Possibilistic Graphical Models
Graphical modeling is an important method to efficiently represent and analyze uncertain information in knowledge-based systems. Its most prominent representatives are Bayesian networks and Markov networks for probabilistic reasoning. which have been well
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C. Borgelt Otto-von-Guericke University, Magdeburg, Germany
J. Gebhardt TU Braunsweig, Braunsweig, Germany R. Kruse Otto-von-Guericke University, Magdeburg, Germany
Abstract
Graphical modeling is an important method to efficiently represent and analyze uncertain information in knowledge-based systems. Its most prominent representatives are Bayesian networks and Markov networks for probabilistic reasoning, which have been well-known for over ten years now. However, they suffer from certain deficiencies, if imprecise information has to be taken into account. Therefore possibilistic gmphical modeling has recently emerged as a promising new area of research. Possibilistic networks are a noteworthy alternative to probabilistic networks whenever it is necessary to model both uncertainty and imprecision. Imprecision, understood as set-valued data, has often to be considered in situations in which information is obtained from human observers or imprecise measuring instruments. In this paper we provide an overview on the state of the art of possibilistic networks w.r.t. to propagation and learning algorithms.
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Introduction
A major requirement concerning the acquisition, representation, and analysis of information in knowledge-based systems is to develop an appropriate formal and semantic framework for the effective treatment of uncertain and imprecise data [32]. In this paper we consider this requirement w.r.t. a task that frequently occurs in applications, namely the task to identify the true state w0 of a given world section. We assume that possible states of the domain under consideration can be described by stating the values of a finite set of attributes (or variables). The set of all possible (descriptions of) states, i.e., the Cartesian product of the attribute domains, we call the frame of discernment n (also called universe of discourse). The task to identify the true state consists in combining generic knowledge about the relations between the values of the different attributes (usually derived from background expert knowledge about the domain or from databases of sample cases) and evidential knowledge about the current values of some of the attributes (obtained, for instance, from observations). The goal is to find a description of the true state w0 that is as specific as possible. G. Della Riccia et al. (eds.), Computational Intelligence in Data Mining © Springer-Verlag Wien 2000
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C. Borgelt, J. Gebhardt and R. Kruse
As an example consider medical diagnosis. Here the true state w0 is the current state of health of a given patient. All possible states can be characterized by attributes describing properties of patients (like sex or age) or symptoms (like fever or high blood pressure) or the presentness or absence of diseases. The generic knowledge consists in a model of the medical competence of a physician, who knows about the relations between symptoms and diseases in the context of other properties of the patient. It may be gathered from medical textbooks or reports. The evidential knowledge is ob
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