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Invex and generalized convex fuzzy mappings

✍ Scribed by Yu-Ru Syau

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
95 KB
Volume
115
Category
Article
ISSN
0165-0114

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✦ Synopsis

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 di erentiability 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 di erentiable convex (resp. preinvex) fuzzy mapping is pseudo-convex (resp. invex). In addition su cient optimality conditions are obtained for pseudo-convex, invex, and pseudo-invex fuzzy mappings.

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