Abstract In this paper we present a fuzzy multidimensional approach for the measurement of the ‘leaving no one behind’ principle underlying the Sustainable Development Goals (SDGs) in European countries. In particular, we consider a two-step procedure. First, we compute the degree to which an individual is ‘left behind’ in each specific dimension. We then propose alternatives to measure the extent to which an individual is ‘left behind’ in a multidimensional setting. We illustrate our proposal taking as a reference the ‘at risk of poverty or social exclusion’ (AROPE) framework (dimensions, indicators and union criteria). The results highlight that although the average ‘left behind’ (LB) level and AROPE are largely consistent across European countries, our fuzzy measure provides valuable additional information, both in individual and aggregate terms, on persons who are further away from those better positioned and how far they are.

中文翻译：

---

衡量欧洲国家“不让任何人掉队”的原则：一种基于 AROPE 的模糊逻辑方法

摘要 在本文中，我们提出了一种模糊多维方法，用于衡量欧洲国家可持续发展目标 (SDG) 背后的“不让任何人掉队”原则。特别地，我们考虑一个两步程序。首先，我们计算个人在每个特定维度上“落后”的程度。然后，我们提出替代方案来衡量一个人在多维环境中“落后”的程度。我们以“处于贫困或社会排斥风险”(AROPE) 框架（维度、指标和工会标准）为参考来说明我们的提案。结果强调，尽管欧洲国家的平均“落后”（LB）水平和 AROPE 基本一致，但我们的模糊测量提供了有价值的附加信息，