Study On A Sort Of Fuzzy Linear Programming

Mathematical programming is one of the areas to which fuzzy set theory has been applied extensively. This dissertation studies mainly a sort of fuzzy linear programming ---possibilistic linear programming. By means of possibility theory, possibilistic linear programming with fuzzy trapezoidal number coefficients is discussed.In the following, we list the main works in our paper:(1) We introduce briefly the concepts of fuzzy mathematics and three fundamental principles—decomposition theorem, representation theorem and extension theorem. We also present the concepts of fuzzy number and some simple properties.(2) We consider how to solve fuzzy mathematical programming and introduce the basicprinciple of possibility measure and fuzzy integral.(3) We generalize the principles of how to solve linear programming and fuzzy linearprogramming. Then methods for solving possibilistic linear programming with fuzzy trapezoidal number coefficients are proposed.(4) On basis of the decomposition theorem, multi-objective linear programming and multi-objective fuzzy linear programming are discussed.