The notions of ideals and filters have studied in many algebraic (crisp) fuzzy structures and used to study their various properties, representations and characterizations. In addition to their theoretical roles, they have used in some areas of applied mathematics. In a recent paper, Arockiarani and Antony Crispin Sweety have generalized and studied these notions with respect to the concept of neutrosophic sets introduced by Smarandache to represent imprecise, incomplete and inconsistent information. In this article, we aim to deepen the study of these important notions on a given lattice in the neutrosophic setting. We show their various properties and characterizations, in particular, we pay attention to their characterizations based on of the lattice min and max operations. In addition, we study the notion of prime single-valued neutrosophic ideal (resp. filter) as interesting kind and we discuss some its set-operations, complement and associate sets.
Zedam, Lemnaouar; Milles, Soheyb; and Bennoui, Abdelhamid
(R1466) Ideals and Filters on a Lattice in Neutrosophic Setting,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 16,
2, Article 21.
Available at: https://digitalcommons.pvamu.edu/aam/vol16/iss2/21