Applied Fuzzy Arithmetic

An Introduction with Engineering Applications

By: Michael Hanss

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Hardcover | 11 February 2005

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272 Pages

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23.5 x 15.88 x 1.91

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Applied Fuzzy Arithmetic provides a well-structured compendium that offers both a deeper knowledge about the theory of fuzzy arithmetic and an extensive view on its applications in the engineering sciences, making it a resource for students, researchers, and practical engineers. The first part of the book gives an introduction to the theory of fuzzy arithmetic, which aims to present the subject in a well-organized and comprehensible form. The derivation of fuzzy arithmetic from the original fuzzy set theory and its evolution towards a successful implementation is presented with existing formulations of fuzzy arithmetic included and integrated in the overall context. The second part of the book presents a diversified exposition of the application of fuzzy arithmetic, addressing different areas of the engineering sciences, such as mechanical, geotechnical, biomedical, and control engineering.

Industry Reviews

From the reviews: "The book is an extensive, systematic and lucidly written treatise on the subject of fuzzy numbers, their processing, and applications. ! Overall, the book brings a comprehensive and timely material on the important topic of processing fuzzy numbers and thus offers an interesting insight into the applied aspects of fuzzy sets." (Witold Pedrycz, Zentralblatt MATH, Vol. 1085, 2006) "This book deals with the application of fuzzy set theory to mechanical engineering. ! the presence of detailed accounts of such applications is a very important feature of this book, likely to attract the interest of mechanical or civil engineers and to bring these methods to their research areas. ! is a noticeable step toward a mature processing of fuzzy intervals, namely, a better understanding of how to correctly handle them and what to do with them in practice." (Didier Dubois, SIAM Review, Vol. 49 (3), 2007)

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Introduction to Fuzzy Arithmetic
The Theory of Fuzzy Sets	p. 3
Classical Sets	p. 3
Terminology and Notation	p. 3
Basic Definitions	p. 4
Operations for Domain-Compatible Classical Sets and Relations	p. 9
Further Operations for Classical Relations	p. 12
Fuzzy Sets	p. 14
Terminology and Notation	p. 14
Basic Definitions	p. 16
Operations for Domain-Compatible Fuzzy Sets and Relations	p. 25
Further Operations for Fuzzy Relations	p. 37
The Extension Principle	p. 41
Elementary Fuzzy Arithmetic	p. 45
Fuzzy Numbers and Fuzzy Vectors	p. 45
Fuzzy Numbers	p. 45
Fuzzy Vectors	p. 51
Elementary Fuzzy Arithmetical Operations	p. 51
Elementary Operations on L-R Fuzzy Numbers	p. 53
Elementary Operations on Discretized Fuzzy Numbers	p. 62
Elementary Operations on Decomposed Fuzzy Numbers	p. 73
Standard Fuzzy Arithmetic	p. 79
Definition of Standard Fuzzy Arithmetic	p. 79
Application of Standard Fuzzy Arithmetic	p. 81
Drawbacks and Limitations of Standard Fuzzy Arithmetic	p. 87
Advanced Fuzzy Arithmetic - The Transformation Method	p. 99
Fuzzy-Parameterized Models	p. 99
General and Reduced Transformation Method	p. 100
Simulation of Fuzzy-Parameterized Systems	p. 100
Analysis of Fuzzy-Parameterized Systems	p. 108
Extended Transformation Method	p. 116
Simulation of Fuzzy-Parameterized Systems	p. 116
Analysis of Fuzzy-Parameterized Systems	p. 117
Classification Criterion	p. 118
Efficient Implementation of the Transformation Method	p. 122
Multi-Dimensional Array Structure	p. 122
Thinning of the Decomposition Pattern	p. 124
Piecewise Multilinear Sparse-Grid Interpolation	p. 125
Additions to Fuzzy Arithmetic	p. 127
Uncertainty Processing with Fuzzy Arithmetic	p. 127
Inverse Fuzzy Arithmetic	p. 132
Defuzzification of Fuzzy Numbers	p. 139
Measures for Fuzzy Numbers	p. 141
Imprecision of Fuzzy Numbers	p. 141
Eccentricity of Fuzzy Numbers	p. 142
Applications in the Engineering Sciences
Mechanical Engineering	p. 147
Simulation, Analysis, and Identification of Structural Joint Connections	p. 147
Simulation and Analysis of a Bolted Lap Joint under Tangential Friction Load	p. 147
Simulation and Analysis of a Bolted Joint Connection under Axial Load	p. 154
Identification of the Uncertain Model Parameters of a Bolted Joint	p. 159
Fuzzy Sensitivity Analysis of an Orthotropic Plate	p. 168
Frequency Response Function of a Clamped Plate	p. 180
Simulation and Analysis of the Vibrations of an Engine Hood	p. 186
Geotechnical Engineering	p. 193
Contaminant Flow in Thin Layers	p. 193
Identification of the Uncertain Hydraulic Conductivities in Transversely Isotropic Porous Media	p. 208
Biomedical Engineering	p. 217
Simulation and Analysis of the Human Glucose Metabolism	p. 217
Enhanced Parameter Identification for the Model of the Human Glucose Metabolism	p. 224
Control Engineering	p. 231
References	p. 245
Index	p. 253
Table of Contents provided by Publisher. All Rights Reserved.

Applied Fuzzy Arithmetic

An Introduction with Engineering Applications

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Hardcover

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