Triangular norms. Position paper III: Continuous t-norms

Erich Peter Klement, Radko Mesiar, Endre Pap

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Abstract

This third and last part of a series of position papers on triangular norms (for Parts I and II see (E.P. Klement, R. Mesiar, E. Pap, Triangular norms, Position paper I: basic analytical and algebraic properties, Fuzzy Sets and Systems, in press; E.P. Klement, R. Mesiar, E. Pap, Triangular norms. Position paper II: general constructions and parameterized families, submitted for publication) presents the representation of continuous Archimedean t-norms by means of additive generators, and the representation of continuous t-norms by means of ordinal sums with Archimedean summands, both with full proofs. Finally some consequences of these representation theorems in the context of comparison and convergence of continuous t-norms, and of the determination of continuous t-norms by their diagonal sections are mentioned.

Original languageEnglish
Pages (from-to)439-454
Number of pages16
JournalFuzzy Sets and Systems
Volume145
Issue number3
DOIs
Publication statusPublished - Aug 1 2004

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Keywords

  • Additive generator
  • Continuous triangular norm
  • Ordinal sum

ASJC Scopus subject areas

  • Logic
  • Artificial Intelligence

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