In this paper, we propose the use of compensatory fuzzy logic to extend mathematical morphology (MM) operators to gray-level images, in a similar way than fuzzy logic is used, naming it compensatory fuzzy mathematical morphology (CFMM). We study the compliance with the four principles of quantification and analyze the robustness of these operators by comparing them with Classic MM and fuzzy mathematical morphology (FMM), in the context of the processing of magnetic resonance images under noisy conditions. We observed that operators of CFMM are more robust, relative to noise, than MM and FMM ones, for the type of images used. As an additional result of this work, we developed a library for CFMM operators, plus an additional graphical user interface, which brings together the new operators with a wide range of operators of FMM and Classic MM.