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.
We would like to express our gratitude to the referee for his/her useful comments on this paper.
Dedicated to Professor Tamaki Tanaka’s 60th birthday.
"On the ordinal structure of the weighted set relation." Nihonkai Math. J. 32 (2) 91 - 105, 2021.