In real decision situations a decision maker (DM) is often confronted with the problem that the information which is necessary for constructing a classical decision model is not available, or the cost for getting this information seems too high. Subsequently, the DM abstains from constructing a decision model; the DM fears that this model is not an authentic image of the real problem. Fuzzy set...

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The topic of this article is decision procedures for satisfiability modulo theories (SMT) of arbitrary quantifier-free formulæ. We propose an approach that decomposes the formula in such a way that its definitional part, including the theory, can be compiled by a rewrite-based firstorder theorem prover, and the residual problem can be decided by an SMT-solver, based on the Davis-Putnam-Logemann...

In most contemporary approaches to decision making, a decision problem is described by a sets of states and set of outcomes, and a rich set of acts, which are functions from states to outcomes over which the decision maker (DM) has preferences. Most interesting decision problems, however, do not come with a state space and an outcome space. Indeed, in complex problems it is often far from clear...

Classical decision theory models behaviour in terms of utility maximisation where utilities represent rational preference relations over outcomes. However, empirical evidence and theoretical considerations suggest that we need to go beyond this framework. We propose to represent goals by higherorder functions or operators that take other functions as arguments where the max and argmax operators...

Decision theory has been plagued with a variety of problems almost from the start. Some, like the Ellsberg paradox [Ellsberg, 1961] merely seem to point to the problems actual people have in calculating probabilities and utilities. Others, like the Newcomb paradox and its relatives, have motivated a re-foundation of decision theory on causal grounds rather than evidential grounds [Joyce, 1999]....

By combining information theory, statistical decision theory, and maximum entropy to address the decision fusion problems, a statistical decision fusion theory is obtained. The theory explains why decision fusion is so difficult and why the performance of decision fusion systems does not always meet expectations. The theory suggests how statistical decision systems such as the conceptual "Famil...

In this paper, we argue that replacing the expectation of the loss in statistical decision theory with the median of the loss leads to a viable and useful alternative to conventional risk minimization particularly because it can be used with heavy tailed distributions. We investigate three possible definitions for such medloss estimators and derive examples of them in several standard settings....