### Abstract

An application of fuzzy mathematical programming techniques to multiple objective design problems is presented. Two examples dealing with multiobjective design of mechanical and structural systems are considered. The fundamental assumption in fuzzy mathematical programming applications dealing with the use of linear membership functions is critically examined. Several nonlinear shapes for membership functions of the fuzzy sets are chosen consistent with varying perceptions of the designer, and are analysed to determine their impact on the overall design process. These shapes correspond to what we define as the coefficient of membership satiation. It is shown that the fuzzy min operator together with linear as well as nonlinear membership functions yield Pareto-optimal solutions to the original multiobjective problem. It is seen that final design for both examples is strongly influenced by the sign of membership satiation coefficient.

Original language | English (US) |
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Title of host publication | Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference |

Publisher | Publ by AIAA |

Pages | 403-413 |

Number of pages | 11 |

Edition | pt 1 |

State | Published - 1990 |

Externally published | Yes |

Event | 31st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. Part 3 (of 4): Structural Dynamics I - Long Beach, CA, USA Duration: Apr 2 1990 → Apr 4 1990 |

### Other

Other | 31st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. Part 3 (of 4): Structural Dynamics I |
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City | Long Beach, CA, USA |

Period | 4/2/90 → 4/4/90 |

### Fingerprint

### ASJC Scopus subject areas

- Architecture
- Engineering(all)

### Cite this

*Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference*(pt 1 ed., pp. 403-413). Publ by AIAA.

**Nonlinear membership functions in the fuzzy optimization of mechanical and structural systems.** / Dhingra, A. K.; Rao, Singiresu S; Kumar, V.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.*pt 1 edn, Publ by AIAA, pp. 403-413, 31st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. Part 3 (of 4): Structural Dynamics I, Long Beach, CA, USA, 4/2/90.

}

TY - GEN

T1 - Nonlinear membership functions in the fuzzy optimization of mechanical and structural systems

AU - Dhingra, A. K.

AU - Rao, Singiresu S

AU - Kumar, V.

PY - 1990

Y1 - 1990

N2 - An application of fuzzy mathematical programming techniques to multiple objective design problems is presented. Two examples dealing with multiobjective design of mechanical and structural systems are considered. The fundamental assumption in fuzzy mathematical programming applications dealing with the use of linear membership functions is critically examined. Several nonlinear shapes for membership functions of the fuzzy sets are chosen consistent with varying perceptions of the designer, and are analysed to determine their impact on the overall design process. These shapes correspond to what we define as the coefficient of membership satiation. It is shown that the fuzzy min operator together with linear as well as nonlinear membership functions yield Pareto-optimal solutions to the original multiobjective problem. It is seen that final design for both examples is strongly influenced by the sign of membership satiation coefficient.

AB - An application of fuzzy mathematical programming techniques to multiple objective design problems is presented. Two examples dealing with multiobjective design of mechanical and structural systems are considered. The fundamental assumption in fuzzy mathematical programming applications dealing with the use of linear membership functions is critically examined. Several nonlinear shapes for membership functions of the fuzzy sets are chosen consistent with varying perceptions of the designer, and are analysed to determine their impact on the overall design process. These shapes correspond to what we define as the coefficient of membership satiation. It is shown that the fuzzy min operator together with linear as well as nonlinear membership functions yield Pareto-optimal solutions to the original multiobjective problem. It is seen that final design for both examples is strongly influenced by the sign of membership satiation coefficient.

UR - http://www.scopus.com/inward/record.url?scp=0025263777&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025263777&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0025263777

SP - 403

EP - 413

BT - Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

PB - Publ by AIAA

ER -