA
by Jinyi Hu
Mathematics 2023, 11(20), 4259; https://doi.org/10.3390/math11204259 - 12 Oct 2023
Viewed by 1391
Abstract
Given that most current linguistic multiattribute decision-making methods do not consider the optimal efficiency of decision-making units and the psychological behavior of decision makers, a linguistic multiattribute decision-making method based on regret theory, data envelopment analysis, and the minimax reference point method is [...] Read more.
Given that most current linguistic multiattribute decision-making methods do not consider the optimal efficiency of decision-making units and the psychological behavior of decision makers, a linguistic multiattribute decision-making method based on regret theory, data envelopment analysis, and the minimax reference point method is proposed. First, based on the decision-maker psychology of regret and avoidance, the perceived utility value of each decision-making unit was calculated using the language regret–joy value function. The subjective and optimal efficiency values of each decision-making unit were obtained using the subjective weighting and data envelopment analysis methods, respectively. Next, we considered the best efficiency as the reference point and the subjective efficiency as the decision preference to establish a minimax reference point model. By solving the model, a set of public weights that minimizes the difference between the efficiency values of all decision-making units and their optimal efficiency values can be obtained to sort the decision-making units and select the best. The feasibility of the method was verified using an example of employee evaluation and selection; the effectiveness of the method was demonstrated through comparative analysis with other methods. Full article
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18 pages, 943 KiB  
Article
Robust Parameter Estimation Framework of a Rainfall-Runoff Model Using Pareto Optimum and Minimax Regret Approach
by Yeonjoo Kim, Eun-Sung Chung, Kwangjae Won and Kyungik Gil
Water 2015, 7(3), 1246-1263; https://doi.org/10.3390/w7031246 - 18 Mar 2015
Cited by 11 | Viewed by 6406
Abstract
This study developed a robust parameter set (ROPS) selection framework for a rainfall-runoff model that considers multi-events using the Pareto optimum and minimax regret approach (MRA). The calibrated parameter sets based on the Nash-Sutcliffe coefficient (NSE) for two events were derived using a [...] Read more.
This study developed a robust parameter set (ROPS) selection framework for a rainfall-runoff model that considers multi-events using the Pareto optimum and minimax regret approach (MRA). The calibrated parameter sets based on the Nash-Sutcliffe coefficient (NSE) for two events were derived using a genetic algorithm. We generated 41 combinations for weighting values between two events for the multi-event objective function and derived 41 Pareto optimum points that were considered as the ROPS candidates. Then, two different approaches for parameter selection were proposed to determine the ROPS among the candidates: one uses NSE only and the other uses four performance measures (NSE, peak flow error, root mean square error and percentage of bias). In the NSE-only method, five events, including two events from the calibration set and three events from the evaluation set, were used, and the ROPS was selected based on the regrets of both the calibration and the evaluation sets. In the multiple (i.e., four) performance measure method, only three events from the evaluation set were used and the ROPS was determined based on the regrets of twelve different cases, including three events with four measures. As a result, while single- and multi-event optimizations produced satisfying results for the calibration events, the optimized parameters from the single-event calibration do not perform well for another event, even one with the same criteria, such as NSE. The results of this study suggest that the optimized parameter set from the well-weighted objective function can successfully simulate not only hydrographs in general but also others, such as peak flow. In addition, the ROPS can be selected by considering the multiple performance measures of multiple validation events, as well as the NSE only of multiple calibration and validation events. Note that the study provides a framework that could be performed reasonably well with a limited number of events. While the computational resources might not be a limiting factor these days, it is still valuable to have such a tool for several reasons: one could utilize it for an operational decision making support tool, as the full searches for an optimal set of parameters might not be performed in the operational facility. It could also be used in a situation where one has a limited number of good-quality observational data for some reason. Full article
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