### Abstract

The problem of converging to any given continuous triangular-norm by a sequence of continuous Archimedean triangular-norms is studied. Such a sequence is built up in a constructive way. The class of well-founded triangular-norms is introduced. It is proved that a sequence of triangular-norms converges to a given continuous triangular-norm if and only if this convergence is uniform. Finally, we prove that every continuous triangular norm is a uniform limit of continuous Archimedean triangular-norms.

Original language | English |
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Pages (from-to) | 273-282 |

Number of pages | 10 |

Journal | Fuzzy Sets and Systems |

Volume | 100 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Jan 1 1998 |

### Keywords

- Archimedean property
- Ordinal sum
- Triangular norms
- Uniform convergence

### ASJC Scopus subject areas

- Logic
- Artificial Intelligence

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## Cite this

Jenei, S., & Fodor, J. C. (1998). On continuous triangular norms.

*Fuzzy Sets and Systems*,*100*(1-3), 273-282. https://doi.org/10.1016/S0165-0114(97)00063-8