M. Demirci[Vague groups, J. math. Anal. Appl. vol.230, pp. 142-156, 1999] studied the vague group operation on a crisp set as a fuzzy function and estabished the vague group structure on a crisp set. In this paper we consider bi-groups which are studied by A.A.A. Agboola and L.S. Akinola. And we also will define vague bi-groups and fuzzy bi-functions and we investigate some basic operations on the vague bi-group and fuzzy bi-functions.