Tropski problem lastnih vrednosti in uporaba : magistrsko delo

Černe, Nejc (author), Košir, Tomaž (mentor)

Delo obravnava matrike nad tropskim polkolobarjem. Vpeljan je tropski polkolobar in matrike nad tropskim polkolobarjem. Vzpostavljena je povezava med tropskimi matrikami in uteženimi usmerjenimi grafi. Karakterizirane so lastne vrednosti tropskih matrik in pripadajoči lastni podprostori. Pridobljeno znanje se uporabi na matrikah za primerjanje parov alternativ. Za pridobitev vektorja točk, ki pripada alternativam, se obravnava tri metode in njihove lastnosti. Obravnavane metode so Perronova razvrstitev, Hodgeva razvrstitev in tropska razvrstitev. Izpostavljene so medsebojne povezave in razlike med metodami.

• Language: Slovenian
• Keywords: tropska matrika, tropska lastna vrednost, tropski lastni vektor, matrika za primerjanje parov
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2021
• PID: 20.500.12556/RUL-124680
• UDC: 512
• COBISS.SI-ID: 50536195
• Publication date in RUL: 07.02.2021

Secondary language

• Language: English
• Title: Tropical Eigenvalue Problem and Application

Abstract

In the thesis matrices over the tropical semiring are studied. The tropical semiring and matrices over this semiring are introduced. The connection between tropical matrices and weighted directed graphs is established. Tropical eigenvalues and the corresponding tropical eigenspaces are characterized. The acquired knowledge is used on pairwise comparison matrices. To obtain the score vector for the alternatives, three methods and their properties are examined. The methods are the PerronRank, the HodgeRank and the TropicalRank. Connections and differences between these methods are highlighted.

• Keywords: tropical matrix, tropical eigenvalues, tropical eigenvectors, pairwise comparison matrix