<p>Climate finance is central to making the Paris Agreement work, and the New Collective Quantified Goal (NCQG) of at least USD 300 billion per year by 2035 agreed at COP29 in Baku intensifies the long-standing challenge of sharing a collective effort across countries in a way that is seen as fair. This paper proposes a fuzzy multi-criteria goal programming (FMGP) framework to allocate the NCQG across potential contributors. Building on earlier linear multi-criteria work, it treats four equity dimensions often invoked in climate finance debates – responsibility (historical or current emissions), economic capacity (total or per capita income), population and innovation effort – as fuzzy goals rather than rigid constraints. Each goal is represented by a membership function and an aspiration range, and the model searches for allocations that maximise a common satisfaction index while respecting the NCQG envelope. Using 2022 data, the analysis combines four fairness metrics (cumulative versus current emissions and total versus per capita GDP) with five contributor scenarios that gradually widen the pool from a narrow group of traditional donors to a broader coalition including the United States, Gulf states and major emerging economies. The results show that metrics linking cumulative emissions to income, in particular a hybrid specification using cumulative emissions and GDP per capita, generate more balanced and politically plausible contribution profiles than metrics based only on current emissions, and that widening the contributor base spreads the burden but reduces the degree to which equity goals can be satisfied simultaneously. Compared with a linear benchmark, the fuzzy model produces less extreme obligations and narrower contribution ranges, indicating that making “fairness” explicitly fuzzy can support the design of NCQG burden-sharing arrangements that are both transparent and negotiable in the Baku–Belém phase.</p>