Picture Fuzzy N-Soft Sets and Their Applications in Decision-Making Problems.

In this article, firstly, we describe picture fuzzy N-soft sets (PFN-SSs) as a generalization of picture fuzzy sets (PFSs) and N-soft sets (N-SS) by observing that one of the essential concept of neutral grade is missing in intuitionistic fuzzy N-SS (IFN-SS) theory. The concept of neutrality grade can be observed in the situation when we encounter human views including more answers of type: yes, abstain, no, refusal. For instance, in election the election commission or election council issues voting papers for the candidate. The voting outcomes are categorized into 4 groups with the number of papers namely, vote for, abstain, vote against, and refusal voting. Further, We define the fundamental properties of PFN-SS and introduce M-subset, F-subset, compliment, intersections, unions, of PFN-SS and give their examples. Secondly, we define an algorithm to cope with PFN-SS data which is more generalized then the algorithm defined for IFN-SS. To show the advantage and usefulness of the defined technique, we give two examples from real life by utilizing PFN-SS data. The result shows in the comparison that our initiated method is more general and suitable than the IFN-SS, fuzzy N-SS (FN-SS), and N-SS. [ABSTRACT FROM AUTHOR]