<p>Recently, concept-cognitive learning (CCL) is a hot topic in cognitive science and artificial intelligence. In particular, the cognitive results obtained via <i>L</i>-fuzzy concept-cognitive learning (LF-CCL) contain more comprehensive information derived from arbitrary cognitive clues and formal contexts. LF-CCL, as an effective concept cognitive strategy for discovering knowledge, has garnered significant attention. However, existing research on LF-CCL faces several challenges: rigid cognitive pathways and insufficient cognitive flexibility. Hence, to enhance the flexibility and evolutionary ability of LF-CCL, this paper proposes a novel <i>L</i>-fuzzy two-way concept-cognitive learning strategy (LF-DCCL) based on residuated implications from a divergent viewpoint. Specifically, the divergent viewpoint is introduced to LF-CCL to enhance the knowledge evolution ability of the cognitive strategy. The LF-DCCL strategy, different from the existing LF-CCL strategy, primarily focuses on the two-way evolution of <i>L</i>-fuzzy knowledge granules rather than the transformation of <i>L</i>-fuzzy information granules. Moreover, the corresponding algorithms are designed to enable knowledge acquisition via LF-DCCL in massive datasets and the decision value of LF-DCCL in financial investment applications is explored through case analysis. At the same time, our theoretical analysis has proven that different cognitive learning strategies will produce similar cognitive results after being used in multiple iterations. The results obtained from continuous learning and deep reflection on given information, based on specific cognitive circumstances and capabilities, are inherently limited and describable. Finally, we demonstrate the effectiveness and flexibility of the proposed strategy through case analysis and experiments on different datasets, thereby interpreting and facilitating the understanding of LF-DCCL.</p>