For a t-norm Ton [0, 1], a partial order T was recently defined and studied. In this study, for any fixed cc (0, I), we define the set of incomparable elements according to <=(T) and this set is deeply investigated. By means of the equivalence relation, defined in , it is shown the set [0,1]/ similar to, denoting the set of all equivalence classes on t-norms on [0,1] is uncountably infinite. Finally, with the help of any t-norm Ton [0, 1], it is obtained that the family (T-lambda)(lambda is an element of(0,1)) of t-norms on [0,1]. If T is a divisible t-norm, then it is obtained that ([0, 1], <=(T),) is a lattice. Thus, we give an answer to an open problem in . (C) 2014 Elsevier Inc. All rights reserved.