In this paper, we define almost ternary subsemigroups of ternary semigroups. Almost ternary subsemigroups is a one
of generalizations of ternary subsemigroups. We show that the union of two almost ternary subsemigroups is also an almost
ternary subsemigroup. However, the intersection of two almost ternary subsemigroups need not be an almost ternary subsemigroup. Moreover, we define their fuzzifications and provide the relationships between almost ternary subsemigroups and their
fuzzifications.