In this work, we have introduced the notion of T -intuitionistic fuzzy sublattice
by associating the conditions mentioned in the definition of intuitionistic fuzzy
sublattice [22, 23]. So a new equivalent definition is obtained which reduces the
four conditions in only one. Thus, based on an intuitionistic fuzzy triangular norm,
the study of intuitionistic fuzzy sublattices becomes so simple. Moreover, we extend
the notion of an intuitionistic fuzzy ideal to a T -intuitionistic fuzzy ideal w.r.t the
lattice operations and we investigate their various characterizations and properties.
Future work is anticipated in multiple directions. We think it makes sense to
study the notions of intuitionistic fuzzy prime ideals and intuitionistic fuzzy filters
for other types of lattices based on the intuitionistic fuzzy setting