Bounding Uncertainty in Civil Engineering Theoretical Background
Taking an engineering, rather than a mathematical, approach, Bounding uncertainty in Civil Engineering - Theoretical Background deals with the mathematical theories that use convex sets of probability distributions to describe the input data and/or the fi
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Alberto Bernardini and Fulvio Tonon
Bounding Uncertainty in Civil Engineering Theoretical Background
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Prof. Dr. Alberto Bernardini Dipartimento di Costruzioni e Trasporti (DCT) Università degli Studi di Padova Via Marzolo 9 Padova, 35131 Italy E-mail: [email protected] Prof. Dr. Fulvio Tonon The University of Texas at Austin Department of Civil Engineering 1 University Station C1792 Austin, TX 78712-0280 USA E-mail: [email protected]
ISBN 978-3-642-11189-1
e-ISBN 978-3-642-11190-7
DOI 10.1007/978-3-642-11190-7 Library of Congress Control Number: 2009942254 c 2010 Springer-Verlag Berlin Heidelberg
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Preface
The theories described in the first part of this book summarize the research work that in past 30-40 years, from different roots and with different aims, has tried to overcome the boundaries of the classical theory of probability, both in its objectivist interpretation (relative frequencies of expected events) and in its subjective, Bayesian or behavioral view. Many compelling and competitive mathematical objects have been proposed in different areas (robust statistical methods, mathematical logic, artificial intelligence, generalized information theory). For example, fuzzy sets, bodies of evidence, Choquet capacities, imprecise previsions, possibility distributions, and sets of desirable gambles. Many of these new ideas have been tentatively applied in different disciplines to model the inherent uncertainty in predicting a system’s behavior or in back analyzing or identifying a system’s behavior in order to obtain parameters of interest (econometric measures, medical diagnosis, …). In the early to mid-1990s, the authors turned to random sets as a way to formalize uncertainty in civil engineering. It is far from the intended mission of this book to be an all comprehensive presentation of the subject. For an updated and clear synthesis, the interested reader could for example refer to (Klir 2005). The particular point of view of the authors is centered on the applications to civil engineerin
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