Three-way conceptual knowledge updating in incomplete contexts

We usually encounter incomplete data in daily life due to the uncertainty of data and limitation of data acquisition technology. In formal concept analysis, the incomplete formal context is used to reflect uncertain relation between objects and attributes caused by missing data. The conceptual knowledge of the incomplete formal context is presented by a kind of three-way concept called partially-known formal concept. As time passes and technology matures, some initially missing data becomes obtainable, the incomplete formal context is updated accordingly, and the corresponding concepts change as well. However, obtaining partially-known concepts from the updated context based on definition is time-consuming and does not fully utilize the conceptual knowledge implicit in the original context. In order to make full use of existing conceptual knowledge and acquire new concepts quickly and efficiently, we discuss how to obtain new partially-known formal concepts by updating original partially-known formal concepts, and design corresponding concept updating algorithms. Finally, through data experiments, we validate that our proposed concept update algorithm can significantly improve the efficiency of concept acquisition, especially when the updating rate is small.