Fuzzy Randomness

This book, for the first time, provides a coherent, overall concept for taking account of uncertainty in the analysis, the safety assessment, and the 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 . The completely new algorithms are described in detail and illustrated by way of demonstrative examples.