This study deals with two approaches to uncertainty quantification methodology. In the first approach, an uncertainty quantification methodology is proposed and applied to the estimation of nuclear reactor fuel peak cladding temperature (PCT) uncertainty. The proposed method adopts the use of Latin hypercube sampling (LHS). The independency between the input variables is verified through a correlation coefficient test. The uncertainty of the output variables is estimated through a goodness-of-fit test on the sample data. In the application, the approach taken to quantifying the total mean and total 95\% probability PCTs is given. Emphasis is placed upon the PCT uncertainty estimation due to models`` or correlations`` uncertainties with the assumption that significant sources of PCT uncertainty are determined.
In the second approach, an uncertainty quantification methodology is proposed for a severe accident analysis which has large uncertainties. The proposed method adopts the concept of probabilistic belief measure to transform an analyst``s belief on a top event into the equivalent probability of that top event. For the purpose of comparison, analyses are done by 1) applying probability theory regarding the occurring probability of top event as a physical probability or a frequency, 2) applying fuzzy set theory with fuzzy numbered occurring probability of top event, and 3) transforming the analysts`` belief on the top event into equivalent probability by the probabilistic belief measure method.