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We present a novel surrogate modeling methodology based on a combination of space mapping and fuzzy systems. Fine model data, the so-called base set, is assumed available in the region of interest. Although we do not assume any particular location of the base points, it is preferable that they form a uniform mesh. The standard space-mapping surrogate is established using available fine model data. The fuzzy system is then set up to interpolate the differences between the space-mapping surrogate and the fine model at all base points. Our new methodology offers significant advantages with respect to some of the previous space-mapping approaches to modeling, which are: (1) it handles any base set and (2) the number of space-mapping parameters does not limit the accuracy of the surrogate. Moreover, it exhibits comparable or better accuracy than the recently published modeling technique utilizing space mapping and radial basis functions. We also consider a hierarchical fuzzy space-mapping modeling, which relies on a fuzzy interpolation of space-mapping parameters and subsequent fuzzy interpolation of the residuals between the fine and surrogate model. Examples demonstrate the robustness of our approach and give a comparison with other space-mapping-based modeling techniques.