The Research And Expansion On Optimal Solution Of Fuzzy LP

With the development of fuzzy theory, research on fuzzy linear programming has become very popular because real world is often uncertain. In term of the difference in the form of fuzzinesss, fuzzy linear programming can be divided into two classes: One is that the objective function or constraints are uncertain, but their coefficients and constant belong to real numbers. The other is that at least one of the coefficients of the objective function and constraint are fuzzy numbers. In spite of different methods to a fuzzy optimal solution to the two classes of fuzzy linear programming, these methods have similar ideas: First is to fuzzify the objective function and constraints, i.e. , to display the definition of fuzzy membership function. Second is to transfer the fuzzy linear programming into one general linear programming, based on the fuzzy decision, then we can obtain the fuzzy optimal solution by solving this linear programming.Zimmermann's methods is used to solve the first class of fuzzy linear programming. On the basis of this methods, many scholars studied simplex algorithm of fuzzy linear programming. However, we found that these methods hold only under proper conditions. Therefore, it is undoubted that studying an algorithm which holds under more general conditions is very meaningful. So, we have carried on the research on this problem in this paper. This paper has four chapters. Matrix form of the simplex method , the definition, properties and operation of fuzzy sets and the definition of fuzzy linear programming have been introduced in the first chapter. Then, in the second chapter, it is generalized some results of the first class of fuzzy linear programming in our country and abroad. In the third chapter,we discussed the relationship between the optimal value and parameter of parametric linear programming (L\). Our results show that the optimal value with a parameter is a monotone decreasing sectionally continuous linear function G\ about parameter A, and the membership function of fuzzy objective sets are a linear function, written as C\. Then we prove that the optimal fuzzy decision of fuzzy linear programming is the intersection ofthe two functions. Moreover, we proved that when the fuzzy decision is equal to 0.5, the optimal solution to fuzzy linear programming can be obtained if the linear programming (Lo) and (la) have identical optimal basic. And that if these conditions are not satisfied, the fuzzy decision is greater than 0.5. Furthermore, the value of optimal solution are decided by the fuzzy decision A. At the same time: when the fuzzy linear programming is degenerate, results mentioned above still hold. At last, a method to fuzzy linear programming with fuzzy constraints is presented, and it is illustrated that the conclusion of this paper are correct and this algorithm is more simplex algorithm by numerical example. In the last chapter, latest research on fuzzy linear programming has been introduced.