ℒ -Fuzzy Cosets of ℒ -Fuzzy Filters of Residuated Multilattices

Autor: Pierre Carole Kengne, Blaise Bleriot Koguep Njionou, Daquin Cèdric Awouafack, Luc Eméry Diékouam Fotso
Rok vydání: 2022
Předmět:
Zdroj: International Journal of Mathematics and Mathematical Sciences. 2022:1-14
ISSN: 1687-0425
0161-1712
DOI: 10.1155/2022/6833943
Popis: This paper mainly focuses on building the ℒ -fuzzy filter theory of residuated multilattices. Firstly, we introduce the concepts of ℒ -fuzzy filter and ℒ -fuzzy deductive system of residuated multilattices. Then, we highlight their properties and show how they are linked. Secondly, we introduce the concept of prime ℒ -fuzzy filter and propose some illustrative examples. Then, we bring out their properties and show how they are related to the concept of ℒ -fuzzy prime filter. Thirdly, we characterize ℒ -fuzzy maximal filter and maximal ℒ -fuzzy filter by atoms and coatoms. In the case where ℒ is a distributive lattice, we prove that maximal ℒ -fuzzy filters are prime. Finally, we are interested in ℒ -fuzzy cosets of an ℒ -fuzzy filter, and we prove that the set of all ℒ -fuzzy cosets of any ℒ -fuzzy filter of a residuated multilattice is a residuated multilattice.
Databáze: OpenAIRE
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