|Title:||Fuzzy posets with fuzzy order applied to fuzzy ordered groups||Journal:||Filomat||Volume:||28||Issue:||9||First page:||1835||Last page:||1848||Issue Date:||1-Jan-2014||Rank:||M22||ISSN:||0354-5180||DOI:||10.2298/FIL1409835S||Abstract:||
In the framework of lattice valued structures we investigate fuzzy sub-posets of a given poset, in which the underlying set ornand the order are fuzzy and the reflexivity is specially defined. We introduce and investigate particular fuzzy sub-posets, e.g, fuzzy up-sets and down-sets, fuzzy convex sub-posets, fuzzy intervals etc. We describe the structure of the lattice of all fuzzy orders contained in a given crisp ordering. Then we apply these in defining a fuzzy ordered subgroup of an ordered group. Main features of fuzzy ordered subgroups are introduced and investigated like fuzzy positive and negative cone and fuzzy convex subgroups.
|Keywords:||Fuzzy ordered group | Fuzzy ordering | Fuzzy poset||Publisher:||University of Niš||Project:||Development of methods of computation and information processing: theory and applications
Provincial Secre-tariat for Science and Technological Development, Autonomous Province of Vojvodina, Grant “Ordered structures and applications”
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