This paper is concerned with the development of a procedure to automatically calculate the parameters of weighting functions used in the design of a H_∞ controller for a Dynamic Positioning System, seeking to achieve a desired system performance. The H_∞ synthesis problem is formulated as a multi-criterion optimization problem. A Genetic Algorithm is then employed to search for suitable solutions. To cope with the imprecision and vagueness that arises in the description of objective functions, and constraints of the process and actuators, concepts from the fuzzy logic are incorporated into the solution. A multi-objective fuzzy optimization is stated and a fuzzy convex decision-making is established.