This thesis deals with filtering of multidimensional signals. A large part of the thesis is devoted to a novel filtering method termed “Normalized convolution”. The method performs local expansion of a signal in a chosen filter basis which not necessarily has to be orthonormal. A key feature of the method is that it can deal with uncertain data when additional certainty statements are available...

This paper presents the extension of results on reasoning with totally ordered belief bases to the partially ordered case. The idea is to reason from logical bases equipped with a partial order expressing relative certainty and to construct a partially ordered deductive closure. The difficult point lies in the fact that equivalent definitions in the totally ordered case are no longer equivalent...

Elicitation methods in decision-making under risk allow us to infer the utilities of outcomes as well as the probability weights from the observed preferences of an individual. An optimally efficient elicitation method is proposed, which takes the inevitable distortion of preferences by random errors into account and minimizes the effect of such errors on the inferred utility and probability we...

We consider the finite-time optimal basket liquidation problem for a von Neumann-Morgenstern investor with constant absolute risk aversion (CARA). As underlying continuous-time liquidity model, we use a multi-asset extension of the nonlinear price impact model of Almgren (2003). We show that the expected utility of sales revenues, taken over a large class of adapted strategies, is maximized by ...

Certainty is an epistemic quality or, as philosophers are used to say, an epistemic modality. It is not easily accounted for as such; but things get even more complicated due to the fact that certainty is often confused with other epistemic modalities. Since I cannot discuss here the quite sophisticated technical treatments of certainty, I focus on disentangling certainty from and relating it t...

Fuzzy Water Quality Index (FWQI) was applied in order to assess the degree of drinking water resources in Yazd province, Iran. Thisstudy has also offered the creation of a new fuzzy water quality index (FWQI) to evaluate this tool’s applicability. 12 chemicalparameters including toxic and non-toxic heavy metals measured in 71 groundwater samples collected from drinking water resourcesin rural a...

The San Francisco Police Department (SFPD) recently implemented an optimization-based decision support system for deploying patrol officers. It forecasts hourly needs, schedules officers to maximize coverage, and allows fine tuning to meet human needs. The fine-tuning mode helps captains evaluate schedule changes and suggests alternatives. The system also evaluates policy options for strategic ...