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https://open.uns.ac.rs/handle/123456789/30467| Title: | Distributivity of aggregation operators and their application in utilitytheory Distributivnost operacija agregacije i njihova primena u teoriji korisnosti |
Authors: | Jočić Dragan | Keywords: | aggregation operator, t-norm, t-conorm, GM-operation,uninorm, nullnorm, distributivity, conditional distributivity, utility function;operacija agregacije, t-norma, t-konorma, GM-operacija, uninorma, nulanorma, distributivnost, uslovna distributivnost, funkcija korisnosti | Issue Date: | 28-Feb-2015 | Publisher: | Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu University of Novi Sad, Faculty of Sciences at Novi Sad |
Abstract: | <p>Disertacija je posvećena rešavanju jednačina distributivnosti gde nepoznate funkcije pripadaju nekim poznatim klasama operacija agregacije i primeni dobijenih rešenja u teoriji korisnosti. Dobijeni rezultati se generalno mogu podeliti u tri grupe. Prvu grupu čine rezultati iz Glave 2 dobijeni rešavanjem jednačina distributivnosti između GM-operacija agregacije i oslabljenih uninormi, GM-operacija agregacije i oslabljenih nulanormi, kao i GM-operacija agregacije i operacija agregacije bez neutralnog i absorbujućeg elementa. Druga grupa rezultata, takođe iz Glave 2, je dobijena rešavanjem jednačina uslovne (oslabljene) distributivnosi neprekidne nulanorme u odnosu na neprekidnu t-konormu, i neprekidne nulanonorme u odnosu na uninorme iz <br />klasa U<sub>min</sub> ∪U<sub>max</sub>. Treća grupa rezultata (Glava 3) je proistekla iz primene dobijenih rezultata o uslovoj distributivnosti nulanorme u odnosu na t-konormu u teoriji korisnosti.</p> <p>This dissertation is devoted to solving distributivity equations involving some well-known classes of aggregation operators, and application the obtained results to utility theory. In general, the obtained results can be divided into three groups. The first group are results from Chapter 2 obtained by solving distributivity equations between GM-aggregation operators and relaxed nullnorm, GM-aggregation operators and relaxed uninorms, as well as GM-aggregation operators and aggregation operators without neutral and absorbing element. The second group are results, also from Chapter 2, obtained by solving conditional (relaxed) distributivity of continuous nullnorm with respect to continuous t-conorm, as well as continuous nullnorm with respect to uninorms from the classes U<sub>min</sub> ∪ U<sub>max</sub>. The third group are results (Chapter 3) arising from the application results on conditional distributivity of nullnorm with respect to t-conorm in utility theory.</p> |
URI: | https://open.uns.ac.rs/handle/123456789/30467 |
| Appears in Collections: | PMF Teze/Theses |
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