1,286 research outputs found
Dealing with Interaction Between Bipolar Multiple Criteria Preferences in PROMETHEE Methods
In this paper, we consider the bipolar approach to Multiple Criteria Decision
Analysis (MCDA). In particular we aggregate positive and negative preferences
by means of the bipolar PROMETHEE method. To elicit preferences we consider
Robust Ordinal Regression (ROR) that has been recently proposed to derive
robust conclusions through the use of the concepts of possible and necessary
preferences. It permits to take into account the whole set of preference
parameters compatible with the preference information provided by the Decision
Maker (DM)
Enabling Explainable Fusion in Deep Learning with Fuzzy Integral Neural Networks
Information fusion is an essential part of numerous engineering systems and
biological functions, e.g., human cognition. Fusion occurs at many levels,
ranging from the low-level combination of signals to the high-level aggregation
of heterogeneous decision-making processes. While the last decade has witnessed
an explosion of research in deep learning, fusion in neural networks has not
observed the same revolution. Specifically, most neural fusion approaches are
ad hoc, are not understood, are distributed versus localized, and/or
explainability is low (if present at all). Herein, we prove that the fuzzy
Choquet integral (ChI), a powerful nonlinear aggregation function, can be
represented as a multi-layer network, referred to hereafter as ChIMP. We also
put forth an improved ChIMP (iChIMP) that leads to a stochastic gradient
descent-based optimization in light of the exponential number of ChI inequality
constraints. An additional benefit of ChIMP/iChIMP is that it enables
eXplainable AI (XAI). Synthetic validation experiments are provided and iChIMP
is applied to the fusion of a set of heterogeneous architecture deep models in
remote sensing. We show an improvement in model accuracy and our previously
established XAI indices shed light on the quality of our data, model, and its
decisions.Comment: IEEE Transactions on Fuzzy System
On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation
In this paper we propose the notion of continuous-time dynamic spectral
risk-measure (DSR). Adopting a Poisson random measure setting, we define this
class of dynamic coherent risk-measures in terms of certain backward stochastic
differential equations. By establishing a functional limit theorem, we show
that DSRs may be considered to be (strongly) time-consistent continuous-time
extensions of iterated spectral risk-measures, which are obtained by iterating
a given spectral risk-measure (such as Expected Shortfall) along a given
time-grid. Specifically, we demonstrate that any DSR arises in the limit of a
sequence of such iterated spectral risk-measures driven by lattice-random
walks, under suitable scaling and vanishing time- and spatial-mesh sizes. To
illustrate its use in financial optimisation problems, we analyse a dynamic
portfolio optimisation problem under a DSR.Comment: To appear in Finance and Stochastic
A statistical inference method for the stochastic reachability analysis.
The main contribution of this paper is the characterization of reachability problem associated to stochastic hybrid systems in terms of imprecise probabilities. This provides the connection between reachability problem and Bayesian statistics. Using generalised Bayesian statistical inference, a new concept of conditional reach set probabilities is defined. Then possible algorithms to compute the reach set probabilities are derived
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