Academic Bibliography

 Search 200 years of publications by Ghent University researchers.
Advanced search
2 files | 884.77 KB
Add to list
  1. Search results
  2. The pseudo-inverse of a monotone func...

The pseudo-inverse of a monotone function between complete lattices and its use in generating t-norms and t-conorms

Yanyan Dong, Bin Pang and Bernard De Baets (UGent)
(2024) FUZZY SETS AND SYSTEMS. 478.
Author
Organization
Abstract
In this paper, we introduce the concept of pseudo-inverse of a monotone function between complete lattices. Using this pseudo-inverse, we provide methods for generating t-norms and t-conorms on a complete lattice via a complete inf-homomorphism and a complete sup-inf-homo-morphism, respectively. In particular, when we consider an injective complete inf-homomorphism and an injective complete sup-inf-homomorphism, these methods can be seen as generalizations of the right-continuous multiplicative generator theorem of t-norms and the left-continuous multiplicative generator theorem of t-conorms in the classical setting, respectively. We discuss some properties of these generated t-norms and t-conorms on a complete lattice. As an application, we present a method for constructing a *-(pre)betweenness relation from a given (pseudo)metric.
Keywords
t-Norm, t-Conorm, Pseudo-inverse, Complete lattice, Complete inf-homomorphism, *-betweenness relation, TRIANGULAR NORMS, ADDITIVE GENERATORS, ORDINAL SUMS

Downloads

  • Download
    (...).pdf
    • full text (Published version)
    • |
    • UGent only
    • |
    • PDF
    • |
    • 691.03 KB
  • Download
    BIN PANG The pseudo inverse of a monotone function between complete lattices.pdf
    • full text (Published version)
    • |
    • open access
    • |
    • PDF
    • |
    • 193.74 KB

Citation

Please use this url to cite or link to this publication:

MLA
Dong, Yanyan, et al. “The Pseudo-Inverse of a Monotone Function between Complete Lattices and Its Use in Generating t-Norms and t-Conorms.” FUZZY SETS AND SYSTEMS, vol. 478, 2024, doi:10.1016/j.fss.2023.108837.
APA
Dong, Y., Pang, B., & De Baets, B. (2024). The pseudo-inverse of a monotone function between complete lattices and its use in generating t-norms and t-conorms. FUZZY SETS AND SYSTEMS, 478. https://doi.org/10.1016/j.fss.2023.108837
Chicago author-date
Dong, Yanyan, Bin Pang, and Bernard De Baets. 2024. “The Pseudo-Inverse of a Monotone Function between Complete Lattices and Its Use in Generating t-Norms and t-Conorms.” FUZZY SETS AND SYSTEMS 478. https://doi.org/10.1016/j.fss.2023.108837.
Chicago author-date (all authors)
Dong, Yanyan, Bin Pang, and Bernard De Baets. 2024. “The Pseudo-Inverse of a Monotone Function between Complete Lattices and Its Use in Generating t-Norms and t-Conorms.” FUZZY SETS AND SYSTEMS 478. doi:10.1016/j.fss.2023.108837.
Vancouver
1.
Dong Y, Pang B, De Baets B. The pseudo-inverse of a monotone function between complete lattices and its use in generating t-norms and t-conorms. FUZZY SETS AND SYSTEMS. 2024;478.
IEEE
[1]
Y. Dong, B. Pang, and B. De Baets, “The pseudo-inverse of a monotone function between complete lattices and its use in generating t-norms and t-conorms,” FUZZY SETS AND SYSTEMS, vol. 478, 2024.
@article{01HNZ725WY88CGHNTV6QC2FSR2,
  abstract     = {{In this paper, we introduce the concept of pseudo-inverse of a monotone function between complete lattices. Using this pseudo-inverse, we provide methods for generating t-norms and t-conorms on a complete lattice via a complete inf-homomorphism and a complete sup-inf-homo-morphism, respectively. In particular, when we consider an injective complete inf-homomorphism and an injective complete sup-inf-homomorphism, these methods can be seen as generalizations of the right-continuous multiplicative generator theorem of t-norms and the left-continuous multiplicative generator theorem of t-conorms in the classical setting, respectively. We discuss some properties of these generated t-norms and t-conorms on a complete lattice. As an application, we present a method for constructing a *-(pre)betweenness relation from a given (pseudo)metric.}},
  articleno    = {{108837}},
  author       = {{Dong, Yanyan and  Pang, Bin and De Baets, Bernard}},
  issn         = {{0165-0114}},
  journal      = {{FUZZY SETS AND SYSTEMS}},
  keywords     = {{t-Norm,t-Conorm,Pseudo-inverse,Complete lattice,Complete inf-homomorphism,*-betweenness relation,TRIANGULAR NORMS,ADDITIVE GENERATORS,ORDINAL SUMS}},
  language     = {{eng}},
  pages        = {{21}},
  title        = {{The pseudo-inverse of a monotone function between complete lattices and its use in generating t-norms and t-conorms}},
  url          = {{http://doi.org/10.1016/j.fss.2023.108837}},
  volume       = {{478}},
  year         = {{2024}},
}
Altmetric
View in Altmetric
Web of Science
Times cited: