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Possibilistic Graphical Models: From Reasoning to Decision Making

  • Nahla Ben Amor
Conference paper
  • 1.3k Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8256)

Abstract

Graphical models are important tools to efficiently represent and analyze uncertain information in knowledge-based systems. The most prominent representatives of these models refer to probability theory. In particular, Bayesian networks [27, 29] have been largely developed and used in real world applications. However, such networks are only appropriate when all numerical data are available, which is not always the case. Indeed, there are some situations such as the case of total ignorance, which are not well handled and which can make the probabilistic reasoning unsound. Therefore non-probabilistic graphical modeling has recently emerged as a promising new area of research. In particular, possibilistic networks [4, 8, 21] appear as noteworthy alternative to probabilistic networks whenever it is necessary to model both uncertainty and imprecision. In fact possibility theory [15] offers a natural and simple model to handle such data and presents an appropriate framework for experts to express their opinions numerically or qualitatively. This leads to two variants of possibilistic networks: product-based networks and min-based networks (also known as qualitative possibilistic networks). The first part of this talk adresses the reasoning problem in possibilistic networks. Several propagation algorithms will be presented with a focus on qualitative networks. The second part concerns the decisional aspect in possibility theory and in particular the sequential decision making in possibilistic decision trees. In fact, the development of possibilistic decision theory has lead to the proposition of a series of possibilistic criteria, namely: optimistic and pessimistic possibilistic qualitative criteria [17], possibilistic likely dominance [14, 20], binary possibilistic utility [23] and possibilistic Choquet integrals [32]. Thus a theoretical study on the complexity of the problem of finding an optimal strategy depending on the monotonicity property of the optimization criteria will be proposed. Details about different parts of this talk can be found in [1-5].

Keywords

Graphical models Possibility theory Causality Propagation algorithms Decision making Possibilistic decision trees 

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Nahla Ben Amor
    • 1
  1. 1.Laboratoire de Recherche Opérationnelle, de Décision et de Contrôle de processus (LARODEC), Institut Supérieur de Gestion TunisUniversité de TunisTunisia

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