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A global optimization method for linear programming for finding the fuzzy priority vector in fuzzy analytic hierarchy process(AHP) is developed in this paper. Some rigorous mathematical definition and theorems for the optimization method are stated and proved. Instead of performing complicated computations, the graphical approach([18, p.30]) is used to find the fuzzy priority vector for the fuzzy pairwise comparison matrix(FPCM). This graphical approach is applied to New Product Development (NPD) project screening, which is a multiple criteria decision making(MCDM) problem. NPD is largely uncertain, because of competition accompanied with modern technology and market changes. It always leads to failure of new product development. The final project screening decision is obtained from the overall global fuzzy rates of the projects with respect to the screening criteria.