On continuous triangular norms

Sándor Jenei, János C. Fodor

Research output: Contribution to journalArticle

22 Citations (Scopus)

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 languageEnglish
Pages (from-to)273-282
Number of pages10
JournalFuzzy Sets and Systems
Volume100
Issue number1-3
DOIs
Publication statusPublished - Jan 1 1998

Keywords

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

ASJC Scopus subject areas

  • Logic
  • Artificial Intelligence

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