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Malmquist Productivity Index with Grey Data

机译：灰色数据的Malmquist生产率指数

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Malmquist Productivity Index (MPI) is widely used method to measure the productivity changes of Decision Making Units (DMUs) between two time periods. Although the conventional MPI requires accurate data, in many real life conditions the input and output data of DMUs usually involve uncertainty and only lower and upper bounds of data could be obtained. Grey (number) theory is one of the theories which are used for describing uncertainty. A grey number, with both a lower and upper bounds, is called an interval grey number. The purpose of this paper is to measure the productivity changes under uncertainty conditions based on the interval grey number theory. In the paper, new grey MPI models are proposed to measure productivity changes of DMUs which have interval data. A numerical example is provided to illustrate the application of the proposed models. Results of the numerical example show us that the proposed models are easy to handle and applicable for real life problems.
机译：Malmquist生产率指数（MPI）被广泛用于测量两个时间段之间决策部门（DMU）生产率的变化。尽管常规的MPI需要精确的数据，但在许多现实生活中，DMU的输入和输出数据通常都具有不确定性，并且只能获得数据的上下限。灰色（数字）理论是用于描述不确定性的理论之一。具有上下限的灰度数称为间隔灰度数。本文的目的是基于区间灰数理论来测量不确定条件下的生产率变化。在本文中，提出了新的灰色MPI模型来测量具有间隔数据的DMU的生产率变化。提供了一个数值示例来说明所提出模型的应用。数值例子的结果表明，所提出的模型易于处理，适用于现实生活中的问题。

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