Research On Arithematic In Interval Optimal Model

Because of complexity of practice or subjectivity of cognition, there exits a lot of uncertainties in realistic life and many fields including engineering technology. These uncertainties include randomness and fuzziness. The uncertainty usually brings about great difficulty in making decision for decision maker in mathematical programming. So under the uncertain environments research on optimal problems is very important from the theoretical as well as from the practical point view. This thesis takes action about a kind of uncertain programming including interval numbers. The main contributions of this dissertation can be summarized as follows:First of all, operation and compositor between interval numbers are summarized. Homology and dissimilarity between interval number and grey number are compared. The distance of interval numbers and perfect project are defined. The compositor of various projects is gained by using the distance. So the multi-attribute decision making problem which weight is given positively but other attribute values are interval numbers is solved.Further, the solution of linear programming whose objective function and ' constrained function are interval numbers is discussed. The programming is transformed into general linear programming and is solved on the base of satisfactory degree of interval number and parameter. The optimal solution of the general linear programming is the effective solution of the uncertain programming. A kind of programming which has triangular fuzzy numbers coefficients is also investigated. Related models of its and operation and compositor of triangular fuzzy number are introduced. The method of transformation and solution is as same as the previous model.Lastly, interval bilevel programming is researched in the thesis. Interval bilevel linear programming, solution and parameter programming is given. Solution set and optimal value will change along with the diversification of parameter.Thetransformation of interval price control problem is also on the base of satisfactory degree. Then the exact model is solved by penalty function method.The selection of satisfactory degree and parameter in the process is stochastic. So it will influence the solution. Parameter can affect solution set and optimal value of interval bilevel linear programming. But what about the effect and the function between them is unknown. Although examples were given to explain feasibility of the arithmetic, they are not managed to practices all along.