Concepts have been adopted in concept-cognitive learning (CCL) and conceptual clustering for concept classification and concept discovery. However, the standard CCL algorithms are incapable of tackling continuous data directly, and some standard conceptual clustering methods mainly focus on the attribute information, ignoring the object information that is also important to improve clustering analysis and concept classification ability. Therefore, in this article, we present a novel concept learning method, called the fuzzy-based concept learning model (FCLM), to address these two issues by exploiting concept hierarchical relations in concept lattices. More specifically, we first show some new related notions for FCLM based on a regular fuzzy formal decision context; among these notions, the object-oriented and attribute-oriented fuzzy concept similarities are used to achieve the concept similarity measure in concept lattices. Moreover, a novel fuzzy concept learning framework is designed, and its corresponding learning algorithms are developed. Finally, we conduct some experiments on various real-world datasets to demonstrate that the proposed method can achieve the state-of-the-art classification performance among similarity-based learning methods. In addition, we further verify the effectiveness of our method in concept discovery on the MNIST dataset.