Further Research On Fuzzy Linear Programming Problems

In chapter 1 of this thesis, the basic theory of fuzzy sets is introduced, including the definition and operation of fuzzy sets, the method to confirmmembership function, the measure of fuzziness, operation of fuzzy numbers.Besides, basic knowledge of fuzzy optimization is introduced in chapter 2, in-cluding fuzzy extremum, tile primary types of fuzzy linear programming, andthe study status of fuzzy linear programming is briefly introduced.Further research on linear programming problems with fuzzy constraintand linear programming with fuzzy coefficients in constraints is made in chap-ter 3. Discusses how to select the optimal value of linear programming withfuzzy constraint. A new concept of optimal solution is defined, by designingalgorithm, numerical examples illustrate the merits of the approach. Furthermore, discusses the solution when constraint's change is nonlinear, select a newobject set, so that the parameterλstill satisfyλ≥0.5. An algorithm is pre-sented and numerical examples illustrate the feasibility of newly selected objectset.For linear progralnming with fuzzy coefficients in constraints, two satisfac-tory functions are discussed first in this thesis, by deep analysis, educed thatthey are of the same form, and the general form is presented. Based on theanalysis of satisfactory functions, the feasibility of solving linear programlningproblems with fuzzy coefficients in constraints by satisfactory function methodis discussed in this thesis, and point out that the satisfactory function methodcould not solve fuzzy linear programming problems very well. A new methodof solving linear programming problems with fuzzy coefficients in constraints ispresented, and finally numerical example illustrates the merits of the approach.