## Fuzzy Sets in Engineering Design and ConfigurationAs understanding of the engineering design and configuration processes grows, the recognition that these processes intrinsically involve imprecise information is also growing. This book collects some of the most recent work in the area of representation and manipulation of imprecise information during the syn thesis of new designs and selection of configurations. These authors all utilize the mathematics of fuzzy sets to represent information that has not-yet been reduced to precise descriptions, and in most cases also use the mathematics of probability to represent more traditional stochastic uncertainties such as un controlled manufacturing variations, etc. These advances form the nucleus of new formal methods to solve design, configuration, and concurrent engineering problems. Hans-Jurgen Sebastian Aachen, Germany Erik K. Antonsson Pasadena, California ACKNOWLEDGMENTS We wish to thank H.-J. Zimmermann for inviting us to write this book. We are also grateful to him for many discussions about this new field Fuzzy Engineering Design which have been very stimulating. We wish to thank our collaborators in particular: B. Funke, M. Tharigen, K. Miiller, S. Jarvinen, T. Goudarzi-Pour, and T. Kriese in Aachen who worked in the PROKON project and who elaborated some of the results presented in the book. We also wish to thank Michael J. Scott for providing invaluable editorial assis tance. Finally, the book would not have been possible without the many contributions and suggestions of Alex Greene of Kluwer Academic Publishers. 1 MODELING IMPRECISION IN ENGINEERING DESIGN Erik K. Antonsson, Ph.D., P.E. |

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Página 55

Therefore the concept of

MOO problems ( Soland , 1979 ) . Definition 1 : A solution X eS is

if there is no X ES such that f ; ( X ) = f ( x * ) , i = 1 , . . , k , and f ; ( X ) < f ; ( X® ) for

...

Therefore the concept of

**Pareto**-**optimality**is frequently used in the context ofMOO problems ( Soland , 1979 ) . Definition 1 : A solution X eS is

**Pareto**-**optimal**if there is no X ES such that f ; ( X ) = f ( x * ) , i = 1 , . . , k , and f ; ( X ) < f ; ( X® ) for

...

Página 58

Consequently , d need not be defined and the

solution is guaranteed . ... 4 : For w ; > 0 , b ; = F , and 15 p < 0o , if X * is an

optimal solution of the goal programming formulation , then X * is

. 3 .

Consequently , d need not be defined and the

**Pareto**-**optimality**of the optimumsolution is guaranteed . ... 4 : For w ; > 0 , b ; = F , and 15 p < 0o , if X * is an

optimal solution of the goal programming formulation , then X * is

**Pareto**-**optimal**. 3 .

Página 71

Lemma 8 : For a 20 , if X® is an optimum solution to Eq . ( 44 ) , then X * is weakly

X is an optimum solution to Eq . ( 44 ) , then X * is

Lemma 8 : For a 20 , if X® is an optimum solution to Eq . ( 44 ) , then X * is weakly

**Pareto**-**optimal**. If X is unique , then it is**Pareto**-**optimal**. Lemma 9 : For a > 0 , ifX is an optimum solution to Eq . ( 44 ) , then X * is

**Paretooptimal**. Theorem 5 ...### Opinião das pessoas - Escrever uma crítica

Não foram encontradas quaisquer críticas nos locais habituais.

### Índice

o cr A CON Engineering Design with Imprecision | 10 |

Chapter 3 | 20 |

Chapter 2 | 48 |

Direitos de autor | |

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### Outras edições - Ver tudo

Fuzzy Sets in Engineering Design and Configuration Hans-Jürgen Sebastian,Erik K. Antonsson Pré-visualização limitada - 2012 |

Fuzzy Sets in Engineering Design and Configuration Hans-Jürgen Sebastian,Erik K. Antonsson Pré-visualização indisponível - 2011 |

Fuzzy Sets in Engineering Design and Configuration Hans-Jurgen Sebastian,Erik K Antonsson Pré-visualização indisponível - 1996 |

### Palavras e frases frequentes

Aachen additional aggregation algorithm allows alternatives applied approach assessment attributes base brake called combined completely components computed concepts configuration consider consistent constraints cost crisp criteria decision defined denotes described design variables determined developed domain Engineering engineering design evaluation example feasible Figure formulation fuzzy constraints fuzzy goals fuzzy sets given goals hierarchy illustrate imprecise individual induced integral introduced knowledge known KONWERK layout linguistic linguistic variables maximal means measure membership functions method minimization modules necessary objective functions obtained operator optimization optimum overall parameter Pareto-optimal performance performance variable possible preference presented problem production relations represented requirements Research respect restrictions selection shown solution solve space specification stage step strategy structure Table task techniques temperature theory uncertain uncertainty values weighting