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2021 On the ordinal structure of the weighted set relation
Yousuke Araya
Author Affiliations +
Nihonkai Math. J. 32(2): 91-105 (2021).

Abstract

In this paper, inspired by Chen-Köbis-Köbis-Yao, we investigate the ordinal structure of the weighted set relation in the framework of set optimization problem. Using characterization theorems of set relations via nonlinear scalarization technique, we give relationships between traditional set relations and the weighted set relations.

Acknowledgments

We would like to express our gratitude to the referee for his/her useful comments on this paper.

Dedication

Dedicated to Professor Tamaki Tanaka’s 60th birthday.

Citation

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Yousuke Araya. "On the ordinal structure of the weighted set relation." Nihonkai Math. J. 32 (2) 91 - 105, 2021.

Information

Received: 3 September 2021; Revised: 24 September 2021; Published: 2021
First available in Project Euclid: 3 May 2022

Subjects:
Primary: 46A40 , 49J53
Secondary: 06F20

Keywords: Nonlinear scalarization , Ordinal structure , Set relations , The weighted set relations

Rights: Copyright © 2021 Niigata University, Department of Mathematics

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Vol.32 • No. 2 • 2021
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