Abstract: In uncertain environments, the input and output values of DMUs are interval numbers. In order to solve the cross-evaluation problem of decision-making-units (DMUs) that is neither cooperative nor competitive, by taking the minimum sum of the average deviations forinput scores and output scores as the goal,two neutral models are constructed for evaluating DMUs under the best and worst production conditions. From the perspective of the proposed neutral models, the sum of the average deviations for input scores and output scores of the DMUs reaches the minimum. The research results show the effectiveness of the neutral interval cross efficiency models and solve the problem of neutral evaluation in uncertain environments, which can ensure the objectivity of evaluation and make the evaluation results more credible and realistic.

Key words: data envelopment analysis, interval number, deviation, neutral secondary goal

摘要： 在不确定性环境下,当决策单元(DMU)的投入产出数据为区间数形式时,为解决决策单元之间既不是合作也不是竞争关系时的交叉评价问题,本文提出一种中立型区间交叉效率模型。从所有被评价者的角度出发解决评价权重的选取问题,以决策单元投入得分的平均偏差与产出得分的平均偏差之和最小化为目标,建立决策单元在最佳和最差两种生产状态下的中立型区间交叉效率模型。在本文提出的中立型模型视角下,DMU的投入得分平均偏差和产出得分平均偏差之和达到最小。算例结果表明该中立型区间交叉效率模型的有效性,解决了不确定性环境下的交叉评价问题,保证评价的客观公正,更加符合现实。

关键词: 数据包络分析, 区间数, 偏差值, 中立型