Dynamic fuzzy neighborhood rough set approach for interval-valued information systems with fuzzy decision

Nowadays, many extended rough set models are proposed to acquire valuable knowledge from interval-valued information system. These existing models mainly focus on different forms of similarity relations. However, most of these similarity relations are qualitative rather than quantitative, which is not reasonable in some practical cases. In addition, with the arrival of new objects and the removal of obsolete objects, the interval-valued information system with fuzzy decision (IvIS_FD) is always changing with time. Therefore, how to efficiently mining knowledge from dynamic IvIS_FD is a meaningful topic. Motivated by these two issues, we study the dynamic fuzzy neighborhood rough set approach for IvIS_FD, aiming to effectively update the rough approximations when the IvIS_FD evolves over time. Firstly, δ -fuzzy neighborhood relation is defined to describe the similarity relation between objects quantitatively. Secondly, we introduce a novel fuzzy neighborhood rough set model and its matrix representation suitable for IvIS_FD. On this basis, we discuss the incremental mechanisms to update fuzzy neighborhood approximations when multiple objects are added to or deleted from an IvIS_FD, respectively. Meanwhile, corresponding dynamic algorithms are designed and explained. Finally, experiments are performed on nine public data sets to evaluate the performance of the dynamic fuzzy neighborhood rough set model. Experimental results verify that the proposed model is effective and efficient for updating rough approximations in dynamic IvIS_FD.