An Approach To Fuzzy Linear Programming Based On Fuzzy Numbers Distance

Fuzzy mathematics is a brand-new subject. It has grown quite rapid from the famous cybernatic expert L.A.Zadeh originated. Its applied scopes are especially abroad. It is used in many fields, such as science, engineering course, farmer, medicine, and social science. The fuzzy optimization is an important embranchment of Fuzzy mathematics. Since 1970, the fuzzy optimization, especially the fuzzy linear programming problems have received people's great concern, and much research achievements have been made. In this paper, we discuss a kind of them, which is the fuzzy linear programming that the object coefficents are real numbers and the constraint coefficents are fuzzy numbers. For this kind programming, there are different solve methods from different points of view by in-depth and broad research.In this paper, we leave from distance, first present a new distance between interval numbers, according to relations between the interval numbers and fuzzy numbers, give the distance between fuzzy numbers, then rank fuzzy numbers with the help of the new distance between fuzzy numbers, then fix a real number as referring object, make sure the big and small according to the distance between the fuzzy numbers and referring object, specially give the comparative formula of triangular fuzzy numbers. Finally we transform fuzzy linear programming into crisp linear programming, according to the comparative formula of triangular fuzzy numbers. Thus we get an approach to the fuzzy linear programming problem under constraint conditions with fuzzy coefficients.This paper consists of three chapters. Firstly, it introduces the basic concepts about the fuzzy sets, especially the interval numbers, the fuzzy numbers and their operations, which are the essential tools for the fuzzy linear programming. Secondly, it introduces linear programming, especially gives a usual method about linear programming-simplex method, and introduces the fuzzy linear programming, gives the types of fuzzy linear programming. And finally, it gives several methods about the fuzzy linear programming, especially it gives...