Triangular norms. Position paper III

Continuous t-norms

Erich Peter Klement, Radko Mesiar, E. Pap

Research output: Contribution to journalArticle

62 Citations (Scopus)

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

Fingerprint

Triangular Norm
T-norm
Fuzzy systems
Fuzzy sets
Additive Generator
Ordinal Sum
Representation Theorem
Fuzzy Systems
Fuzzy Sets
Series

Keywords

  • Additive generator
  • Continuous triangular norm
  • Ordinal sum

ASJC Scopus subject areas

  • Statistics and Probability
  • Electrical and Electronic Engineering
  • Statistics, Probability and Uncertainty
  • Information Systems and Management
  • Computer Vision and Pattern Recognition
  • Computer Science Applications
  • Artificial Intelligence

Cite this

Triangular norms. Position paper III : Continuous t-norms. / Klement, Erich Peter; Mesiar, Radko; Pap, E.

In: Fuzzy Sets and Systems, Vol. 145, No. 3, 01.08.2004, p. 439-454.

Research output: Contribution to journalArticle

Klement, Erich Peter ; Mesiar, Radko ; Pap, E. / Triangular norms. Position paper III : Continuous t-norms. In: Fuzzy Sets and Systems. 2004 ; Vol. 145, No. 3. pp. 439-454.
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