The Embarrassingly Simple Calculus of Possibility Theory
Possibility theory is the mathematically rigorous heir to fuzzy set theory and can be used very efficiently for the quantification of polymorphic uncertainty in both forward and inverse problems.
We discuss how a possibility measure can be derived from an axiomatic basis, and how - equipped with some suitable principles - this provides a mathematical framework for imprecise probabilities. We then see how possibility distributions arise very naturally in many situations and which techniques are available for modeling possibilistic membership functions. Finally, many problems of possibilistic calculus may be expressed in a simple and general manner for which we consider several numerical solution approaches. Special emphasis is put on the intuitiveness, applicability, and simplicity of the presented results.
Dominik Hose received his bachelor's and master's degree in Simulation Technology from the University of Stuttgart (Germany) in 2015 and 2017. Currently, he is a phd student under the supervision of Michael Hanss at the University of Stuttgart. Most importantly, the REC-Workshop hosted by the Risk Institute in 2018 was his first UQ conference ever to attend and it sparked his passion for imprecise probabilities. Dominik's research focuses on solutions to inverse problems in possibility theory and their numerical implementation.