Distributivity of aggregation operators and their application in utilitytheory

Abstract

<p>Disertacija je posvećena re&scaron;avanju jednačina distributivnosti gde&nbsp;nepoznate funkcije pripadaju nekim poznatim klasama operacija agregacije&nbsp;i primeni dobijenih re&scaron;enja u teoriji korisnosti. Dobijeni rezultati se generalno mogu podeliti u tri grupe. Prvu grupu čine rezultati iz Glave 2 dobijeni re&scaron;avanjem jednačina distributivnosti između GM-operacija agregacije i&nbsp;oslabljenih uninormi, GM-operacija agregacije i oslabljenih nulanormi, kao i&nbsp;GM-operacija agregacije i operacija agregacije bez neutralnog i absorbujućeg&nbsp;elementa. Druga grupa rezultata, takođe iz Glave 2, je dobijena re&scaron;avanjem&nbsp;jednačina uslovne (oslabljene) distributivnosi neprekidne nulanorme u odnosu&nbsp;na neprekidnu t-konormu, i neprekidne nulanonorme u odnosu na uninorme iz&nbsp;<br />klasa U_min &cup;U_max. Treća grupa rezultata (Glava 3) je proistekla iz primene dobijenih rezultata o uslovoj distributivnosti nulanorme u odnosu na t-konormu&nbsp;u teoriji korisnosti.</p>

<p>This dissertation is devoted to solving distributivity equations involving some well-known classes of aggregation operators, and application&nbsp;the obtained results to utility theory. In general, the obtained results can&nbsp;be divided into three groups. The first group are results from Chapter 2 obtained by solving distributivity equations between GM-aggregation operators&nbsp;and relaxed nullnorm, GM-aggregation operators and relaxed uninorms, as&nbsp;well as GM-aggregation operators and aggregation operators without neutral&nbsp;and absorbing element. The second group are results, also from Chapter 2,&nbsp;obtained by solving conditional (relaxed) distributivity of continuous nullnorm with respect to &nbsp;continuous t-conorm, as well as continuous nullnorm&nbsp;with respect to uninorms from the classes U_min &cup; U_max. The third group are&nbsp;results (Chapter 3) arising from the application results on conditional distributivity of nullnorm with respect to t-conorm in utility theory.</p>