Abstract
In this paper, the concepts of inverse alpha level and weak inverse alpha level of multi-fuzzy set together with their properties are introduced. It is shown that the inverse alpha level is always contained in the weak inverse alpha level. It is further demonstrated that as the union of the alpha levels of two multi-fuzzy sets is contained in the alpha level of their union, it is only the converse that is obtainable for the case of inverse alpha level as well as weak inverse alpha level. Moreover, related results are also provided.