Invex and generalized convex fuzzy mappings

In this paper we introduce the concepts of pseudo-convexity, invexity and pseudo-invexity for fuzzy mappings of one variable based on the notion of differentiability proposed by Goetschel and Voxman [4], and investigate the relationship between convex fuzzy mappings, preinvex fuzzy mappings and these classes of fuzzy mappings. We shall prove that pseudoconvex fuzzy mappings and invex fuzzy mappings are pseudo-invex, and that a differentiable convex (resp. preinvex) fuzzy mapping is pseudo-convex (resp. invex). In addition sufficient optimality conditions are obtained for pseudo-convex, invex, and pseudo-invex fuzzy mappings. (C) 2000 Elsevier Science B.V. All rights reserved.