Affiliations: Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića Novi Sad, Serbia | University of Tuzla, Faculty of Sciences, Mathematics Department, Univerzitetska, Tuzla, Bosnia and Herzegovina
Note: [] Corresponding author. Branimir Šešelja, Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, Novi Sad 21000, Serbia. E-mails: [email protected] (Branimir Šešelja); [email protected] (Andreja Tepavčević); [email protected] (Mirna Udovičić).
Abstract: Fuzzy (lattice valued) posets are investigated with the order being a fuzzy relation on a fuzzy set. In this framework, fuzzy chains and generally fuzzy lattices are investigated. These are applied to fuzzy lattice ordered subgroups of lattice ordered groups. Lattice ordered subgroups are characterized in terms of cuts, and a special construction of fuzzy lattice valued subgroups is presented. In addition, classical totally ordered groups are characterized by their lattice valued subgroups. An application to ordered groups of real numbers is given.
