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The fundamental-measure theory (FMT) developed at the end of the 1980s for hard-sphere inhomogeneous fluids has revolutionized density functional theories (DFTs), allowing one to describe accurately for the first time highly confined fluids. However, in order to apply DFTs to real fluids, less rigorous coarse-graining approaches have always been used for perturbative contributions in addition to the FMT hard-sphere treatment. With the aim to propose a formally consistent description avoiding this duality, a possible route is the generalization of the fundamental-measure theory for potentials different from the purely hard repulsive term. This is the main purpose of this work, achieved considering the square-well fluid as initial case test. As a reference for the bulk fluid, the statistical associating fluid theory for the square-well monomer has been selected, and a suitable functional has been developed and validated through comparison against Monte Carlo molecular simulations. This opens up a new class of efficient non-local DFTs directly applicable to mixtures of complex fluids.

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