This paper focuses on the dataset-free Blind Image Super-Resolution (BISR). Unlike existing dataset-free BISR methods that focus on obtaining a degradation kernel for the entire image, we are the first to explicitly design a spatially-variant degradation model for each pixel. Our method also benefits from having a significantly smaller number of learnable parameters compared to data-driven spatially-variant BISR methods. Concretely, each pixel's degradation kernel is expressed as a linear combination of a learnable dictionary composed of a small number of spatially-variant atom kernels. The coefficient matrices of the atom degradation kernels are derived using membership functions of fuzzy set theory. We construct a novel Probabilistic BISR model with tailored likelihood function and prior terms. Subsequently, we employ the Monte Carlo EM algorithm to infer the degradation kernels for each pixel. Our method achieves a significant improvement over other state-of-the-art BISR methods, with an average improvement of 1 dB (2X). Code will be released.