Related papers: Decision Making with Partially Consonant Belief Fu…

The main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern's utility theory for probabilistic lotteries as…

In this paper, we formulate a qualitative "linear" utility theory for lotteries in which uncertainty is expressed qualitatively using a Spohnian disbelief function. We argue that a rational decision maker facing an uncertain decision…

In this paper we present a propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (A, c), where A is a many-valued proposition and c is…

A primary motivation for reasoning under uncertainty is to derive decisions in the face of inconclusive evidence. However, Shafer's theory of belief functions, which explicitly represents the underconstrained nature of many reasoning…

While belief functions may be seen formally as a generalization of probabilistic distributions, the question of the interactions between belief functions and probability is still an issue in practice. This question is difficult, since the…

The aim of this paper is to propose a generalization of previous approaches in qualitative decision making. Our work is based on the binary possibilistic utility (PU), which is a possibilistic counterpart of Expected Utility (EU).We first…

Probabilistic Soft Logic has been proposed and used in several applications as an efficient way to deal with inconsistency, uncertainty and relational representation. In several applications, this approach has led to an adequate description…

We revisit games in partition function form, i.e. cooperative games where the payoff of a coalition depends on the partition of the entire set of players. We assume that each coalition computes its worth having probabilistic beliefs over…

Humans currently use arguments for explaining choices which are already made, or for evaluating potential choices. Each potential choice has usually pros and cons of various strengths. In spite of the usefulness of arguments in a decision…

In this chapter a general mathematical framework for probabilistic theories of operationally understood circuits is laid out. Circuits are comprised of operations and wires. An operation is one use of an apparatus and a wire is a…

The stability rule for belief, advocated by Leitgeb [Annals of Pure and Applied Logic 164, 2013], is a rule for rational acceptance that captures categorical belief in terms of $\textit{probabilistically stable propositions}$: propositions…

Defining and modeling the relation of inclusion between continuous belief function may be considered as an important operation in order to study their behaviors. Within this paper we will propose and present two forms of inclusion: The…

Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…

We consider variable selection in high-dimensional linear models where the number of covariates greatly exceeds the sample size. We introduce the new concept of partial faithfulness and use it to infer associations between the covariates…

Approaches to decision-making under uncertainty in the belief function framework are reviewed. Most methods are shown to blend criteria for decision under ignorance with the maximum expected utility principle of Bayesian decision theory. A…

Linear representations for a subclass of boolean symmetric functions selected by a parity condition are shown to constitute a generalization of the linear constraints on probabilities introduced by Boole. These linear constraints are…

We construct the belief function that quantifies the agent, beliefs about which event of Q will occurred when he knows that the event is selected by a chance set-up and that the probability function associated to the chance set up is only…

In this work we cast the problem of binary classification in terms of estimating a partition on Bernoulli data. When the explanatory variables are all categorical, the problem can be modelled using the language of boolean functions. We…

We provide and axiomatize a representation for preferences over lotteries that generalizes the expected utility model. Since the representation uses different utility functions to evaluate different lotteries, the preferences can be…

If uncertainty is modelled by a probability measure, decisions are typically made by choosing the option with the highest expected utility. If an imprecise probability model is used instead, this decision rule can be generalised in several…