Fuzzy Quadratic Programming Problems With Soft Constraint

The fuzzy quadratic programming is a model in vague situation. Usually, it is the first step to solve this model that converted the linear membership function to membership form, but this technique may not guarantee the wishes of the decision maker. If the nonlinear membership function is used to describe the membership,the difficulty of solving the model will increase. In this paper, we use the second membership function or normal membership function to describe the satisfaction of fuzzy constraints, and then established two models with different membership functions. The main content of the paper include the following.1. Some solving methods based on linear membership function are summa-rized. Based on this, other solutions of the model are explored.2. We propose a class of adjustable quadratic membbership function for decision makers, and then establish a fuzzy quadratic programming model with quadratic membership function.3. Based on fuzzy quadratic programming model with gaussian membership function, we replace normal function approximately using quadratic function at the close point, and discuss the optimal solution after the replacement.4. The simple graphic method is given for the fuzzy quadratic programming that objective function is circular and parabolic.The advantage of our method is that the quadratic function is the same as objective function of the model. The form of function can be adjusted, and it also avoid the influence came from other nonlinear function. This method not only enriches the content of fuzzy quadratic programming, but also provides a way to solve the mathematical planning issues in fuzzy environment.