Abstract

The concepts of ( Φ 1, Φ 2)-convexity, Φ 1-B-vexity and Φ 1-convexity for fuzzy mappings are introduced through the so-called “fuzzy max” order among fuzzy numbers. We show that the class of ( Φ 1, Φ 2)-convex fuzzy mappings, Φ 1-B-vex fuzzy mappings and Φ 1-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 Φ 1-B-vex fuzzy mappings by proposing the concept of Φ 1-B-vex sets. In addition some basic properties of fuzzy mappings from the standpoint of convex analysis are discussed.

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