Fuzzy Randomness

The subject of the book is the comprehensive consideration of uncertainty in the numerical analysis, the safety assessment, and the design of structures. Stochastic as well as non-stochastic uncertainty is treated on the basis of the superordinated uncertainty model fuzzy randomness. This new uncertainty model contains the special cases of real valued random variables and fuzzy variables and permits to take account of both uncertainty characteristics simultaneously. The book introduces to the problem of uncertainty and provides a current survey of relevant uncertainty models and their application in civil engineering. The necessary, special mathematical basics of the fuzzy set theory and the theory of fuzzy random variables are explained in an engineering manner and illustrated by way of examples. Basic ideas and methods for appropriately quantifying uncertain structural parameters are presented and demonstrated by means of characteristic examples. For processing uncertainty in structural analysis, safety assessment, and structural design completely new algorithms are introduced and described in detail as fuzzy structural analysis, fuzzy probabilistic safety assessment, and fuzzy cluster design. The application of the new methods is demonstrated for selected examples from civil engineering, their essential advantages are emphasized. For the first time this represents a coherent, overall concept for considering uncertainty in civil engineering.§The book in particular addresses to civil engineers and requires a university degree as well as basic knowledge in stochastics. But also for mechanical engineers, colleagues from applied mathematics, and other people who are interested in uncertainty problems the book represents a suitable introduction to the problem of uncertainty modeling and provides general solutions and algorithms, which may also be applied to problems from other fields beyond engineering.This book, for the first time, provides a coherent, overall concept for taking account of uncertainty in the analysis, the safety assessment, and the design of structures. The reader is introduced to the problem of uncertainty modeling and familiarized with particular uncertainty models. For simultaneously considering stochastic and non-stochastic uncertainty the superordinated uncertainty model fuzzy randomness, which contains real valued random variables as well as fuzzy variables as special cases, is presented. For this purpose basic mathematical knowledge concerning the fuzzy set theory and the theory of fuzzy random variables is imparted. The body of the book comprises the appropriate quantification of uncertain structural parameters, the fuzzy and fuzzy probabilistic structural analysis, the fuzzy probabilistic safety assessment, and the fuzzy cluster structural design. The completely new algorithms are described in detail and illustrated by way of demonstrative examples.