Joint propagation of probability and possibility in risk analysis: Towards a formal framework

This paper discusses some models of Imprecise Probability Theory obtained by propagating uncertainty in risk analysis when some input parameters are stochastic and perfectly observable, while others are either random or deterministic, but the information about them is partial and is represented by possibility distributions. Our knowledge about the probability of events pertaining to the output of some function of interest from the risk analysis model can be either represented by a fuzzy probability or by a probability interval. It is shown that this interval is the average cut of the fuzzy probability of the event, thus legitimating the propagation method. Besides several independence assumptions underlying the joint probability-possibility propagation methods are discussed and illustrated by a motivating example. Key-words: Random sets, possibility distributions, fuzzy random variables, independence.