Optimization Subject To Fuzzy Relation Constraints With Addition-min Composition

In this paper,we study the fuzzy relation inequalities with Addition-Min composit ion and optimization problem with these fuzzy relation constraints.Firstly,a sufficient and necessary condition of the maximal solution is given based on it's definition and related properties.Based on this condition,this inequality system is equivalently conve rted into a series of linear inequalities,which can greatly reduce the difficulty of solving the problem.In order to solve the optimization problem subject to the fuzzy rela tion constraints with Addition-Min composition,an approximation problem is establishe d by constructing second order continuous differentiable function to smooth the constraint function.We give the conclusions that feasible region,optimal value of the approximate problem converge to the feasible region,optimal value and optimal solution of the original problem respectively.The validity of smoothing method for solving the-constrained problem is proved theoretically.Finally,examples and numerical experime nts are given to illustrate the validity and effectiveness of the smoothing method.