Habilitation thesis of John Klein

Algebraic and metric structures for belief functions

Uncertainty theories are mathematical frameworks allowing to perform inference, i.e. evaluate (based on observed data) how likely candidate solutions are as values of an unknown variable. The theory of belief functions is one such framework that formally encompasses probability theory. In this work, I will present a number of related uncertainty theories and discuss their discrepancies with the theory of belief functions. I will then review several aspects regarding the structure of the space where belief functions live. In particular, I will touch order theoretic, metric and algebraic structures of belief spaces.

defended on 07/12/2017