The debate on the choice of the ideal spatial weights matrix (W) is long-standing in applied spatial statistics and econometrics. While some authors point out aspects related to possible misspecification from the choice of the wrong W, others suggest that there is little difference in practical and interpretation terms at least between geography-based spatial weights matrices. A particular difficulty in defining W may therefore emerge especially when it may imply spillovers based not only on geography, but also on socio-economic variables (for instance, differences in the endowment of amenities or industrial activity). Even when guessing correctly the factors behind W, defining the way they influence spillovers may be particularly difficult. To this aim, we propose an approach to defining W based on fuzzy logic, which allows to deal in a flexible way with its numerical specification. We set up Monte Carlo simulations to evaluate how a fuzzy W can approximate different types of spatial weights matrices, and in settings with spatial dependence of different strength, with particular reference to the estimation of the regression coefficients.