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â„’-Fuzzy Cosets of â„’-Fuzzy Filters of Residuated Multilattices

Author

Listed:
  • Pierre Carole Kengne
  • Blaise Bleriot Koguep Njionou
  • Daquin Cèdric Awouafack
  • Luc Eméry Diékouam Fotso
  • Frederic Mynard

Abstract

This paper mainly focuses on building the â„’-fuzzy filter theory of residuated multilattices. Firstly, we introduce the concepts of â„’-fuzzy filter and â„’-fuzzy deductive system of residuated multilattices. Then, we highlight their properties and show how they are linked. Secondly, we introduce the concept of prime â„’-fuzzy filter and propose some illustrative examples. Then, we bring out their properties and show how they are related to the concept of â„’-fuzzy prime filter. Thirdly, we characterize â„’-fuzzy maximal filter and maximal â„’-fuzzy filter by atoms and coatoms. In the case where â„’ is a distributive lattice, we prove that maximal â„’-fuzzy filters are prime. Finally, we are interested in â„’-fuzzy cosets of an â„’-fuzzy filter, and we prove that the set of all â„’-fuzzy cosets of any â„’-fuzzy filter of a residuated multilattice is a residuated multilattice.

Suggested Citation

  • Pierre Carole Kengne & Blaise Bleriot Koguep Njionou & Daquin Cèdric Awouafack & Luc Eméry Diékouam Fotso & Frederic Mynard, 2022. "â„’-Fuzzy Cosets of â„’-Fuzzy Filters of Residuated Multilattices," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2022, pages 1-14, September.
    • Handle: RePEc:hin:jijmms:6833943
    DOI: 10.1155/2022/6833943
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