### Abstract

The Archimedean components of triangular norms (which turn the closed unit interval into an abelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordinal sums and additive generators, new types of left-continuous triangular norms are constructed.

Original language | English |
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Pages (from-to) | 239-255 |

Number of pages | 17 |

Journal | Journal of the Australian Mathematical Society |

Volume | 78 |

Issue number | 2 |

Publication status | Published - Apr 2005 |

### Fingerprint

### Keywords

- Archimedean component
- Semigroup
- Triangular norm

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of the Australian Mathematical Society*,

*78*(2), 239-255.

**Archimedean components of triangular norms.** / Klement, Erich Peter; Mesiar, Radko; Pap, E.

Research output: Contribution to journal › Article

*Journal of the Australian Mathematical Society*, vol. 78, no. 2, pp. 239-255.

}

TY - JOUR

T1 - Archimedean components of triangular norms

AU - Klement, Erich Peter

AU - Mesiar, Radko

AU - Pap, E.

PY - 2005/4

Y1 - 2005/4

N2 - The Archimedean components of triangular norms (which turn the closed unit interval into an abelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordinal sums and additive generators, new types of left-continuous triangular norms are constructed.

AB - The Archimedean components of triangular norms (which turn the closed unit interval into an abelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordinal sums and additive generators, new types of left-continuous triangular norms are constructed.

KW - Archimedean component

KW - Semigroup

KW - Triangular norm

UR - http://www.scopus.com/inward/record.url?scp=18944384460&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18944384460&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:18944384460

VL - 78

SP - 239

EP - 255

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 2

ER -