Rating alternatives from pairwise comparisons by solving tropical optimization problems

Николай Кимович Кривулин

doi:10.1109/FSKD.2015.7381933

Rating alternatives from pairwise comparisons by solving tropical optimization problems

Кафедра статистического моделирования

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › научная › рецензирование

7 Цитирования (Scopus)

Аннотация

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.

Язык оригинала	английский
Название основной публикации	2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)
Редакторы	Zhuo Tang, Jiayi Du, Shu Yin, Ligang He, Renfa Li
Издатель	Institute of Electrical and Electronics Engineers Inc.
Страницы	162-167
ISBN (электронное издание)	978-1-4673-7682-2, 978-1-4673-7681-5
DOI	https://doi.org/10.1109/FSKD.2015.7381933
Состояние	Опубликовано - 2015
Событие	2015 12th International Conference on Fuzzy Systems and Knowledge Discovery - Zhangjiajie, Китай Продолжительность: 15 авг 2015 → 17 авг 2015 Номер конференции: 12

конференция

конференция	2015 12th International Conference on Fuzzy Systems and Knowledge Discovery
Сокращенный заголовок	FSKD'15
Страна	Китай
Город	Zhangjiajie
Период	15/08/15 → 17/08/15

Предметные области Scopus

Теория принятия решений (разное)
Теория управления и исследование операций
Алгебра и теория чисел

Доступ к документу

10.1109/FSKD.2015.7381933

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Цитировать

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

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

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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",

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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",

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

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

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

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › научная › рецензирование

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AU - Кривулин, Николай Кимович

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PY - 2015

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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

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DO - 10.1109/FSKD.2015.7381933

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

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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

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