Research The Problem Of Gray Optimization And The Bilevel Programming With Fuzzy Relation Constraint

Gray system theory is a new method that studies problem of little research data and poor data uncertainties. Its experimental observation data has no any special requirements and limitations, and therefore it is a very broad application area. The hierarchical system is the main form of social organized management, multilevel programming is fundamental model used to study this kind of systematical problem. It has a distinct background and a wide range of practical applicability.This paper mainly includes the problem of gray optimization and the bilevel linear programming with fuzzy relation constraint. The problem of gray optimization includes the researching on gray general DEA model and the studying on grey traveling salesman problem. Paper gives the basic model and an algorithm about gray general DEA problems and gray TSP problem. It also studies the approximate lower bound of the gray TSP problem. Fuzzy bilevel linear programming is the bilevel linear programming with fuzzy relation constraint.First of all, it provides the background, origin, development and application of the gray system theory and the hierarchical system. And, the basic model of the bilevel decision-making system and the associated knowledge are given. Then, it introduces some knowledge about the fuzzy mathematics and fuzzy programming.Secondly, the theory of gray system is induced. The basic concept, the basic theorem, and the algorithm are briefly introduced.Once again, combined with the characteristics of gray system we propose the model about gray general DEA problems and gray TSP problem. And, combined with knowledge of gray linear programming we give the solving method about gray general DEA problems and gray TSP problem. Finally, bilevel linear programming are divided into resources distribute problem, price control problem and general bilevel linear programming, their basic model, definition and theorem are given. Then, for the bilevel linear programming problem with fuzzy relation constraints we give the model, and give the solving method.