Quasi-stationary sections of a deformable linear object (DLO) hanging freely from two extreme points can be modeled either by catenaries or parabolic curves, depending on the conditions of the UAVs. DLO transportation is an instance of a leader-follower platoon team strategy, in which the local quadrotor control must cope with the dynamic perturbations due to the DLO linking the quadrotors. The quadrotor team control has two phases, one achieving a spatial configuration with equal energy consumption, the other is to manage the horizontal motion which is the transportation process per se. We propose a Model Reference Adaptive Control (MRAC) for the quadrotors team, which uses fuzzy modeling of the error in order to modulate the activation of the adaptation rules applied to proportional-derivative (PD) controller parameters, which are derived as error gradient descent rules. In this paper, we contribute the parabolic representation of the DLO and improved follow the leader control, testing the MRAC stability and robustness under a series of experiments.