Study Of Fuzzy Linear Programming With Triangular Fuzzy Variables

With the application of fuzzy optimization in many fields, the fuzzy optimization problems are more and more important. So under the uncertain environments research on optimal problems is very important from the theoretical as well as from the practical point view. The dissertation takes action about a kind of uncertain linear programming problem with interval numbers and fuzzy numbers in objective programming respectively. The main contributions of this dissertation can be summarized as follows:First of all, this paper discusses some basic concepts of interval number and induces a few normal ranking methods, and then the axiom of an order relation is analyzed thoroughly.Furthermore, some basic concepts, as well as the properties and operations of fuzzy set, are introduced. As an emphasis, fuzzy-number-comparison classification and evaluation criteria is interpreted. In the meanwhile, a new ranking method of triangular fuzzy numbers is proposed based on preference relation. The ranking method is proved to be a fuzzy order relation. Finally a numerical example is presented to illustrate the efficiency of the method.At last, in the thesis the fuzzy linear programming with fuzzy variables is discussed. In many fields including engineering technology, there are many problems in which the variables are fuzzy numbers, and the linear programming problem becomes a fuzzy linear programming problem with fuzzy variables. A new solving method is given, as the improved simplex method is used into the fuzzy linear programming problem with fuzzy variables. Besides, study of the fuzzy linear programming problem and the general model for fuzzy linear programming problem with fuzzy variables by applying the new ranking method of fuzzy numbers, and a numerical example is presented to illustrate the efficiency of the method. Finally, the fuzzy linear programming problems used in drug purchase of raw materials and in examples to illustrate this.