Some Results On Fuzzy Optimization

With the application of fuzzy optimization in many fields, the fuzzy optimization problems are more and more important. How to slove this kind of problems in the way of convinent and efficient has become a hot point of research. This paper mainly studies two kinds of fuzzy optimization problems, i.e., fuzzy linear programming problems with fuzzy coefficients and optimization problems with fuzzy relation constraints. In what follows, we will introduce the main results of the paper briefly.In the second chapter, fuzzy linear programming problems with fuzzy coefficients in the constraints are discussed. Because of fuzzy numbers in both left and right sides in the constraints, the methods for ranking fuzzy numbers must be considered. In this chapter, a new ranking method is proposed. This method is intuitionistic, easily computed and it can be used to compare arbitrary two fuzzy numbers. And based on various ranking methods, fuzzy linear programming problems are solved.The third chapter focuses on a class of optimization problems with fuzzy relation constraints. According to the characteristic of the solution set of fuzzy relation equation and fuzzy relation inequality, we convert the original problem to a finite number of sub-problems and solve them respectively. In section 3.4, the optimization problems with nonlinear and smooth objective function and FRJ constraints are discussed, and a general numerical algorithm is given. Through some examples, it can be seen that the iteration times of this algorithm are very small and the computation time is short. The last section focuses on the optimization problems with fuzzy relation equation constraints. The composition is max-product and the objective function is linear. Finally we give a numerical algorithm similar to the one given in section 3.4.