Fuzzy Randomness

sections dealing with fuzzy functions and fuzzy random functions are certain to be of special interest. The reader is expected to be in command of the knowledge gained in a basic university mathematics course, with the inclusion of stochastic elements. A specification of uncertainty in any particular case is often difficult. For this reason Chaps. 3 and 4 are devoted solely to this problem. The derivation of fuzzy variables for representing informal and lexical uncertainty reflects the subjective assessment of objective conditions in the form of a membership function. Techniques for modeling fuzzy random variables are presented for data that simultaneously exhibit stochastic and nonstochastic properties. The application of fuzzy randomness is demonstrated in three fields of civil engineering and computational mechanics: structural analysis, safety assessment, and design. The methods of fuzzy structural analysis and fuzzy probabilistic structural analysis developed in Chap. 5 are applicable without restriction to arbitrary geometrically and physically nonlinear problems. The most important forms of the latter are the Fuzzy Finite Element Method (FFEM) and the Fuzzy Stochastic Finite Element Method (FSFEM).

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

Autorentext

Univ.-Prof. Dr.-Ing. habil. Bernd MÖLLER ( 1941): studies in civil engineering (University of Technology, Dresden), main studies in constructional and structural engineering. Since 1996: Professor for Structural Analysis (University of Technology, Dresden).
Dr.-Ing. Michael BEER ( 1970): studies in civil engineering (University of Technology, Dresden), main studies in constructional and structural engineering. Since 2003: project manager of the DFG research project BE 2570/1 for funding the own occupation.

Klappentext

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.

Inhalt
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.