**Abstract: **When no samples are available to estimate a probability distribution, we have to invite some domain experts to evaluate the belief degree that each event will occur. Perhaps some people think that the belief degree is subjective probability or fuzzy concept. However, it is usually inappropriate because both probability theory and fuzzy set theory may lead to counterintuitive results in this case. In order to rationally deal with belief degrees, an uncertainty theory was founded in 2007 and subsequently studied by many researchers. Nowadays, uncertainty theory has become a branch of mathematics for modeling belief degrees.