|Title:||Fuzzy ordered structures and fuzzy lattice ordered groups||Journal:||Journal of Intelligent and Fuzzy Systems||Volume:||27||Issue:||3||First page:||1119||Last page:||1127||Issue Date:||1-Jan-2014||Rank:||M22||ISSN:||1064-1246||DOI:||10.3233/IFS-131075||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.
|Keywords:||fuzzy chain | fuzzy lattice | fuzzy lattice ordered group | fuzzy ordering | Fuzzy poset||Publisher:||IOS Press|
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