The aim of this paper is to study some level forms of triangular inequality of 2-fuzzy metric spaces which will be useful for application to fixed point problems. For this aim, we first define the concept of 2-fuzzy pre-metric spaces that have weaker axioms than 2-fuzzy metric spaces with the fundamental properties. Then, we investigate the level form inequalities in 2-fuzzy metric spaces equvalent to the triangular inequalities of 2-fuzzy metric spaces by also analyzing the conditions under in which these are provided. Finally, we prove a fixed point theorem for 2-fuzzy metric spaces by considering the obtained level forms of triangular inequalities.Publisher's Versio
