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Harnessing renewable energy (RE) sources to power desalination systems can migrate the pressures of freshwater scarcity and fossil fuel depletion. In this paper, a novel mathematical framework was developed to assess the sustainability of different RE-powered desalination systems, which is very essential for their portfolio selection, by resorting to the fuzzy multi-attribute decision making (MAMD) methods. In the framework, an evaluation system including ten attributes from four dimensions is introduced, while fuzzy triangular numbers and interval values are employed to capture the epistemic and aleatory uncertainties of decision information, respectively. More importantly, three fuzzy MADM methods were proposed in the framework to make the following methodological contributions: (1) fuzzy decision-making trial and evaluation laboratory-based analytic network process (DANP) offers a reliable weighting result by addressing the interrelationships among the attributes; (2) fuzzy full consistency method (FUCOM) can easily but rigorously quantify the qualitative attributes by using the simplified pair-wise comparisons; (3) interval vector-aided technique for order of preference by similarity to ideal solution (VATOPSIS) generates a rational ranking sequence by incorporating the balance among multi-attributes. To illustrate the proposed framework, six RE-powered desalination systems were studied, showing that the solar thermal-powered multi-effect distillation would be the best option under current conditions. Finally, the effectiveness and advantages of the proposed framework were verified by results comparison and discussion. Image 1 • A framework was proposed to assess the sustainability of RE-powered desalination. • The mathematical framework can address both the epistemic and aleatory uncertainties. • A fuzzy DANP approach was used to assign the weights to the interrelated attributes. • A fuzzy FUCOM method was developed to easily quantify the qualitative attributes. • An interval VATOPSIS method was introduced to rationally rank the alternatives. [ABSTRACT FROM AUTHOR]