The concept of gyrogroups is a generalization groups which do not explicitly have associativity. In this paper, the notion fuzzy gyronorms on introduced. relations metrics (in sense George and Veeramani), are studied. Also, metric structures normed discussed. Finally completion gyrogroup with an invariant We mainly show that if d G (Gˆ,dˆ) space (G,d); then for any continuous t-norm ⁎, standard...

‎The decomposition $Gamma=BH$ of a group $Gamma$ into a subset B ‎and a subgroup $H$ of $Gamma$ induces‎, ‎under general conditions‎, ‎a ‎group-like structure for B‎, ‎known as a gyrogroup‎. ‎The famous‎ concrete realization of a gyrogroup‎, ‎which motivated the emergence ‎of gyrogroups into the mainstream‎, ‎is the space of all ‎relativistically admissible velocities along with a binary ‎mbox{...