Affiliations: Department of Mathematical Sciences, Technology and Humanities – DCETH, Rural Federal University of SemiArid – UFERSA, Campus Angicos, Rio Grande do Norte, Brazil | Group of Logic, Language, Information, Theory and Applications – LOLITA, Department of Informatics and Applied Mathematics – DIMAp, Federal University of Rio Grande do Norte – UFRN, Natal, Rio Grande do Norte, Brazil
Note: [] Corresponding author. Ivan Mezzomo, Department of Mathematical Sciences, Technology and Humanities – DCETH, Rural Federal University of SemiArid – UFERSA, Campus Angicos, Rio Grande do Norte 59515-000, Brazil. Tel.: +55 84 9621 8118; Fax: +55 84 3531 2547; E-mail: [email protected]
Abstract: In this paper we consider the notion of Fuzzy Lattices, which was introduced by Chon (Korean J. Math 17 (2009), No. 4, 361-374). We propose some new notions for Fuzzy Ideals and Filters and provide a characterization of Fuzzy Ideals via α-level Sets and Support. Some types of ideals and filters, such as: Fuzzy Principal Ideals (Filters), Proper Fuzzy Ideals (Filters), Prime Fuzzy Ideals (Filters) and Fuzzy Maximal Ideals (Filters) are also provided. Some properties (analogous to the classical theory) are also proved and the notion of Homomorphism from fuzzy lattices as well as the demonstration of some important propositions about it are also provided.
