针对传统语言群决策方法专家权重难以合理求取且决策属性值为不确定语言变量的问题，提出一种基于蒙特卡洛经验模态分解（Mentor Carlo-Empirical Mode Decomposition， MC-EMD）提取专家语言评价信息的多属性大群体决策方法。考虑专家期望偏差越小为宜，建立偏差最小单目标优化模型求解属性权重；运用EMD方法分解各专家的综合语言评价值，得到客观趋势成分和主观随机成分，以客观趋势成分的均值作为评价结果；鉴于不同专家顺序可能有不同的分解结果，从而导致评价结果的不确定性，基于蒙特卡罗思想随机抽取专家排序，通过计算模拟获取专家评价的总体客观趋势，并借以进行方案优选排序。案例分析验证了该方法的有效性和可行性。
Traditional linguistic group decision-making (GDM) methods are usually required to determine decision makers' (DMs') weights, by which the assessment information of all DMs can be aggregated. However, the weighting methods are generally of different judgment scale, and they also have too much man-made subjectivism. Meanwhile, uncertain linguistic assessment information is practically convenient and demanded when applied to large GDM. Accordingly, a method for multi-attribute large GDM with uncertain linguistic assessment information is proposed in this paper, based on Mentor Carlo empirical mode decomposition (MC-EMD).
First of all, uncertain additive linguistic variables and their expected deviation are defined, and a unified approach for hybrid assessment information, which is due to different assessment scale, is also presented. Then, considering that the DMs' expected deviation is usually required as small as possible when GDM with linguistic assessment information, a single-objective optimization model based on minimum deviation is established to compute the attribute weights. After that, the empirical mode decomposition (EMD) method, which can preferably decompose nonlinear and non-stationary time series, is used to decompose the DMs' comprehensive linguistic assessment value sequence, thus the subjective random components and objective trend components can be acquired, and the mean value of objective trend components is regarded as GDM result. Furthermore, considering that the DMs' comprehensive linguistic assessment value sequence do not have time series characteristic and the sequence permutation is randomly generated, different sequence permutation may have different EMD decomposition results (also may not result in decomposition), thus leading to the uncertainty of GDM result, in this paper, the DMs' comprehensive linguistic assessment value sequence permutations are randomly generated by Monte Carlo (MC) method, let p(1 ≤ p ≤ r!, r is the number of DMs, generally r>11) be the preset random sampling number of MC, computational simulation method is used to find an appropriate p, which can ensure a lower volatility of the overall objective tendency of DMs' assessment information and a higher stability of the alternatives ranks, and by which the best alternative can be chosen. A specific case is presented at the end of this paper to illustrate the effectiveness and feasibility of the proposed method. Compared with information integration methods of traditional linguistic GDM, the MC-EMD method extracts assessment information directly without determining DMs' weights, to eliminate the subjective factors influence to a greater extent, thus the GDM result is more coincident with the objective assessment law. Additionally, the GDM algorithm of this paper can be conveniently organized to execute and also be easily achieved by programming in computer, therefore, it is especially applicable for the emergency decision-making.
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