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