This document developed a fuzzy supervisory control based on fuzzy logic for a four-Tank multivariable system. A hierarchical control structure was established which basic principle is to decompose and coordinate highly complex systems and work them as subsystems. This hierarchical system was shaped by two layers. The first was a supervisory layer, in which initially the variable with major weight was found within the process to establish a hierarchy of variables, this was calculated through the decomposition into singular values of the Hankel matrix, also, considering the behavior of the plant in face of reference changes, it was sought to retune in line the parameters of the controllers arranged in the regulatory layer, this using fuzzy logic. The regulatory layer is the one that receives the parameters, which worked with independent control loops based on the structure of PID controllers that regulated the behavior of the four-Tank system.