A generalization of the Mulholland inequality for continuous Archimedean t-norms

Susanne Saminger-Platz, Bernard De Baets, Hans De Meyer

Research output: Contribution to journalArticlepeer-review

Abstract

It is well known that dominance between strict t-norms is closely related to the Mulholland inequality, which can be seen as a generalization of the Minkowski inequality. However, strict t-norms constitute only one part of the class of continuous Archimedean t-norms, the basic elements from which all continuous t-norms are composed. In this paper, dominance between continuous Archimedean t-norms is shown to be related to a generalization of the Mulholland inequality. We provide sufficient and necessary conditions for its fulfillment.
Original languageEnglish
Pages (from-to)607-614
Number of pages8
JournalJournal of Mathematical Analysis and Applications
Volume345
Issue number1
DOIs
Publication statusPublished - 2008

Fields of science

  • 101 Mathematics
  • 101004 Biomathematics
  • 101027 Dynamical systems
  • 101013 Mathematical logic
  • 101028 Mathematical modelling
  • 101014 Numerical mathematics
  • 101020 Technical mathematics
  • 101024 Probability theory
  • 102001 Artificial intelligence
  • 102003 Image processing
  • 102009 Computer simulation
  • 102019 Machine learning
  • 102023 Supercomputing
  • 202027 Mechatronics
  • 206001 Biomedical engineering
  • 206003 Medical physics
  • 102035 Data science

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