Three-way convex systems and three-way fuzzy convex systems

In this paper, we study convex systems under the frame of three-way decision theory. Firstly, we give the notion of three-way convex systems. We obtain an equivalence characterization of three-way convex systems. Then, we propose the concept of three-way fuzzy convex systems in term of L-convex systems. Some related examples are presented. Finally, we establish a one-to-one correspondence between three-way convex systems and three-way fuzzy convex systems. (C) 2019 Elsevier Inc. All rights reserved.