Calculation vs. Subjective Assessment with Respect to Fuzzy Probability

When a sample is drawn from a population with infinite elements, it is impossible to precisely get the probability distribution of the population from the sample. Particularly, when the size of the sample is small, the estimated values of the probabilities must be so imprecise that they would be represented by some fuzzy numbers. In that case, we can use the interior-outer-set model to calculate a fuzzy probability distribution, or invite some experts to review the sample and to subjectively assess. In this paper, with simulation experiments and inquiring experts, we prove that, the results from the calculation and the subjective assessment are very near in terms of the fuzzy expected value and the standard deviation. It implies that the interior-outer-set model can replace experts to give fuzzy probabilities.