A characterization of the Hamacher family of t-norms

J. Fodor, Tibor Keresztfalvi

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

Starting from a fuzzy conjunction, there are two main ways of defining a fuzzy implication operator. A functional equation for t-norms is obtained and studied which describes the equality of these two implications when the underlying conjunction has a particular form defined from a t-norm. The solution makes clear that this functional equation, together with an additional condition, provides a complete characterization of the Hamacher family of t-norms having positive parameter.

Original languageEnglish
Pages (from-to)51-58
Number of pages8
JournalFuzzy Sets and Systems
Volume65
Issue number1
DOIs
Publication statusPublished - Jul 11 1994

Fingerprint

T-norm
Functional equation
Fuzzy Implication Operator
Equality
Family

Keywords

  • Conjunctions
  • Fuzzy logic
  • Hamacher family of t-norms
  • Implications
  • t-norms

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 Hamacher family of t-norms. / Fodor, J.; Keresztfalvi, Tibor.

In: Fuzzy Sets and Systems, Vol. 65, No. 1, 11.07.1994, p. 51-58.

Research output: Contribution to journalArticle

Fodor, J. ; Keresztfalvi, Tibor. / A characterization of the Hamacher family of t-norms. In: Fuzzy Sets and Systems. 1994 ; Vol. 65, No. 1. pp. 51-58.
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