Thai Journal of Mathematics : (2018) 35-49 Special Issue (ACFPTO2018) on : Advances in fixed point theory towards real world optimization problems http://thaijmath.in.cmu.ac.th Online ISSN 1686-0209 B-Well-Posedness for Set Optimization Problems Involving Set Order Relations Pham Thi Vui ‡ , Lam Quoc Anh † and Rabian Wangkeeree ‡ 1 † Department of Mathematics, Teacher College, Can Tho University, Can Tho, Vietnam e-mail: quocanh@ctu.edu.vn ‡ Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand e-mail: rabianw@nu.ac.th(R. Wangkeeree) ptvui@ctu.edu.vn (P.T. Vui) Abstract: In this paper, both pointwise and global B-well-posedness for set optimization problems involving three kinds of set order relations are investigated. We give characterizations and sufficient and/or necessary conditions of these types of well-posedness. Moreover, pointwise L-well-posedness and relationships between these kinds of pointwise well-posedness are studied. Keywords: B-well-posedness; generalized B-well-posedness; pointwise B-well- posedness; pointwise L-well-posedness; set optimization problem 2000 Mathematics Subject Classification: 49J53; 49K40; 90C31 (2000 MSC) 1 Introduction Set order relations were firstly introduced by Kuroiwa et al. in [1] and then they were generalized in [2]. These concepts gave a new way, so-called set approach, to formulate the optimal of set-valued optimization problems [3]. In this approach, all images of the set-valued objective mapping were compared by set order relations [4,5], and hence it is a truely natural and practical approach. Therefore, this field 1 Corresponding author e-mail : rabianw@nu.ac.th(R. Wangkeeree) Copyright c ⃝ 2018 by the Mathematical Association of Thailand. All rights reserved.