Fuzzy convexity and multiobjective convex optimization problems

In this paper, based on the more restrictive definition of fuzzy convexity due to Ammar and Metz [1], several useful composition rules are developed. The advantages in using the more restrictive definition of fuzzy convexity are that local optimality implies global optimality, and that any convex combination of such convex fuzzy sets is also a convex fuzzy set. As shown in this paper, these properties are laking in the usual convex fuzzy sets. In addition, to illustrate the applications in fuzzy convex optimization, two examples in multiple objective programming are considered.