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– In this paper, the notions of smarandache soft semigroups (SS-semigroups) introduced for the first time. An SS-semigroup ( , ) is basically a parameterized collection of subsemigroups which has F A is basically a parameterized collection of subsemigroups which has atlest a proper soft subgroup of ( , ). Some new type of SS-semigroup is also presented here such as F A. Some new type of SS-semigroup is also presented here such as smarandache weak commutative semigroup, smarandache weak cyclic semigroup, smarandache hyper subsemigroup etc. Some of their related properties and other notions have been discussed with sufficient amount of examples
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