A characterization of the ordering of continuous t-norms

Erich Peter Klement, Radko Mesiar, E. Pap

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

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
Volume86
Issue number2
Publication statusPublished - 1997

Fingerprint

T-norm
Sufficient Conditions
Monotonicity
Simplify
Necessary Conditions
Generalise

Keywords

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

ASJC Scopus subject areas

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

Cite this

A characterization of the ordering of continuous t-norms. / Klement, Erich Peter; Mesiar, Radko; Pap, E.

In: Fuzzy Sets and Systems, Vol. 86, No. 2, 1997, p. 189-195.

Research output: Contribution to journalArticle

Klement, EP, Mesiar, R & Pap, E 1997, 'A characterization of the ordering of continuous t-norms', Fuzzy Sets and Systems, vol. 86, no. 2, pp. 189-195.
Klement, Erich Peter ; Mesiar, Radko ; Pap, E. / A characterization of the ordering of continuous t-norms. In: Fuzzy Sets and Systems. 1997 ; Vol. 86, No. 2. pp. 189-195.
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