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The optimal group consensus models for 2-tuple linguistic preference relations

机译：二元组语言偏好关系的最优群体共识模型

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摘要

We establish in this paper the optimization model of group consensus of 2-tuple linguistic preferential relations (LPRGCO Model), put forward three kinds of solutions to this model, and discover in it the convergence of group consensus. To detect the LPRGCO Model, we first build two kinds of optimal matrices as standards to measure the group consensus of 2-tuple linguistic preference relations (LPRs). And to analyze consensus deviations, we then adopt three types of measures, namely, the individual degree of consistency regarding alternative decision pairs, the deviational degree of the group consensus regarding alternative decision pairs, and the degree of group consensus regarding the original 2-tuple LPRs. On the basis of the previous analysis we not only construct an optimization model to probe into the deviation of the group consensus of 2-tuple LPRs by minimizing the weighted arithmetic average of deviation degrees of individual consistency, but also point out three feasible solutions to this optimization model: the optimal solution, satisfactory solutions, and non-inferior solutions. Accordingly, we discover different conditions in terms of the three solutions. And hence, we can from the aforementioned discussion draw a conclusion that the deviation of group consensus either decreases or stays invariant as the number of decision makers (DM) increases. To expatiate on the practical value of the model proposed, we will display in this paper numerical examples.
机译：本文建立了二元语言优先关系的群体共识优化模型（LPRGCO模型），提出了该模型的三种解决方案，并在其中发现了群体共识的收敛性。为了检测LPRGCO模型，我们首先建立两种最优矩阵作为标准，以测量2元组语言偏好关系（LPR）的群体共识。为了分析共识偏差，我们采用三种类型的度量，即关于备选决策对的个体一致性程度，关于备选决策对的小组共识偏差程度以及关于原始2元组的小组共识程度LPR。在前面的分析的基础上，我们不仅构造了一个优化模型，通过最小化个体一致性偏差度的加权算术平均值，来探讨2元组LPR的群体共识偏差，并且为此指出了三个可行的解决方案。优化模型：最优解，满意解和非劣等解。因此，我们根据三种解决方案发现了不同的条件。因此，我们可以从前面的讨论得出一个结论，即随着决策者（DM）数量的增加，群体共识的偏差会减小或保持不变。为了说明所提出模型的实用价值，我们将在本文中显示数值示例。

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