Dynamic maintenance of variable precision fuzzy neighborhood three-way regions in interval-valued fuzzy decision system

As a typical generalization of classical rough set, variable precision fuzzy neighborhood rough set (VPFNRS) can effectively handle the datasets with noise. At the same time, the three-way regions induced by VPFNRS can determine some decision rules. However, data usually changes over time in real life, such as the addition of new objects and the removal of obsolete objects. Therefore, the rules determined by the three-way regions may change with time. To address this issue, we investigate the dynamic maintenance of the variable precision fuzzy neighborhood three-way regions under the background of interval-valued fuzzy decision system (IvFDS), aiming to effectively update the three-way regions in dynamic environment. Firstly, the δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta$$\end{document}-fuzzy neighborhood relation and its induced δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta$$\end{document}-fuzzy neighborhood class are defined. On this basis, a novel VPFNRS model suitable for IvFDS is proposed. Secondly, the variable precision fuzzy neighborhood three-way regions induced by the proposed model and its matrix representations are introduced. Subsequently, the matrix-based incremental mechanisms to update the three-way regions when the objects change are constructed. Meanwhile, corresponding incremental algorithms are designed. Finally, a series of numerical comparative experiments are executed on nine datasets, and the results indicate that incremental algorithms are not only effective, but also highly efficient under the dynamic data environment.