Multi-granulation fuzzy rough sets based on overlap functions with a new approach to MAGDM

Abstract

A common approach to constructing fuzzy rough sets (FRSs) is using t-norms. Furthermore, establishing multi-granulation fuzzy rough sets (MGFRSs) is also usually undertaken by means of t-norms. However, most of these sets cannot satisfy the property that upper approximations contain lower approximations under fuzzy binary relations, which is imperative for rough set models. The overlap function is a type of aggregate function that is widely used in multi-attribute decision-making (MADM), image processing and other fields. In this paper, two novel types of MGFRS models under n-dimensional overlap functions are established to overcome the shortcomings of existing models, which are then applied to the multi-attribute group decision-making (MAGDM) problem. First, idempotent n-dimensional overlap functions are used to establish optimistic and pessimistic MGFRSs. These new models fully preserve the important properties of the traditional MGFRS model. Second, through the theoretical analysis of MGFRS based on overlap functions (OMGFRS) and in combination with the TOPSIS method, a solution mechanism for the MAGDM method is proposed. Finally, to fully illustrate this decision-making method, an effective example is developed. A comparison with available methods indicates that this approach is more suitable and has wider adaptability, and that is can be used to handle decision-making problems.