Description of Uncertain Structural Parameters as Fuzzy Random Variables
Structural parameters that possess the uncertainty characteristic fuzzy randomness are modeled as fuzzy random variables [119, 124]. For each fuzzy random variable it is necessary to generate the fuzzy probability distribution function, the fuzzy probabil
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Springer-Verlag Berlin Heidelberg GmbH
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Bernd Moller Michael Beer
Fuzzy Randomne§§ Uncertainty in Civil Engineering and Computational Mechanics
With 234 Figures
Springer
Univ.-Prof. Dr. -Ing. habil. Bernd Moller Dr. -Ing. Michael Beer Institute of Structural Analysis (Lehrstuhl ffir Statik) Dresden University of Technology MommsenstraBe 13 01062 Dresden Germany
E-mail: [email protected] E-mail: [email protected]
ISBN 978-3-642-07312-0
ISBN 978-3-662-07358-2 (eBook)
DOI 10.1007/978-3-662-07358-2
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Everything is vague to a degree you do not realize till you have tried to make it precise. Bertrand Russell
Nature has never attended a course in probability theory. This poignant philosophical statement underlines the fact that the phenomenon of uncertainty cannot be described by means of probability theory alone. Data and models encountered in the natural sciences and engineering are more or less characterized by uncertainty. With the inclusion of interval variables and random variables classical mathematical models are available for the treatment of uncertainty. In recent years work on the formulation of new mathematical models for describing uncertainty has intensified. This work is based on chaos theory, convex modeling, fuzzy set theory, and fuzzy randomness. The aim of these uncertainty models is to handle data exhibiting, in particular, nonstochastic properties and informal uncertainty. Fuzzy randomness is a generalized uncertainty model that permits the simultaneous consideration of stochastic, lexical, and informal uncertaint
