The optimization of the consecutive-k-out-of-n system is to find the optimal assignment of components that maximizes the system reliability. Many efforts have been devoted to the component assignment problems (CAPs) for such systems, however, uncertainties about the reliability data of components and the system structure have never been deeply studied in CAPs. Due to the insufficiency of relative data and system complexities, uncertainties inevitably exist in many real engineering problems. This paper extends the LK heuristic using a non-probabilistic graphical model called evidential network, and interval-valued importance measures to perform the optimization of linear consecutive-k-out-of-n: F systems under parametric uncertainty (related to the reliability data of components) and model uncertainty (related to the system structure). The extended LK heuristics are applied to an oil pipeline system and an illustrative example system to show their feasibility and applicability. The originality of this work lies in the extension of the CAPs to consider different kinds of uncertainties and the proposition of heuristics to find the near optimal assignment of components under uncertainties according to the preference level of the decision maker.