The purpose of this paper is to define n-Fuzzy sets and study their relationship with intuitionistic fuzzy sets, Pythagorean fuzzy sets and Fermatean fuzzy sets. The n-Fuzzy sets can deal with more uncertain situations than intuitionistic fuzzy sets, Pythagorean fuzzy sets and Fermatean fuzzy sets because of its larger range of describing the membership grades. The set operations, score function, accuracy function and Euclidean distance of n-Fuzzy sets will study. Finally, we study the Sanchez$^{,}$s approach for medical diagnosis and extend this concept with the notion of n-Fuzzy set.