In this paper, we introduce the notions of -fuzzy s-ideal, -fuzzy m-ideal, -fuzzy l-ideal and -fuzzy ideal of multilattice. We obtain some relationships between these four types of -fuzzy ideals. In addition, we define different types of -fuzzy submultilattices. We show that any -fuzzy s-ideal is an -fuzzy r-submultilattice and  the converse is not always true. Finally, we define the -fuzzy congruence relation on a multilattice and give some characterizations. We also prove that the -fuzzy congruence relation induces the -fuzzy l-ideal.

multilattice, ideals, submultilattices, congruence relation, -fuzzy sets.

Received: February 21, 2021; Revised: April 9, 2021; Accepted: July 20, 2021; Published: August 10, 2021

How to cite this article: Pierre Carole Kengne, Daquin Cédric Awouafack, Blaise Blériot Koguep and Celestin Lele, -fuzzy ideals and -fuzzy congruences of multilattices, Advances in Fuzzy Sets and Systems 26(2) (2021), 145-174. DOI: 10.17654/FS026020145

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License 

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