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https://open.uns.ac.rs/handle/123456789/29359| Title: | Algebraic Analysis of some Classes of Fuzzy Ordered Structures Algebarska analiza nekih klasa fazi uređenih struktura |
Authors: | Udovičić Mirna | Keywords: | poset, lattice, fuzzy subset, fuzzy poset, fuzzy group, fuzzy order, fuzzy weak order, fuzzy ordered group, fuzzy lattice ordered group;poset, mreža, rasplinuti podskup, rasplinuti poset, rasplinuta grupa, rasplinuti poredak, slabi rasplinuti poredak, raplinuta uređena grupa, rasplinuta mrežno uređena grupa | Issue Date: | 18-Aug-2014 | Publisher: | Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu University of Novi Sad, Faculty of Sciences at Novi Sad |
Abstract: | <p>Neka je A neprazan skup i ℒ = (L, ≤) proizvoljna mreža sa nulom i jedinicom. Svako preslikavanje µ: A → L zovemo rasplinuti podskup od A. U ovoj tezi proučavali smo rasplinute posete i relacije rasplinutog poretka. Uveli smo neke nove pojmove: rasplinuta uređena grupa, rasplinuti pozitivan konus, rasplinuti negativan konus, rasplinuta mrežno uređena grupa. Posmatrajući strukturu svih relacija slabog rasplinutog poretka koje su podskup klasične relacije poretka ≤ , došli smo do zaključka da ova struktura predstavlja kompletnu mrežu. Takođe, važan zadatak je bio da ispitamo egzistenciju rasplinute mrežno uređene podgrupe <i>l</i> –uređene grupe koja nije linearno uređena. Bitan rezultat je rasplinuta mrežno uređena podgrupa date mrežno uređene grupe G, koja je konstruisana pomoću mreže svih kompleksnih <em>l</em> –podgrupa od G.</p> <p>Let A be a nonempty set, and let <em>ℒ</em> = (L, ≤) be a lattice with 0 and 1. The mapping: µ: A → L is called a fuzzy subset of A. In this work we investigated fuzzy posets and fuzzy ordering relations. We introduced some new notions: fuzzy ordered groups, fuzzy positive cone, fuzzy negative cone, fuzzy lattice ordered group. Considering a structure of all weak fuzzy orderings contained in the crisp order ≤, we concluded that this structure represents a complete lattice. Also, an important task was to investigate the existence of a fuzzy lattice ordered subgroup of an <em>l</em>–ordered group which is not linearly ordered. A main result is a fuzzy lattice ordered subgroup of a given lattice ordered group G, which is constructed by the lattice of all convex <em>l</em>-subgroups of G.</p> |
URI: | https://open.uns.ac.rs/handle/123456789/29359 |
| Appears in Collections: | PMF Teze/Theses |
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