The multi-fuzzy N-soft set and its applications to decision-making

The goal of this paper is to introduce a novel hybrid model called multi-fuzzy N -soft set, and to design an adjustable decision-making methodology for solving problems where the inputs appear in this form. The new model enhances the virtues of multi-fuzzy set theory with the benefits of N -soft sets, two models that have been extensively investigated in recent years. The theoretical setting that arises allows us to incorporate data on the occurrence of ratings or grades (the defining characteristic of N -soft sets) in a multi-fuzzy environment. We perform a set-theoretical analysis of multi-fuzzy N -soft sets in order to establish the fundamental properties of their behavior. Then we develop a highly adaptable approach to decision-making in this new setting. This methodology takes advantage of a flexible procedure for the conversion of the original data to a hesitant N -soft setting, where we can resort to scores. Examples illustrate its application and the role of each parameter in the decision-making procedure.