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 TI-groups due to J. N. Mordeson.