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Ω-Algebarski sistemi

dc.contributor.advisorŠešelja, Branimir
dc.contributor.otherMarković, Petar
dc.contributor.otherŠešelja, Branimir
dc.contributor.otherTepavčević, Andreja
dc.contributor.otherĆirić, Miroslav
dc.creatorEdeghagba Elijah, Eghosa
dc.date.accessioned2017-05-14T21:04:10Z
dc.date.available2017-05-14T21:04:10Z
dc.date.available2020-07-03T13:38:29Z
dc.date.issued2017-03-30
dc.identifier.urihttp://www.cris.uns.ac.rs/DownloadFileServlet/Disertacija148672818177245.pdf?controlNumber=(BISIS)104206&fileName=148672818177245.pdf&id=7225&source=NaRDuS&language=srsr
dc.identifier.urihttp://nardus.mpn.gov.rs/handle/123456789/8066
dc.identifier.urihttp://www.cris.uns.ac.rs/record.jsf?recordId=104206&source=NaRDuS&language=srsr
dc.identifier.urihttp://www.cris.uns.ac.rs/DownloadFileServlet/IzvestajKomisije149087458652551.pdf?controlNumber=(BISIS)104206&fileName=149087458652551.pdf&id=7344&source=NaRDuS&language=srsr
dc.description.abstractThe research work carried out in this thesis is aimed   at fuzzifying algebraic and relational structures in the framework of Ω-sets, where Ω is a complete lattice. Therefore we attempt to synthesis universal algebra and fuzzy set theory. Our  investigations of Ω-algebraic structures are based on Ω-valued equality, satisability of identities and cut techniques. We introduce Ω-algebras, Ω-valued congruences,  corresponding quotient  Ω-valued-algebras and  Ω-valued homomorphisms and we investigate connections among these notions. We prove that there is an Ω-valued homomorphism from an Ω-algebra to the corresponding quotient Ω-algebra. The kernel of an Ω-valued homomorphism is an Ω-valued congruence. When dealing with cut structures, we prove that an Ω-valued homomorphism determines classical homomorphisms among the corresponding quotient structures over cut  subalgebras. In addition, an  Ω-valued congruence determines a closure system of classical congruences on cut subalgebras. In addition, identities are preserved under Ω-valued homomorphisms. Therefore in the framework of Ω-sets we were able to introduce Ω-attice both as an ordered and algebraic structures. By this Ω-poset is defined as an Ω-set equipped with  Ω-valued order which is  antisymmetric with respect to the corresponding Ω-valued equality. Thus defining the notion of pseudo-infimum and pseudo-supremum we obtained the definition of Ω-lattice as an ordered structure. It is also defined that the an Ω-lattice as an algebra is a bi-groupoid equipped with an Ω-valued equality fulfilling some particular lattice Ω-theoretical formulas. Thus using axiom of choice we proved that the two approaches are equivalent. Then we also introduced the notion of complete Ω-lattice based on Ω-lattice. It was defined as a generalization of the classical complete lattice. We proved results that characterizes Ω-structures and many other interesting results. Also the connection between Ω-algebra and the notion of weak congruences is presented. We conclude with what we feel are most interesting areas for future work.en
dc.description.abstractTema ovog rada je fazifikovanje algebarskih i relacijskih struktura u okviru omega- skupova, gdeje Ω kompletna mreza. U radu se bavimo sintezom oblasti univerzalne algebre i teorije rasplinutih (fazi) skupova. Naša istraživanja omega-algebarskih struktura bazirana su na omega-vrednosnoj jednakosti,zadovoljivosti identiteta i tehnici rada sa nivoima. U radu uvodimo omega-algebre,omega-vrednosne kongruencije, odgovarajuće omega-strukture, i omega-vrednosne homomorfizme i istražujemo veze izmedju ovih pojmova. Dokazujemo da postoji Ω -vrednosni homomorfizam iz Ω -algebre na odgovarajuću količničku Ω -algebru. Jezgro Ω -vrednosnog homomorfizma je Ω- vrednosna kongruencija. U vezi sa nivoima struktura, dokazujemo da Ω -vrednosni homomorfizam odredjuje klasične homomorfizme na odgovarajućim količničkim strukturama preko nivoa podalgebri. Osim toga, Ω-vrednosna kongruencija odredjuje sistem zatvaranja klasične kongruencije na nivo podalgebrama. Dalje, identiteti su očuvani u Ω- vrednosnim homomorfnim slikama.U nastavku smo u okviru Ω-skupova uveli Ω-mreže kao uredjene skupove i kao algebre i dokazali ekvivalenciju ovih pojmova. Ω-poset je definisan kao Ω -relacija koja je antisimetrična i tranzitivna u odnosu na odgovarajuću Ω-vrednosnu jednakost. Definisani su pojmovi pseudo-infimuma i pseudo-supremuma i tako smo dobili definiciju Ω-mreže kao uredjene strukture. Takodje je definisana Ω-mreža kao algebra, u ovim kontekstu nosač te strukture je bi-grupoid koji je saglasan sa Ω-vrednosnom jednakošću i ispunjava neke mrežno-teorijske formule. Koristeći aksiom izbora dokazali smo da su dva pristupa ekvivalentna. Dalje smo uveli i pojam potpune Ω-mreže kao uopštenje klasične potpune mreže. Dokazali smo još neke rezultate koji karakterišu Ω-strukture.Data je i veza izmedju Ω-algebre i pojma slabih kongruencija.Na kraju je dat prikaz pravaca daljih istrazivanja.sr
dc.languageen
dc.publisherУниверзитет у Новом Саду, Природно-математички факултетsr
dc.rightsopenAccessen
dc.sourceУниверзитет у Новом Садуsr
dc.subjectFuzzy seten
dc.subjectrasplinuti skupsr
dc.subjectOmega-algebresr
dc.subjectOmega- vrednosni homomorfizmisr
dc.subjectΩ-vrednosne kongruencijesr
dc.subjectSlabe kongruecijesr
dc.subjectΩ -skupsr
dc.subjectΩ-algebrasen
dc.subjectΩ-valued homomorphismsen
dc.subjectΩ-valued congruencesen
dc.subjectWeak congruencesen
dc.subjectΩ-seten
dc.subjectΩ-poseten
dc.subjectΩ-latticeen
dc.subjectComplete Ω-latticeen
dc.subjectΩ-valued Equalityen
dc.subjectClosure systemen
dc.subjectΩ-posetsr
dc.subjectΩ-mrezasr
dc.subjectKompletna Ω mrezasr
dc.subjectΩ vrednosna jednakostsr
dc.subjectSistem zatvaranjasr
dc.titleΩ-Algebraic Structuresen
dc.title.alternativeΩ-Algebarski sistemisr
dc.typedoctoralThesissr
dc.rights.licenseBY
dcterms.abstractШешеља, Бранимир; Тепавчевић, Aндреја; Шешеља, Бранимир; Ћирић, Мирослав; Марковић, Петар; Едегхагба Елијах, Егхоса;
dc.identifier.fulltexthttp://nardus.mpn.gov.rs/bitstream/id/36882/IzvestajKomisije9273.pdf
dc.identifier.fulltexthttp://nardus.mpn.gov.rs/bitstream/id/36883/Disertacija9273.pdf


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