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"Leaving no one behind" (LNOB) constitutes one of the core principles underpinning the 2030 Agenda for Sustainable Development. We propose a complementary fuzzy logic approach to identify countries left behind in human development and each of its dimensions. We find that the countries left furthest behind at the beginning of the century were those that most reduced gaps with respect to better performing countries after two decades. Nevertheless, we cannot clearly speak of convergence in human development. There are notable exceptions, such as the Central African Republic, Liberia, Yemen, Haiti or Venezuela, which despite the improvement in their Human Development Index worryingly increased their gaps in human development dimensions relative to the rest of the world. Our analysis highlights significant advantages of using the proposed fuzzy-based LNOB approach to incorporate the moral imperative of leaving no country behind in the measurement of human development. [ABSTRACT FROM AUTHOR]