Estimation of Possibility-Probability Distributions

Abstract

We demonstrate a theory for evaluating the likelihood of a probability by way of possibility distributions. This theory derives from the standard probability distribution theory by using the possibility to define an arbitrary function whose values are bounded by [0,1] that represents the confidence that one may have in the outcomes. In other words, when in classic probability theory the probability of an event is represented by an integral of the probability mass over this event, in possibility theory the probability of an event is the integral of the probability mass times the confidence function over the whole space. This theory is then extended in order to define a similar notion to probability distributions, namely Possibility-Probability distributions, which represent, as for probabilities, the possibilities of a calculated probability for a given fuzzy event. In this context, we aim to define an estimation method of such a Possibility-Probability distribution in the case of experimental samples and the corresponding distribution. © Springer-Verlag Berlin Heidelberg 2010.