In this paper, the remuneration of fixed costs of distribution networks with distributed generation is evaluated by means of an efficient planning strategy that includes the concept of fuzzy robustness of a given solution plan. As a key contribution, it is included the possibility of choice among different conductor sizes in order to assess the deep costs by overcapacity introduced by distributed generation. A single-stage multicriteria nonlinear problem is stated using three different criteria: investment cost in lines and transformers or distributed generators, power losses cost and unserved energy cost. Pareto or efficient plans are identified using the -Constraint/Weighting method and solved by Benders decomposition algorithm.Uncertainty associated to load demand and power injections of distributed resources are integrated using a fuzzy power flow in order to obtain the robustness indexes of each Pareto solution. The annualized fixed charge rate (AFCR) associated to new and existing distribution lines and transformers or distributed generators is assessed through a with-without analysis permitting to compute the annual avoided charge rate (AACR) in order to send incentives or charges to distributed generation promoters by the avoided or added investment costs on the system. The model is programmed in GAMS mathematical modeling language. The effectiveness of the proposal is demonstrated through a real 201-node distribution network.