This contribution is intended to promote possibility theory as a maturing general framework for the quantification of epistemic and aleatory uncertainties. For this purpose, we revisit Zadeh’s Extension Principle in the context of imprecise probabilities. Therein the aggregation of the possibility distributions is performed by the minimum-operator, corresponding to non-interactivity of the uncertain variables. Yet, this notion is not equivalent to well-established terms from probability theory such as stochastic independence. In order to use possibilistic calculus for propagating multivariate imprecise probabilities through models, we present suitable aggregation operations, corresponding to simple modifications of the Extension Principle, and we prove preservation of probability-possibility consistency, the fundamental concept in possibility theory. For the purpose of demonstration, the possibilistic solutions of two benchmark problems of uncertainty quantification are presented.
Possibilistic calculus as a conservative counterpart to probabilistic calculus - ScienceDirect