In this paper,first,we study fuzzy ideals on abundant semigroups by using Green*-relations L*,R* on semigroups defined by Fountain in and the natural partial order theory on abundant semigroups introduced by Lawson in [3],and give some properties of fuzzy ideals on such semigroups.

In this paper,we study the natural partial order on perfect rectangular bands of type-A semigroups.

The natural partial order on a regular semigroup with a Q-regular*-transversal is characterized,and the conditions of the partial order on regular semigroups with a Q-regular-transversal to satisfy ■-majorization(minorization) and ρ-majorization(mino-rization) are concluded.