e-book
Fuzzy Randomness: Uncertainty in Civil Engineering and Computational Mechanics
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 uncertainty. Initial drafts for the uncertainty model "fuzzy randomness" were developed about 25 years ago. This book considers these developments and enhances fuzzy randomness in such a way that it may be applied in the fields of civil engineering and computational mechanics. These further scientific developments are based on the results of research work carried out under the supervision of the leading author at the Institute of Structural Analysis of Dresden University of Technology with the much-appreciated financial support of the "Deutsche Forschungsgemeinschaft (DFG)" (German Research Foundation).
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