Under uncertain environment, how to deal with data with complex relationships has been a hot topic of research. Network formal context was proposed by the combination of an adjacency matrix and formal context, which is a useful tool for knowledge discovery and rule extraction. In this paper, we propose the concept of linguistic concept weighted network formal context (LCWNFC), which not only handles the fuzzy relationship between objects, but also solves the problem that people are used to expressing information by linguistic values. In order to describe formal concept based on LCWNFC more detailed and complete, we further define two object induced weighted network linguistic three-way concepts (weighted network OEL-concepts) and discuss related properties. In different cognition and environments, the criteria for determining whether there exist relationships between objects are different. Subsequently, two dynamic knowledge discovery algorithms are given based on LCWNFC, together with examples to illustrate the rationality and effectiveness of the proposed algorithms.