## 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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A Pareto - optimal solution is

A Pareto - optimal solution is

**obtained**by Find X e S which max ał such that a SME ( 40 ) Eq . ( 40 ) can be restated as Find X ES which max UF : ( 41 ) Theorem 4 : If x ' is an optimum solution to Eq . ( 41 ) , then X * is Pareto ...Página 75

Results

Results

**obtained**with six objectives considered simultaneously . Obj . Linear Hyperb . Sine Expon . Quad . Log Expon . Func . ( k = 1 ) ( k = -1 ) ɛx102 3.132 4.121 3.408 3.11 2.847 2.899 3.462 F12 0.1687 0.2634 0.1754 0.1422 0.1882 ...Página 82

where the fuzzy Pareto - optimal solutions

where the fuzzy Pareto - optimal solutions

**obtained**depend on the value of a . By varying the value of a , a series of fuzzy Pareto - optimal solutions can be**obtained**. Table 4. Objective function values for single objective ...### Opinião das pessoas - Escrever uma crítica

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### Índice

MODELING IMPRECISION | 1 |

MULTIPLE OBJECTIVE DESIGN | 53 |

INTELLIGENT SYSTEMS | 89 |

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

addition aggregation algorithm alternatives application approach assessment attributes base bounds brake cabin called combined completely components computed conceptual conceptual hierarchy configuration consider consistent constraints cost crisp criteria cycle 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 illustrate imprecise individual induced integral introduced knowledge known KONWERK layout linguistic linguistic variables maximal means measure membership functions method minimization modules necessary needed 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 uncertainty values weighting