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Rating alternatives from pairwise comparisons by solving tropical optimization problems. / Кривулин, Николай Кимович.

2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). ed. / Zhuo Tang; Jiayi Du; Shu Yin; Ligang He; Renfa Li. Institute of Electrical and Electronics Engineers Inc., 2015. p. 162-167.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Harvard

Кривулин, НК 2015, Rating alternatives from pairwise comparisons by solving tropical optimization problems. in Z Tang, J Du, S Yin, L He & R Li (eds), 2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). Institute of Electrical and Electronics Engineers Inc., pp. 162-167, 2015 12th International Conference on Fuzzy Systems and Knowledge Discovery, Zhangjiajie, China, 15/08/15. https://doi.org/10.1109/FSKD.2015.7381933

APA

Кривулин, Н. К. (2015). Rating alternatives from pairwise comparisons by solving tropical optimization problems. In Z. Tang, J. Du, S. Yin, L. He, & R. Li (Eds.), 2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD) (pp. 162-167). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/FSKD.2015.7381933

Vancouver

Кривулин НК. Rating alternatives from pairwise comparisons by solving tropical optimization problems. In Tang Z, Du J, Yin S, He L, Li R, editors, 2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). Institute of Electrical and Electronics Engineers Inc. 2015. p. 162-167 https://doi.org/10.1109/FSKD.2015.7381933

Author

Кривулин, Николай Кимович. / Rating alternatives from pairwise comparisons by solving tropical optimization problems. 2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). editor / Zhuo Tang ; Jiayi Du ; Shu Yin ; Ligang He ; Renfa Li. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 162-167

BibTeX

@inbook{d89d1b7516d44ab98cfd21bc126650de,
title = "Rating alternatives from pairwise comparisons by solving tropical optimization problems",
abstract = "We consider problems of rating alternatives based on their pairwise comparison under various assumptions, including constraints on the final scores of alternatives. The problems are formulated in the framework of tropical mathematics to approximate pairwise comparison matrices by reciprocal matrices of unit rank, and written in a common form for both multiplicative and additive comparison scales. To solve the unconstrained and constrained approximation problems, we apply recent results in tropical optimization, which provide new complete direct solutions given in a compact vector form. These solutions extend known results and involve less computational effort. As an illustration, numerical examples of rating alternatives are presented.",
keywords = "tropical mathematics, idempotent semifield, constrained optimization problem, matrix approximation, reciprocal matrix, pairwise comparison, analysis of preferences",
author = "Кривулин, {Николай Кимович}",
year = "2015",
doi = "10.1109/FSKD.2015.7381933",
language = "English",
pages = "162--167",
editor = "Zhuo Tang and Jiayi Du and Shu Yin and Ligang He and Renfa Li",
booktitle = "2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
address = "United States",
note = "2015 12th International Conference on Fuzzy Systems and Knowledge Discovery, FSKD'15 ; Conference date: 15-08-2015 Through 17-08-2015",

}

RIS

TY - CHAP

T1 - Rating alternatives from pairwise comparisons by solving tropical optimization problems

AU - Кривулин, Николай Кимович

N1 - Conference code: 12

PY - 2015

Y1 - 2015

N2 - We consider problems of rating alternatives based on their pairwise comparison under various assumptions, including constraints on the final scores of alternatives. The problems are formulated in the framework of tropical mathematics to approximate pairwise comparison matrices by reciprocal matrices of unit rank, and written in a common form for both multiplicative and additive comparison scales. To solve the unconstrained and constrained approximation problems, we apply recent results in tropical optimization, which provide new complete direct solutions given in a compact vector form. These solutions extend known results and involve less computational effort. As an illustration, numerical examples of rating alternatives are presented.

AB - We consider problems of rating alternatives based on their pairwise comparison under various assumptions, including constraints on the final scores of alternatives. The problems are formulated in the framework of tropical mathematics to approximate pairwise comparison matrices by reciprocal matrices of unit rank, and written in a common form for both multiplicative and additive comparison scales. To solve the unconstrained and constrained approximation problems, we apply recent results in tropical optimization, which provide new complete direct solutions given in a compact vector form. These solutions extend known results and involve less computational effort. As an illustration, numerical examples of rating alternatives are presented.

KW - tropical mathematics

KW - idempotent semifield

KW - constrained optimization problem

KW - matrix approximation

KW - reciprocal matrix

KW - pairwise comparison

KW - analysis of preferences

UR - https://arxiv.org/abs/1504.00800

U2 - 10.1109/FSKD.2015.7381933

DO - 10.1109/FSKD.2015.7381933

M3 - Chapter

SP - 162

EP - 167

BT - 2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)

A2 - Tang, Zhuo

A2 - Du, Jiayi

A2 - Yin, Shu

A2 - He, Ligang

A2 - Li, Renfa

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2015 12th International Conference on Fuzzy Systems and Knowledge Discovery

Y2 - 15 August 2015 through 17 August 2015

ER -

ID: 32915381