Over the last few years, composite indices for ranking or assessing country performance in a wide variety of complex phenomena, such as environmental sustainability, have gained a lot of popularity. However, not all indices allow for detailed spatio-temporal analyses. For instance, if individual indicators to be aggregated are normalized by the Min–Max method, they are converted to a common scale with a range of [0, 1] and it can be difficult to appreciate any absolute change in country performance at the extremes of the range (i.e., when a country scores 0 to 1). In this article, an alternative method for normalizing data in a three-way array of the type units × variables × times, is considered. It normalizes the range of individual indicators, similarly to the Min–Max method, but uses a common reference that allows to “center” them, without forcing them into a closed range. An application to renewable energy consumption data is also shown.

中文翻译：

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环境绩效时空分析的归一化方法：重新审视 Min-Max 方法

在过去几年中，用于在环境可持续性等各种复杂现象中对国家绩效进行排名或评估的综合指数已广受欢迎。然而，并非所有指数都允许进行详细的时空分析。例如，如果要汇总的单个指标通过 Min-Max 方法进行标准化，它们将转换为范围为 [0, 1] 的通用尺度，并且很难理解极端情况下国家表现的任何绝对变化范围的（即，当一个国家得分 0 到 1 时）。在本文中，考虑了一种在单位 × 变量 × 次类型的三路数组中规范化数据的替代方法。它规范化各个指标的范围，类似于 Min–Max 方法，但使用允许“居中”它们的通用参考，没有强迫他们进入一个封闭的范围。还显示了对可再生能源消耗数据的应用。