Abstaract−Multiple set is a new mathematical model to represent vagueness together with multiplicity. Multiple sets are generalization of fuzzy sets, multisets, fuzzy multisets and multi fuzzy sets. In this paper, a modified version for the definition of multiple sets is given and it is shown that the revised definition also satisfies all fundamental properties satisfied by the earlier definition. The notion of αi− cut and strong α− cut are defined and their properties are studied. Finally, multiple complement function is defined and some results related to it are obtained