Relating De Morgan triples with Atanassov's intuitionistic De Morgan triples via automorphisms

In this paper the relation between De Morgan triples on the unit interval and Atanassov's intuitionistic De Morgan triples is presented, showing how to obtain, in a canonical way, Atanassov's intuitionistic De Morgan triples from De Morgan triples. Moreover, we also show that the automorphisms on the unit interval and on L∗ (the intuitionistic value lattice) are in one-to-one correspondence and how automorphisms on L∗ act on Atanassov's intuitionistic De Morgan triples. It is also proved that the action of automorphisms and the canonical construction of De Morgan triples on L∗ commutes.