Dynamical updating fuzzy rough approximations for hybrid data under the variation of attribute values

With the development of the Internet of Things (IoT), more and more hybrid data is being collected by information systems, which are known as Hybrid Information Systems (HIS). Based on a new hybrid distance, novel Gaussian kernel Fuzzy Rough Sets (FRS) for HIS were constructed in our previous study. In real-world applications, with the deepening of cognition and improvements in technology, attribute values in an information system often evolve over time; in particular, there are three cases: when missing values are imputed, error values are corrected, and the values are coarsened or refined. This has posed challenges to developing efficient data analysis algorithms. In this paper, the changing mechanisms of the attribute values and fuzzy equivalence relations in FRS are analyzed. FRS approaches for incrementally updating approximations in HIS are presented. Moreover, two corresponding incremental algorithms are developed. Finally, extensive experiments on eight data sets from the University of California, Irvine (UCI) and an artificial data set show that incremental approaches can effectively improve the performance of updating approximations and not only significantly shorten the computational time, but also increase approximation classification accuracies.