Archimedean components of triangular norms

Erich Klement; Radko Mesiar; Endre Pap

doi:10.1017/s1446788700008065

Archimedean components of triangular norms

Erich Klement, Radko Mesiar, Endre Pap

Institute for Mathematical Methods in Medicine and Data Based Modeling

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	239-255
Journal	Journal of the Australian Mathematical Society
Volume	78
DOIs	https://doi.org/10.1017/s1446788700008065
Publication status	Published - 2005

Fields of science

101 Mathematics
101004 Biomathematics
101027 Dynamical systems
101013 Mathematical logic
101028 Mathematical modelling
101014 Numerical mathematics
101020 Technical mathematics
101024 Probability theory
102001 Artificial intelligence
102003 Image processing
102009 Computer simulation
102019 Machine learning
102023 Supercomputing
202027 Mechatronics
206001 Biomedical engineering
206003 Medical physics
102035 Data science

Access to Document

10.1017/s1446788700008065

Cite this

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title = "Archimedean components of triangular norms",

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.",

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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.

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DO - 10.1017/s1446788700008065

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