This thesis is concentrated on applying classical mathematical programming technique for solving fuzzy number mathematical programming problems. The parameters of the mathematical programming problems are represented by trapezoidal fuzzy number and compared by using linear ranking function. chapter 1, deals with introduction to fuzzy mathematical programming problem with its classification, fundamentals of fuzzy set theory with arithmetic operation of fuzzy numbers, a linear ranking function is introduced to compare trapezoidal fuzzy numbers. Ch2, deals with fuzzy number linear programming problem, Ch3, deals with basic concept of duality and dual simplex method Ch4, deals with the concept of sensitivity analysis in fuzzy number linear programming problem. Ch5, deals with fuzzy number integer programming problems. Ch6, deals with fuzzy number transportation problem Ch7, deals with fuzzy number assignment problem. Ch8, deals with fuzzy travelling salesman problem. Ch9, deals with fuzzy number shortest path problem Ch10, deals with a fuzzy maximal flow problems Ch11, deals with fuzzy number job sequence problem Ch12, deals with concluding remarks and future research.