Four types of grey β-covering models and their applications

To handle the limitations of a fuzzy β-neighborhood, many researchers apply this notion to different structures to allow them to make a suitable decision in some real problems. In this article, we introduce the notions of grey β-neighborhood and grey complementary β-neighborhood, and then we establish the grey β-covering approximation space (GβCAS). The relevant characteristics are also examined. Furthermore, we construct two new GβCAS models to combine the definitions of a grey β-neighborhood and a grey complementary β-neighborhood and explain their relations. In addition, employing grey β-neighbourhoods, we investigate four types of β-neighbourhoods and use them to build four rough approximation models. Hence, in order to give a new approach to MADM in grey β-covering approximation space, we establish a novel methodology based on GCβAS models called multi-attribute grey decision making (MAGDM). Finally, with comparisons to current studies, a numerical example is given to demonstrate the feasibility and usefulness of our suggested methodologies.