On Partial Orders in Complex Fuzzy Logic

A partial ordering ≤ on the unit circle of the complex plane Dinduced by the algebraic product was introduced and it was proved that (D, ≤) is a complete lattice (Dick, 2005). In this letter, it is pointed out that the relation ≤ is not a partial order on D and that (D, ≤) is not a lattice. It is shown that the relation ≤ is a partial order over D° ∪ {1} and a strict partial order over D° - {0}, where D° is the interior of D.