# Ferreira-2004f

### From IEETA

## Article

Title | Fuzzy information on discrete and continuous domains: approximation results |
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Author | Paulo J S G Ferreira, Manuel J. C. S. Reis |

Journal | International Journal of General Systems |

Volume | 33 |

Number | 5 |

Pages | 583-591 |

Month | October |

Year | 2004 |

DOI | [1] |

Group | |

Group (before 2015) | Signal Processing Laboratory |

Indexed by ISI | Yes |

### Abstract

Measures of information based on fuzzy sets have been defined for finite and for continuous universes. In the
continuous case, the measure of information *I*(*f*) depends on the concept of sorting or nonincreasing rearrangement of *f*.

The paper studies the extent to which this measure of information can be approximated as a limit of discrete distributions with *N* distinct values, as *N* tends to infinity. It gives conditions under which there is convergence, and the order of approximation in terms of *N* and the Lipschitz exponent of the possibility function *f*.