([Phi]1, [Phi]2)-Convex fuzzy mappings

Abstract The concepts of (Φ1,Φ2)-convexity, Φ1-B-vexity and Φ1-convexity for fuzzy mappings are introduced through the so-called “fuzzy max” order among fuzzy numbers. We show that the class of (Φ1,Φ2)-convex fuzzy mappings, Φ1-B-vex fuzzy mappings and Φ1-convex fuzzy mappings includes many well-known classes of fuzzy mappings such as convex fuzzy mappings and preinvex fuzzy mappings as its subclasses. We also give a characterization for Φ1-B-vex fuzzy mappings by proposing the concept of Φ1-B-vex sets. In addition some basic properties of fuzzy mappings from the standpoint of convex analysis are discussed.