In this paper, in the setting of additive (ψ)-fuzzy preference structure, T-S weak orders and strict T-S weak orders associated to a fuzzy total interval order structure are investigated. Firstly,we show that the right traces of large preference and strict preference are T-S weak orders in a fuzzy total interval order structure. Then, we give the equivalent statements of two strict weak orders Q1 and Q2 by means of the strict preference P and the large preference relation R in a crisp preference structure. Based on these equivalent statements, the fuzzy versions of Q1 and Q2 are presented in a fuzzy preference structure. Under the conditions that (T,S,N(ψ))is a De Morgan triplet and T is a rotation invariant t-norm, we draw the conclusion that both Q1 and Q2 are strict T-S weak orders through detailed study on fuzzy total interval order structures.