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Soft Computing

, Volume 23, Issue 23, pp 12199–12208 | Cite as

Multiplicative and implicative derivations on residuated multilattices

  • Line N. MaffeuEmail author
  • Celestin Lele
  • Jean B. Nganou
  • Etienne A. Temgoua
Foundations
  • 42 Downloads

Abstract

In this paper, we extend the study of derivations on residuated lattices to residuated multilattices. Special types of derivations (implicative and multiplicative) and their connections with the complemented elements are investigated. In particular, one obtains that the good ideal derivations of a bounded residuated multilattice are completely determined by its complemented elements. Supporting examples of all the notions treated are also included.

Keywords

Multilattice Residuated multilattice Derivation Complemented elements Ideal derivation 

Notes

Acknowledgements

The authors are grateful to the referees whose comments improved the content and the presentation of the paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of DschangDschangCameroon
  2. 2.Department of Mathematics and StatisticsUniversity of Houston-DowntownHoustonUSA
  3. 3.Department of MathematicsEcole Normale SuperieureYaoundéCameroon

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