This paper describes a methodology for the construction of a multidimensional index for sustainability assessment in the context of the Sustainable Development Goals (SDGs) of the UN 2030 Agenda. The methodology is designed to properly capture the multidimensional nature of sustainable development and the SDG framework, introducing an innovative Fuzzy Multidimensional Index to measure the performance of Mediterranean countries. The focus is on agro-food sustainability, in-line with the aims of the Partnership for Research and Innovation in the Mediterranean Area (PRIMA). Drawing on fuzzy set theory, a step-by-step procedure was developed: the underlying dimensions of a set of selected indicators for the SDGs are identified by exploratory factor analysis; an innovative weighting method is applied to aggregate the indicators and calculate the country scores for each dimension and the Fuzzy Multidimensional Index. The PRIMA program will be a first step towards the implementation of innovative solutions, by funding international cooperation projects between countries on both sides of the Mediterranean for a decade: the Fuzzy Multidimensional Index will be the primary source of data for evaluating such projects and policies implemented from them; the Index will therefore be able to close a gap in the availability of appropriate data.