Algebarska analiza nekih klasa fazi uređenih struktura / Algebraic Analysis of some Classes of Fuzzy Ordered Structures

Description

<p>Neka je A neprazan skup&nbsp; i ℒ&nbsp;= (L, &le;) proizvoljna mreža sa nulom i jedinicom. Svako preslikavanje &micro;: A &rarr; 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 &le; , do&scaron;li smo do zaključka da ova struktura predstavlja kompletnu mrežu. Takođe, važan zadatak je bio da ispitamo egzistenciju rasplinute mrežno uređene podgrupe <i>l</i>&nbsp;&ndash;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> &ndash;podgrupa od G.</p> / <p>Let A be a nonempty set, and let <em>ℒ</em> = (L, &le;) be a lattice with 0 and 1. The mapping: &micro;: A &rarr; 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 &le;, 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>&ndash;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>

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1. https://www.cris.uns.ac.rs/DownloadFileServlet/Disertacija140025214520875.pdf?controlNumber=(BISIS)87533&fileName=140025214520875.pdf&id=1974&source=NDLTD&language=en
2. https://www.cris.uns.ac.rs/record.jsf?recordId=87533&source=NDLTD&language=en

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Additional Fields

Identifer	oai:union.ndltd.org:uns.ac.rs/oai:CRISUNS:(BISIS)87533
Date	18 August 2014
Creators	Udovičić Mirna
Contributors	Šešelja Branimir, Madarász-Szilágyi Rozália, Tepavčević Andreja, Ignjatović Jelena
Publisher	Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, University of Novi Sad, Faculty of Sciences at Novi Sad
Source Sets	University of Novi Sad
Language	Serbian
Detected Language	Unknown
Type	PhD thesis