From quasi t-norms and quasi t-conorms we give methods to generate new quasi t-norms and new quasi-t-conorms. Furthermore, between ∧ (resp. ∨) and every quasi t-norm (resp. quasi t-conorm) f (resp. f^*) it is proved the existence of finite sequences of quasi t-norms (resp. quasi t-conorms) lies between ∧ (resp. ∨) and f (resp. f^*). Finally, we give some special cases of complete residuated lattice valued-logic.