On the order of triangular norms - Comments on "A triangular norm hierarchy" by E. Cretu

Erich Peter Klement, Radko Mesiar, E. Pap

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In Cretu (Fuzzy Sets and Systems 120 (2001) 371), the members of the families of Frank, Dubois-Prade, Yager, and Hamacher t-norms, respectively, are compared (in a pointwise way) with the minimum, the product, and the Łukasiewicz t-norm. All these results are well-known and trivial. Moreover, these families of t-norms cannot only be compared with the three basic t-norms above, but all these families are monotone with respect to their index, a fact which is also well known and straightforward to prove (with the exception of the family of Frank t-norms whose monotonicity has been first proven in Butnariu and Klement, Triangular Norm-Based Measures and Games with Fuzzy Coalitions, Kluwer, Dordrecht, 1993).

Original languageEnglish
Pages (from-to)409-413
Number of pages5
JournalFuzzy Sets and Systems
Volume131
Issue number3
DOIs
Publication statusPublished - Nov 1 2002

Fingerprint

Triangular Norm
T-norm
Fuzzy systems
Fuzzy sets
Coalitions
Fuzzy Systems
Exception
Fuzzy Sets
Monotonicity
Monotone
Trivial
Hierarchy
Game
Family

Keywords

  • Order
  • Triangular norms

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

On the order of triangular norms - Comments on "A triangular norm hierarchy" by E. Cretu. / Klement, Erich Peter; Mesiar, Radko; Pap, E.

In: Fuzzy Sets and Systems, Vol. 131, No. 3, 01.11.2002, p. 409-413.

Research output: Contribution to journalArticle

Klement, Erich Peter ; Mesiar, Radko ; Pap, E. / On the order of triangular norms - Comments on "A triangular norm hierarchy" by E. Cretu. In: Fuzzy Sets and Systems. 2002 ; Vol. 131, No. 3. pp. 409-413.
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