Zadeh ??1?? introduced the concept of fuzzy set in 1965. Kramosil and Micha ?lek ??2?? introduced the concept of fuzzy metric space using continuous t-norms in 1975.
Matloka ??3?? introduced bounded and convergent sequences of fuzzy numbers and studied some of their properties in 1986. Sequences of fuzzy numbers also were discussed by Nanda ??4??, Kwon ??5??, Esi ??6??, and many others.
In 2010, Al-Tai defined the fuzzy metric space, the fuzzy sequence, and many other
? concepts, on other base, that the family of fuzzy real numbers is R ?? Z ? Q ? Q . Z is the
family of fuzzy integer numbers, where every r ? Z ??r ? Z?? is a singleton fuzzy set ??fuzzy ?
point?? ??see ??7–12????. Q and Q are the family of fuzzy rational numbers and the family of fuzzy ?
irrational numbers, respectively, where every r ? Q ??r ? Q?? or r? ? Q ??r? ? Q??? is a triangular fuzzy number ??13?? and by using the representation Theorem ??the resolution principle?? ??14??.
In this research, we will consider the fuzzy neighborhood, the limit fuzzy number, the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence, and then we will introduce some results about properties of the above concepts on the base which depended by Al-Tai to define the fuzzy metric space.