Fuzzy Convex Function And Fuzzy Optimization Problems

In the traditional mathematics, the convex function and the generalized convex function are very important, because it involved the minimal and maximal of convex functions in convex set. Meanwhile, when the convex function is applied, local extreme theory can turn to the global extreme theory about the general nonlinear function. Therefore, the convex function is very important in the optimized theory. Also, some results of convex functions are usually similar to the general optimization problem. So, the research of convex function, not only is very important in itself optimized domain, but also it can help to understand the majority of general optimized theory. Thus, this dissertation mainly studies theλ-convex functions andλ-generalized convex functions in fuzzy.This dissertation mainly discuss two problems: first, it introduces some contents ofλ-convex functions,λ-generalized convex function andλ-weakly convex functions, including the definition, the equivalent statements, the properties, the applications in fuzzy nonlinear optimization (the properties of optimum solutions of convex programming and generalized convex programing) and the relationship among them. Second, it introduces the definition and studies the properties ofλ-sub differential, then under the objective functions and constrains are neither differential norλ-convex, it studies some propositions in fuzzy nonlinear optimization, mainly discusses the relationship among the optimal solution of original problem, the saddle points and the optimal solution of dual problem under neither differentiability norλ-convexity.