Through the theory of fuzzy ideas,locally U-abundant subsemigroups of U-abundant semigroups and locally U-superabundant semigroups are given in this paper.

A U-semiabundant semigroup is a generalization of an abundant.It is proved that if S is a U-semiabundant semigroup satisfying PC conditions in which the set of projections forms a subsemigroup,then the nature partial order on S is compatible.If eSe satisfy the regularity condition and L~V-unipotent,R~V-unipotent,and if S is compatible,then eSe satisfy the regularity condition and L~V-majorization and R~V-majorization.