### Abstract

This paper generalizes the geometric representation previously introduced for membership function comprising of finite number of characteristic points. An extended class of membership functions satisfying certain monotonicity conditions can now be expressed as elements in the space of square, integrable function. Specifically, bell-shaped membership functions, which was not possible before, can now be accommodated with this generalized representation. An example interpolation problem is treated using both the finite dimensional approach and generalized approach is included for illustration.

Original language | English |
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Title of host publication | Proceedings of the American Control Conference |

Pages | 1922-1927 |

Number of pages | 6 |

Volume | 3 |

Publication status | Published - 2001 |

Event | 2001 American Control Conference - Arlington, VA, United States Duration: Jun 25 2001 → Jun 27 2001 |

### Other

Other | 2001 American Control Conference |
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Country | United States |

City | Arlington, VA |

Period | 6/25/01 → 6/27/01 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*Proceedings of the American Control Conference*(Vol. 3, pp. 1922-1927)

**Representing membership functions as elements in function space.** / Wong, M. L.; Yam, Y.; Baranyi, P.

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

*Proceedings of the American Control Conference.*vol. 3, pp. 1922-1927, 2001 American Control Conference, Arlington, VA, United States, 6/25/01.

}

TY - GEN

T1 - Representing membership functions as elements in function space

AU - Wong, M. L.

AU - Yam, Y.

AU - Baranyi, P.

PY - 2001

Y1 - 2001

N2 - This paper generalizes the geometric representation previously introduced for membership function comprising of finite number of characteristic points. An extended class of membership functions satisfying certain monotonicity conditions can now be expressed as elements in the space of square, integrable function. Specifically, bell-shaped membership functions, which was not possible before, can now be accommodated with this generalized representation. An example interpolation problem is treated using both the finite dimensional approach and generalized approach is included for illustration.

AB - This paper generalizes the geometric representation previously introduced for membership function comprising of finite number of characteristic points. An extended class of membership functions satisfying certain monotonicity conditions can now be expressed as elements in the space of square, integrable function. Specifically, bell-shaped membership functions, which was not possible before, can now be accommodated with this generalized representation. An example interpolation problem is treated using both the finite dimensional approach and generalized approach is included for illustration.

UR - http://www.scopus.com/inward/record.url?scp=0034842695&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034842695&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0034842695

VL - 3

SP - 1922

EP - 1927

BT - Proceedings of the American Control Conference

ER -