This paper presents a summary of Peter Walley's theory of coherent lower previsions. We
introduce three representations of coherent assessments: coherent lower and upper …

Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk's
Probability and Finance, published in 2001, showed that perfect-information games can be …

Coherent upper and lower probabilities, Choquet capacities of order 2, belief functions and
possibility measures are amongst the most popular mathematical models for uncertainty and …

The personalist conception of probability is often explicated in terms of betting rates
acceptable to an individual. A common approach, that of de Finetti for example, assumes …

In a series of papers published in the 1960's, AP Dempster developed a generalization of
the Bayesian theory of statistical in ference. In A Mathematical Theory of Evidence …

Sets of desirable gambles constitute a quite general type of uncertainty model with an
interesting geometrical interpretation. We give a general discussion of such models and …

The theory of sets of desirable gambles is a very general model which covers most of the
existing theories for imprecise probability as special cases; it has a clear and simple …

This paper analyzes concepts of independence and assumptions of convexity in the theory
of sets of probability distributions. The starting point is Kyburg and Pittarelli's discussion of …

We detail the relationship between sets of desirable gambles and conditional lower
previsions. The former is one the most general models of uncertainty. The latter corresponds …

In the usual approaches to fuzzy set theory the notions of grade of membership, possibility,
and so on are taken as given and axioms are put forward to govern the behaviour of these …