Research On Algorithm Of Linear Programming With Fuzzy Number

Combining with the existing theory and algorithm of fuzzy linear programming and the concept and operation of fuzzy number, fuzzy vector and ranking function, three points of the fuzzy optimization research, a widely used and new task, are studied in this dissertation, which are degenerate problem, parameter affection and algorithm efficiency. First, it deeply investigates the degenerate problem of fuzzy number linear programming (FNLP) and linear programming with fuzzy variables (FVLP), and proposes their revised simplex method respectively, which can avoid the circulation problem. Then, it studies the FNLP with parameter and the FVLP with parameter respectively, describes the behavior of the optimal basis under parametric perturbations of the objective function and the right hand side of the constraints equation and proposes their algorithms respectively, which are expanding and enriching the research of sensitivity analysis of fuzzy linear programming. Last, a revised interior point method of FNLP is proposed, which is an effective algorithm especially for solving the large scale FNLP. These numerical examples of new methods show that these proposed new algorithms are all feasible. This article mainly has several aspects as follows:1. The degenerate problem of FNLP is investigated since it maybe involve in the circulation using the exciting simplex method for solving FNLP. A new problem related to the original problem is constructed. Then it studies the relation of the two problems, and proposes a revised simplex method, which can avoid the circulation problem.2. The degenerate problem of FVLP is investigated since it maybe involves in the circulation using the exciting simplex method for solving FVLP. A new problem related to the original problem is constructed. Then it studies the relation of the two problems, and proposes a revised simplex method, which can avoid the circulation problem.3. The FNLP with parameter is studied, which is an extension of the research of sensitivity analysis of FNLP. Two kinds of FNLP with parameter are defined, then it describes the behavior of the optimal basis under parametric perturbations of the objective function and the right hand side of the constraints equation and proposes their algorithms respectively. That is the relation between parameter and optimal basis. Finally, the step of the algorithm is summarized.4. The FVLP with parameter is studied, which is an extension of the research of sensitivity analysis of FVLP. Two kinds of FVLP with parameter are defined, then it describes the behavior of the optimal basis under parametric perturbations of the objective function and the right hand side of the constraints equation and proposes their algorithms respectively. That is the relation between parameter and optimal basis. Finally, the step of the algorithm is summarized.5. As we know, the interior point method is more effective than the simplex method. However, the traditional interior point method cannot be directly used for solving FNLP. So a revised interior point method of FNLP is proposed in this paper. Above all, these researches, to a certain extent, enrich the existing theory of solving the fuzzy linear programming problems using ranking function.