A characterization of the ordering of continuous t-norms

Erich Peter Klement, Radko Mesiar, Endre Pap

Research output: Contribution to journalArticle

23 Citations (Scopus)


Given two t-norms T1 and T2, it is quite often difficult or even impossible to check directly whether T1≤ T2. In Schweizer and Sklar (1983), a necessary and sufficient condition is given for continuous Archimedean t-norms to be comparable. We simplify this result, proving a sufficient condition which involves only one argument of a one-place function rather than two arguments. This result is applied to show the monotonicity of some well-known classes of t-norms. Next, we generalize the result of Schweizer and Sklar to the case of all continuous t-norms and present also a sufficient condition, which is again easier to check.

Original languageEnglish
Pages (from-to)189-195
Number of pages7
JournalFuzzy Sets and Systems
Issue number2
Publication statusPublished - Jan 1 1997



  • Additive generator
  • Comparison of t-norms
  • Ordinal sum
  • t-norm

ASJC Scopus subject areas

  • Logic
  • Artificial Intelligence

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