Research On Programming Based On Objective Coefficients Of Fuzzy Number

In realistic life and many fields including engineering technology, there exits a lot of uncertainty including stochastic and fuzzy. The uncertainty will bring 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. 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, in the dissertation the linear programming problem whose objective function has interval coefficients is investigated. To maximize the interval objective function, the order relations are defined by the right limit, the left limit, the center and the half with of an interval. The maximization problem with the interval objective functions is converted into a multiobjective problem by using the order relations. Similarly, the minimization problem is also transformed into a multiobjective problem by using the other order relations, so by doing the multiobjective problem a solution of the primitive problem can be obtained.Further, this thesis brings forward a method based on multiobjective coefficients with triangular fuzzy numbers, and lays undue emphasis on the multiobjective problem with general fuzzy numbers in objective coefficients. According to order relations defined between fuzzy numbers, the Pareto less optimal solution and the Pareto optimal solution are defined, then a fuzzy evaluation function is introduced into a multiobjective programming problem, this method results in a multiobjective programming problem been converted into a one objective programming problem, accordingly the solution by this method is the Pareto less optimal solution to the primitive problem, which is given proof A multiobjective problem with general fuzzy number coefficients is also further discussed, by λ_ cutset of fuzzy sets a multiobjective problem can betransformed into a interval linear programming problem, and using the method of the previous chapter, we can obtain the Pareto less optimal solution.Lastly, in the thesis the fuzzy linear programming with fuzzy variables is discussed. In practice, there are many problems in which all decision parametersare fuzzy numbers, and either possibilistic programming or multiobjective programming methods usually solves such problems. Unfortunately, all these methods have shortcomings. So in the fourth chapter a practical method for solving linear programming problems with fuzzy variables is discussed.