Picture m-polar fuzzy soft sets and their application in decision-making problems

The aim of this paper is to introduce a new multiple attribute decision-making model named picture m-polar fuzzy soft sets, which is a combination of the soft sets and picture m-polar fuzzy set. Some operations and properties of the new model, including subset, equality, union, intersection, and complement are discussed.Further, the basic six definitions, three theorems, and six examples on picture m-polar fuzzy soft sets are explained. Lastly, we construct a new methodology to extend the TOPSIS to picture m-polar fuzzy soft sets (i.e., an application of  picture m-polar fuzzy soft sets) in which capable of different objects recognizing belonging to the same family is constructed and illustrated its applicability via a numerical example.