(Phi(1), Phi(2))-convex fuzzy mappings
The concepts Of (Phi(1),Phi(2))-convexity, Phi(1)-B-vexity and Phi(1)-convexity for fuzzy mappings are introduced through the so-called "fuzzy max" order among fuzzy numbers. We show that the class Of (Phi(1),Phi(2))-convex fuzzy mappings, Phi(1)-B-vex fuzzy mappings and Phi(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 Phi(1)-B-vex fuzzy mappings by proposing the concept of Phi(1)-B-vex sets. In addition some basic properties of fuzzy mappings from the standpoint of convex analysis are discussed. (C) 2002 Elsevier B.V. All rights reserved.
(phi(1), phi(2))-convex fuzzy mappings convexity fuzzy numbers