Alpha Level and Inverse Alpha Level Of Multi-Fuzzy Set

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.