Cognitive maps (CMs) were initially for graphical representation of uncertain causal reasoning. Later Kosko suggested Fuzzy Cognitive Maps (FCMs) in which users freely express their opinions in linguistic terms instead of crisp numbers. However, it is not always easy to assign some linguistic term to a causal link. In this paper we suggest a new type of CMs namely, Belief Degree-Distributed FCMs (BDD-FCMs) in which causal links are expressed by belief structures which enable getting the links' evaluations with distributions over the linguistic terms. In addition, we propose a general framework to construct BDD-FCMs by directly using belief structures or other types of structures such as interval values, linguistic terms, or crisp numbers. The proposed framework provides a more flexible tool for causal reasoning as it handles any kind of structures to evaluate causal links.