A revision of sufficient and necessary condition of uncertainty distribution

Nowadays, uncertainty theory has become a branch of axiomatic mathematics and has been studied by many researchers. In particular, uncertainty distribution is one of the most important tools to deal with indeterminate quantity in uncertainty theory. Peng and Iwamura (2010) presented a sufficient and necessary condition of a function being an uncertainty distribution. This paper gives a counterexample to illustrate this condition is not appropriate. A revision of the sufficient and necessary condition is also provided in this paper.