sections dealing with fuzzy functions and fuzzy random functions are certain to be of special interest. The methods of fuzzy structural analysis and fuzzy probabilistic structural analysis developed in Chap. The most important forms of the latter are the Fuzzy Finite Element Method (FFEM) and the Fuzzy Stochastic Finite Element Method (FSFEM).

1 Introduction.- 2 Mathematical Basics for the Formal Description of Uncertainty.- 3 Description of Uncertain Structural Parameters as Fuzzy Variables.- 4 Description of Uncertain Structural Parameters as Fuzzy Random Variables.- 5 Fuzzy and Fuzzy Stochastic Structural Analysis.- 6 Fuzzy Probabilistic Safety Assessment.- 7 Structural Design Based on Clustering.- References.

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.

From the reviews: "The subject of the book is the comprehensive consideration of uncertainty in the numerical analysis, the safety assessment, and the design of structures. … The book in particular is addressed to civil engineers … . But also for mechanical engineers … the book represents a suitable introduction to the problem of uncertainty modeling … . can be instrumental in broadening the interests and background of those who turn to it. The book demonstrates how one goes about taking account of uncertainty modeling and uncertainty models." (Current Engineering Practice – online, Vol. 47, 2004/2005) "The book deals with a new and important subject of mathematical modeling in engineering, i.e. uncertainty models in civil engineering. It contains seven chapters and an extensive reference list. This work is recommended to engineers and scientists in the area of civil engineering, fuzzy analysis and the corresponding numerical methods." (Olivian Simionescu, Zentralblatt MATH, Vol. 1080, 2006) "To my best knowledge, this is the first book that covers fuzzy randomness in a comprehensive way. The motivation of the authors to study fuzzy randomness was to deal with some difficult problems in the field of civil engineering and computational mechanics in a more realistic fashion. … this is an important book. I have no doubt that it will stimulate the use of fuzzy randomness not only in civil engineering and computational mechanics, but in other areas as well." (George J. Klir, International Journal of General Systems, Vol. 34 (3), 2005)

For the first time this book represents a coherent, overall concept for considering uncertainty in civil engineering and other disciplines of standard optimization Comprehensive consideration of uncertainty in the numerical analysis, the safety assessment, and the design of stuctures