Four types of grey β-covering models and their applications

To handle the limitations of a fuzzy fl-neighbourhood, 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 fl-neighbourhood and grey complementary fl-neighbourhood, and then we establish the grey fl-covering approximation space (GflCAS). The relevant characteristics are also examined. Furthermore, we construct two new GflCAS models to combine the definitions of a grey fl-neighbourhood and a grey complementary flneighbourhood and explain their relations. In addition, employing grey fl-neighbourhoods, we investigate four types of fl-neighbourhoods and use them to build four rough approximation models. Hence, in order to give a new approach to MADM in grey fl-covering approximation space, we establish a novel methodology based on GCflAS models called multi-attribute grey decision making (MAyDM). Finally, with comparisons to current studies, a numerical example is given to demonstrate the feasibility and usefulness of our suggested methodologies.