Abstract
The notion of S-α anti fuzzy cosets with representative and S-α anti fuzzy normal subsemi groups are introduced and their characterizations are obtained. It is also proved that the set of all S-α anti fuzzy cosets will form a semigroup under a suitable binary operation and its structural properties are determined. A necessary condition for an S-α anti fuzzy semigroup to be S-α anti fuzzy normal is also proved.
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