### 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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Pages (from-to) | 1922-1927 |

Number of pages | 6 |

Journal | Proceedings of the American Control Conference |

Volume | 3 |

Publication status | Published - Jan 1 2001 |

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

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

Wong, M. L., Yam, Y., & Baranyi, P. (2001). Representing membership functions as elements in function space.

*Proceedings of the American Control Conference*,*3*, 1922-1927.