303 research outputs found
On the use of the Choquet integral with fuzzy numbers in multiple criteria decision support
International audienceThis paper presents a multiple criteria decision support approach in order to build a ranking and suggest a best choice1 on a set of alternatives. The partial evaluations of the alternatives on the points of view can be fuzzy numbers. The aggregation is performed through the use of a fuzzy extension of the Choquet integral. We detail how to assess the coefficients of the aggregation operator by using alternatives which are well-known to the decision maker, and which originate from his domain of expertise
Learning nonlinear monotone classifiers using the Choquet Integral
In der jĂŒngeren Vergangenheit hat das Lernen von Vorhersagemodellen, die eine monotone Beziehung zwischen Ein- und Ausgabevariablen garantieren, wachsende Aufmerksamkeit im Bereich des maschinellen Lernens erlangt. Besonders fĂŒr flexible nichtlineare Modelle stellt die GewĂ€hrleistung der Monotonie eine groĂe Herausforderung fĂŒr die Umsetzung dar. Die vorgelegte Arbeit nutzt das Choquet Integral als mathematische Grundlage fĂŒr die Entwicklung neuer Modelle fĂŒr nichtlineare Klassifikationsaufgaben. Neben den bekannten Einsatzgebieten des Choquet-Integrals als flexible Aggregationsfunktion in multi-kriteriellen Entscheidungsverfahren, findet der Formalismus damit Eingang als wichtiges Werkzeug fĂŒr Modelle des maschinellen Lernens. Neben dem Vorteil, Monotonie und FlexibilitĂ€t auf elegante Weise mathematisch vereinbar zu machen, bietet das Choquet-Integral Möglichkeiten zur Quantifizierung von Wechselwirkungen zwischen Gruppen von Attributen der Eingabedaten, wodurch interpretierbare Modelle gewonnen werden können. In der Arbeit werden konkrete Methoden fĂŒr das Lernen mit dem Choquet Integral entwickelt, welche zwei unterschiedliche AnsĂ€tze nutzen, die Maximum-Likelihood-SchĂ€tzung und die strukturelle Risikominimierung. WĂ€hrend der erste Ansatz zu einer Verallgemeinerung der logistischen Regression fĂŒhrt, wird der zweite mit Hilfe von Support-Vektor-Maschinen realisiert. In beiden FĂ€llen wird das Lernproblem imWesentlichen auf die Parameter-Identifikation von Fuzzy-MaĂen fĂŒr das Choquet Integral zurĂŒckgefĂŒhrt. Die exponentielle Anzahl von Freiheitsgraden zur Modellierung aller Attribut-Teilmengen stellt dabei besondere Herausforderungen im Hinblick auf LaufzeitkomplexitĂ€t und Generalisierungsleistung. Vor deren Hintergrund werden die beiden AnsĂ€tze praktisch bewertet und auch theoretisch analysiert. Zudem werden auch geeignete Verfahren zur KomplexitĂ€tsreduktion und Modellregularisierung vorgeschlagen und untersucht. Die experimentellen Ergebnisse sind auch fĂŒr anspruchsvolle Referenzprobleme im Vergleich mit aktuellen Verfahren sehr gut und heben die NĂŒtzlichkeit der Kombination aus Monotonie und FlexibilitĂ€t des Choquet Integrals in verschiedenen AnsĂ€tzen des maschinellen Lernens hervor
A Multicriteria Approach for the Evaluation of the Sustainability of Re-use of Historic Buildings in Venice
The paper presents a multiple criteria model for the evaluation of the sustainability of projects for the economic re-use of historical buildings in Venice. The model utilises the relevant parameters for the appraisal of sustainability, aggregated into three macro-indicators: intrinsic sustainability, context sustainability and economic-financial feasibility. The model has been calibrated by a panel of experts and tested on two reuse hypotheses of the Old Arsenal in Venice. The tests have proven the model to be a useful support in the early stages of evaluation of re-use projects, where economic improvements are to be combined with conservation, as it supports the identification of critical points and the selection of projects, thus providing not only a check-list of variables to be considered, but an appraisal of trade-offs between economic uses and requirements of conservation.Economic Reuse, Historical Building Conservation
UNIFYING PRACTICAL UNCERTAINTY REPRESENTATIONS: I. GENERALIZED P-BOXES
Pre-print of final version.International audienceThere exist several simple representations of uncertainty that are easier to handle than more general ones. Among them are random sets, possibility distributions, probability intervals, and more recently Ferson's p-boxes and Neumaier's clouds. Both for theoretical and practical considerations, it is very useful to know whether one representation is equivalent to or can be approximated by other ones. In this paper, we define a generalized form of usual p-boxes. These generalized p-boxes have interesting connections with other previously known representations. In particular, we show that they are equivalent to pairs of possibility distributions, and that they are special kinds of random sets. They are also the missing link between p-boxes and clouds, which are the topic of the second part of this study
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
Towards sustainability: An assessment of an urbanisation bubble in China using a hierarchical - stochastic multicriteria acceptability analysis - Choquet integral method
Urbanisation bubbles have become an increasingly serious problem. Attention has been paid to the speed of urbanisation; however, the issue of quality has been neglected, particularly in the case of China. Therefore, the aim of this research is to evaluate Chinaâs urbanisation bubbles by employing a hierarchical - stochastic multicriteria acceptability analysis (SMAA) - Choquet integral method. In order to highlight regional disparities, we measure the urbanisation bubbles at a provincial level. Our study aggregates the urbanisation bubble indices using the Choquet integral preference model, and considers the interactions between various indicators. Furthermore, robust ordinal regression and SMAA are applied to resolve the robustness issues associated with the entire set of weights assigned to the urbanisation bubble composite indicator. In addition, by employing a multiple criteria hierarchy process, the study aggregates urbanisation bubble indices not only at the comprehensive level, but also at the intermediate levels of the hierarchy. Our findings suggest that the ranking of urbanisation bubbles is positively related to the level of regional development. This study contributes to the evaluation of regional urbanisation and sustainable development
Aggregate constrained inventory systems with independent multi-product demand: control practices and theoretical limitations
In practice, inventory managers are often confronted with a need to consider one or more aggregate constraints. These aggregate constraints result from available workspace, workforce, maximum investment or target service level. We consider independent multi-item inventory problems with aggregate constraints and one of the following characteristics: deterministic leadtime demand, newsvendor, basestock policy, rQ policy and sS policy. We analyze some recent relevant references and investigate the considered versions of the problem, the proposed model formulations and the algorithmic approaches. Finally we highlight the limitations from a practical viewpoint for these models and point out some possible direction for future improvements
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