The Study Of Bilevel Decision Making Problem And The Application Of Interval Decision Making Method

Multilevel programming is fundamental model used to study hierarchical system problem, many researchers proceed thorough research to the hierarchical system, and it has been extensively applied in society economy, engineering technique, manage department and military etc. Bilevel programming is the main part of the multilevel programming, attracting the extensive attention in multitudinous in recent years. In fact, most of the realistic decision making systems can be treated as bilevel decision making systems. The research object of this paper is the price control problem of bilevel linear programming and interval decision making problem for making and management of tofu, main works are as follows:Firstly, in this thesis, according to the thorough research to domestic and international present condition, the bilevel linear programming without constraint in the upper level is elaborated in the beginning, the basic model, definition and theorem are given and the interrelated properties are discussed respectively under different hypothesis.Secondly, the theory of fuzzy structured element is induced. The basic concept and the basic theorem are briefly introduced. Sequencing and operations of fuzzy numbers based on the theory of fuzzy structured element are given in the paper. By using the method of fuzzy structured element, we transform price control problem with fuzzy variables into traditional price control problem, and give the algorithm. In addition, we give the definitions and some properties of optimal plane, and give the relationship between optimal solution and optimal plane. Then, the optimal plane algorithm steps of the price control problem is designed, and an example is adopted to verify the effectiveness of the proposed algorithm.Finally, in making of tofu, with the changing of the nature envoronment, the producting condition and market source, the wet profit of tofu in the tofu factory is not distinct, so the wet profit of tofu in the tofu factory takes on interval character. In the fifth chapter, for the problem about making and management of tofu in the tofu factory, we establish interval decision making model of changed producting scale and unchanged one, and give some theorems and a method for solving the interval decision making problem. Then, we solve the above real problem and give the result analysis and advice to the tofu factory.