Concept-cognitive learning (CCL) is an emerging field for studying the representation and processing of knowledge embedded in data. Many efforts are focused on this field due to the interpretability and effectiveness of the formal concept (not pseudo concept). However, the standard CCL methods cannot tackle continuous data directly. Although the current fuzzy-based CCL (FCCL) is a straightforward approach to discovering the knowledge embedded in continuous data, it does not sufficiently utilize the native advantage of concepts in simulating the cognitive mechanism. Then it causes it to be incomplete and complex cognition. Inspired by the memory mechanism, this paper combines the recalling and forgetting mechanisms with CCL, called memory-based concept-cognitive learning (M-FCCL). Specifically, a cosine measure is introduced to describe the relationship of samples and construct cosine-similar granules to learn the concept. Subsequently, a fuzzy three-way concept based on the cosine similar granules is defined to represent and discover knowledge. Furthermore, two memory mechanisms are borrowed for the process of concept cognition for dynamic data classification and knowledge fusion: concept-recalling can enhance the effectiveness of concept learning, and concept-forgetting can effectively reduce the complexity of concept cognition. Finally, some experiments are compared with other methods on 16 benchmark datasets to show that M-FCCL achieves superior performance. Specifically, on these datasets, the proposed M-FCCL method achieves 17.02% and 18.54% classification accuracy gain compared with some advanced CCL mechanisms and popular classification methods.