We generalize min-neighborhood groups to arbitrary T -neighborhood groups, where T is a continuous triangular norm. In particular, we point out that our results accommodate the previous theory on min-neighborhood groups due to T. M. G. Ahsanullah. We show that every T -neighborhood group is T -uniformizable, therefore, T -completely regular. We also present several results of T -neighborhood groups in conjunction with T I -groups due to J. N. Mordeson.