Probability-possibility transformation for small sample size data

Data insufficiency and information incompleteness often exist in engineering practice, resulting in the presence of epistemic uncertainty. Possibility theory is effective in dealing with epistemic uncertainty and has been applied in various domains. In possibility theory, possibility distribution is an essential concept which has to be derived from collected data. Existing methods performs well under large sample size, but may not give satisfactory result under small sample size. In this paper, we study the problem of deriving possibility distribution from data with small sample size. A new probability-possibility transformation method is proposed based on Sison-Glaz´s simultaneous confidence intervals, and experimental results show that the proposed method seems to be effective and have satisfactory performance in terms of coverage probability.