Fuzzy Algorithms For Solving Linear Trilevel Programming Problems

With the development of economy,the decision-making problems in real life are no longer the simple single-level decision-making problems.More and more decision-making problems have multiple levels,and decision makers are in different levels respectivel.Such optimization problems with hierarchical structure are called hierarchical optimization problem.Multi-level programming is a typical hierarchical optimization problem.As a powerful tool to describe this kind of problem,studying its related properties and designing a relatively effective algorithm to solve it,which has very important theoretical significance and practical application value for promoting the continuous development of multi-level prgramming.In this paper,we mainly study the algorithm of linear trilevel programming problem.The main organization of work in the full text is as follows:The first chapter introduces the background and significance of this article,the research status of multi-level programming problem and fuzzy programming,the complexity of multi-level programming,and summarizes the current algorithm for solving multi-level programming problems.The second chapter mainly introduces the optimality conditions,the general model basic concepts and theoretical properties of linear tirlevel programming.Then,introducing the concepts of fuzzy sets and membership functions.In the third chapter,a fuzzy optimization method for solving linear trilevel programming problems is proposed,which combines Kuhn-Tucker transformation method with fuzzy mathematics optimization method.Firstly,the linear tirlevel programming problem is transformed to obtain the bilevel programming problem with complementary constraints in the lower level.Then,the fuzzy optimization method is combined to solve the transformed bilevel programming problem,and a satisfactory solution to the original problem is obtained.Finally,the corresponding example is given to illustrate the solution process.The fourth chapter improves the above method,simplifies the consideration of the membership function of the decision variable,and only considers the satisfaction of the objective function,so that the satisfaction among the upper,middle and lower objective functions can reach an overall satisfaction equilibrium state.Finally,an example is given to show the solution process of the improved algorithm.The fifth chapter summarizes the whole paper and looks forward to the future work.