Grafovi preferencije i njihova primjena

master's thesis

• Author: Adrian Satja Kurdija
• Mentor: Lavoslav Čaklović (mentor)
• Committee member: Lavoslav Čaklović (predsjednik povjerenstva)
• Committee member: Marko Vrdoljak (član povjerenstva)
• Committee member: Zvonimir Bujanović (član povjerenstva)
• Committee member: Boris Guljaš (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-07-13, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Usporedba objekata (alternativa) u parovima često se koristi u kontekstu odlučivanja. Metoda potencijala koristi (težinski) graf preferencije kao osnovnu strukturu generiranu takvim usporedbama. Iz toga grafa, rješavanjem sustava jednadžbi koji uključuje njegovu Laplaceovu matricu, dobiva se funkcija vrijednosti na skupu alternativa koju nazivamo potencijalom. U višekriterijskom ili grupnom odlučivanju (npr. izbornim procedurama), svaki kriterij ili sudionik može se predstaviti grafom preferencije. Multigraf dobiven spajanjem tih grafova koristi se za agregaciju preferencija i generira grupni potencijal. Moguće je postaviti proizvoljne težine da bismo podesili utjecaj pojedinog kriterija ili sudionika na grupni potencijal. Agregaciju grafova preferencije primjenjujemo na izborne procedure. Različiti oblici glasačkih listića generiraju grafove preferencije: tako dobivamo univerzalnu izbornu proceduru koja ne ovisi o obliku glasačkog listića. Još jedna primjena je klasterska analiza skupine na temelju preferencija njezinih članova, gdje valja provesti hijerarhijsku ili particijsku klasterizaciju više grafova preferencije. U tom kontekstu, agregacijski multigraf koristimo za definiranje središta klastera ili udaljenosti dvaju klastera. Opisanu izbornu proceduru, kao i klastersku analizu, za ilustraciju smo primijenili na glasačke preferencije zemalja s Eurosong natjecanja.

Abstract (english)

Pairwise comparison of various objects (alternatives) is common in many procedures related to decision making. Potential Method (PM) uses a (weighted) preference graph as the basic structure generated by such comparisons. This graph implies a value function (called potential) on the set of alternatives. The potential is calculated as a solution of a system of equations involving the Laplacian matrix of the preference graph. In multiple-criteria decision analysis or group decision making (i.e., voting systems), each criterion or decision maker is represented by a preference graph. A multigraph obtained by joining these graphs is used for preference aggregation, generating the group potential. We can set arbitrary weights to adjust the influence of each criterion or decision maker on the group potential. Aggregation of preference graphs is applied to voting systems. Many different forms of voting ballots can generate preference graphs, which gives us a universal (ballot-independent) voting system. Another application is a cluster analysis of the group based on the members’ preferences, where a hierarchical or partitional clustering of their (multiple) preference graphs should be performed. In this context, the multigraph-based aggregation is used to define the center of the cluster or the distance between two clusters. As an illustration, we have applied the described voting system, as well as the cluster analysis, to the voting data from the Eurovision Song Contest.

• Keywords: usporedba objekata; metoda potencijala; Laplaceova matrica; agregacija grafova preferencije; klasterska analiza skupine; hijerahijska klasterizacija; particijska klasterizacija
• Keywords (english): pairwise comparison of objects; potential method; PM; Laplacian matrix; preference aggregation; cluster analysis of the group; hierarchical clustering; partitional clustering
• Language: croatian
• URN:NBN: urn:nbn:hr:217:932693
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-21 12:20:10