Granular computing (GrC) and two-way concept learning (TCL) are influential studies of knowledge processing and cognitive learning. A central notion of two-way concept learning is learning concepts from an arbitrary information granule. Although TCL has been widely adopted for concept learning and formal concept analysis in a fuzzy context, the existing studies of TCL still have some issues: 1) the sufficient and necessary granule concept is only obtained from the necessary granule or sufficient granule concept; 2) the cognitive mechanism ignores integrating past experiences into itself to deal with dynamic data. Meanwhile, concept-cognitive learning (CCL) method still faces challenges, such as incomplete cognitive and weak generalization ability. This paper proposes a novel two-way concept-cognitive learning method for dynamic concept learning in a fuzzy context for these problems and challenges. Unlike TCL, fuzzy-based twoway concept-cognitive learning (F-TCCL) is more flexible and less time-consuming to learn granule concepts from the given clue, and meanwhile, it is good at dynamic concept learning. Moreover, we design a fuzzy-based progressive learning mechanism within this framework under the dynamic environment. Some numerical experiments on public datasets verify the effectiveness of our proposed method. The considered framework can provide a convenient novel method for researching two-way learning and concept-cognitive learning.

Concept-cognitive learning (CCL) and three-way decision (3WD) models provide powerful techniques for knowledge discovery. Some early attempts in the field have successfully combined CCL and 3WD, i.e., three-way concept learning. However, only a few attempts were made to combine CCL with 3WD in a dynamic fuzzy context due to two challenges: 1) three-way concept-cognitive learning incapability; 2) the current incremental three-way concept learning mechanism is insufficient to model real-time updating cognitive procedure. Hence, this paper first shows some new standpoints on improving fuzzy based CCL accuracy and then proposes fuzzy-granular three-way concept-cognitive learning (F3WG-CCL) for concept modeling and dynamic knowledge learning. Specifically, we first define a new F3WG-concept to characterize the knowledge embedded in fuzzy data. Furthermore, a big concept priority principle and an update mechanism are borrowed for concept recognition and dynamic concept cognition. Finally, we show that F3WG-CCL can be implemented simultaneously via theoretical guarantee and sufficient experimental, including 1) achieving state-of-the art dynamic knowledge learning; 2)demonstratingthatthethreeway concept is effective in a fuzzy context; 3) discovering that the big concept is valuable for fuzzy concept recognition. Our work will provide a powerful approach to research fuzzy-based CCL and dynamic knowledge discovery