The berth allocation problem (BAP) in a marine terminal container is defined as the feasible berth allocation to the incoming vessels. In this work, we present two models of fuzzy optimization for the continuous and dynamic BAP. The arrival time of vessels are assumed to be imprecise, meaning that the vessel can be late or early up to a threshold allowed. Triangular fuzzy numbers represent the imprecision of the arrivals. The first model is a fuzzy MILP (Mixed Integer Lineal Programming) and allow us to obtain berthing plans with different degrees of precision; the second one is a model of Fully Fuzzy Linear Programming (FFLP) and allow us to obtain a fuzzy berthing plan adaptable to possible incidences in the vessel arrivals. The models proposed has been implemented in CPLEX and evaluated in a benchmark developed to this end. For both models, with a timeout of 60 min, CPLEX find the optimum solution to instances up to 10 vessels; for instances between 10 and 45 vessels it find a non-optimum solution and for bigger instants no solution is founded.