Abstract
A soft semigroup over a semigroup is a collection of subsemigroups. Similarly, a soft ideal over a semigroup is a collection of ideals of the semigroup. As a natural consequence, the idea of soft ideals of a soft semigroup originates. Soft ideals over a semigroup with a fixed set of parameters form a distributive lattice. Soft sets are a very handy tool. Soft ideals over a semigroup characterize generalized fuzzy ideals and fuzzy ideals with thresholds of S.
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