A dynamic framework for updating neighborhood multigranulation approximations with the variation of objects Abstract   Rough approximations play a significant role in rule extraction and decision making. However, rescanning the entire data set to update the approximations is timeconsuming due to the dynamic characteristics of objects in a neighborhood multigranulation space. In order to reduce the computational time, the neighborhood multigranulation approximations need to be updated in an incremental manner based on previously saved knowledge. Therefore, in this study, we establish a dynamic framework for maintaining the positive, boundary, and negative regions in neighborhood multigranulation spaces when adding or deleting objects from the matrix perspective. First, we explore the incremental mechanisms for updating relevant matrices when adding or deleting multiple objects. Based on the proposed mechanisms, we design the corresponding dynamic algorithms to incrementally update the positive, boundary, and negative regions. Finally, we conduct empirical experiments on benchmark UCI data sets to assess the feasibility and efficiency of our updating algorithms, which demonstrate their promising performance.

A neighborhood rough set model with nominal metric embedding Abstract   Rough set theory is an essential tool for measuring uncertainty, which has been widely applied in attribute reduction algorithms. Most of the related researches focus on how to update the lower and the upper approximation operator to match data characteristics or how to improve the efficiency of the attribute reduction algorithm. However, in the nominal data environment, existing rough set models that use the Hamming metric and its variants to evaluate the relations between nominal objects can not capture the inherent ordered relationships and statistic information from nominal values due to the complexity of data. The missing information will affect the accuracy and validity of the data representation, thereby reducing the reliability of rough set models. To overcome this challenge, we propose a novel object dissimilarity measure, i.e., relative object dissimilarity metric(RODM) that learned from nominal data to replace the Hamming metric and then construct a xcfx88neighborhood rough set model. It extends the classical rough set model to a robust, representative, and effective model which is close to the characteristics of nominal data. Based on the xcfx88neighborhood rough set model, we propose a heuristic twostage attribute reduction algorithm(HTSAR) to perform the feature selection task. Experiments show that the xcfx88neighborhood rough set model can take advantage of more potential knowledge in nominal data and achieve better performance for attribute reduction than the existing rough set model.