Therefore, the paper is organized as follows. Section II describes the network design problem at hand and two mixed integer linear models. In section III, we tackle the nodesegment model with fuzzy constraints and propose an effective approach to solve it. Section IV shows the segment-path model with imprecise coefficients in the constraints and the approach we propose to solve it. Section V explains heuristic methods used to solve the problems that arise in the two previous sections. Finally, section VI summarizes the computational experience carried out over both real and random instances that corroborates the effectiveness of the proposed methodologies