Authors: Šešelja, Branimir
Tepavčević, Andreja 
Udovičić, Mirna
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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