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

Pierre Carole Kengne, Blaise Bleriot Koguep Njionou, Daquin Cèdric Awouafack, Luc Eméry Diékouam Fotso and Frederic Mynard

International Journal of Mathematics and Mathematical Sciences, 2022, vol. 2022, 1-14

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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:6833943

DOI: 10.1155/2022/6833943

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