关键词:  fuzzy set;fuzzy numbers;fuzzy distance;convex fuzzy sets;b-vex fuzzy mapping, logarithmic b-vex fuzzy mapping

Abstract:  The concept of b-vex and logarithmic b-vex for fuzzy mappings are introduced by relax-  ing the definition of convexity of a fuzzy mapping.Most of the basic properties of b-vex fuzzy map- ping are discussed and established for the nondifferentiable case.Necessary and sufficient condi- tions for b-vex fuzzy mapping are presented.Sevaral important results are given for nonlinear fuzzy optimization problems assuming that the objective and constraint functions are b-vex fuzzy map- pings.

Key words:  fuzzy set;fuzzy numbers;fuzzy distance;convex fuzzy sets;b-vex fuzzy mapping, logarithmic b-vex fuzzy mapping