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This paper proposes neutrosophic vague <i>N</i>-soft sets which is composed of neutrosophic vague sets and <i>N</i>-soft sets for the first time. The new hybrid model includes a pair of asymmetric functions: truth-membership and false-membership, and an indeterminacy-membership function. Some useful operations and propositions are given and illustrated by examples. Moreover, a method of priority relation ranking based on neutrosophic vague <i>N</i>-soft sets is presented. The validity of the method is verified by comparison. It is more flexible and reasonable to use this method in our daily life. Finally, a potential application of multi-attribute decision making is presented.