In today’s business a close operation is necessary to decrease the joint total inventory cost. According to Simchi-Levi et al (2000) several international companies have demonstrated that integrating the supply chain has improved the company’s performance and market share. This paper considers an inventory vendor-buyer integrated system in a fuzzy situation by employing the type of fuzzy numbers which are trapezoidal. This model have been developed by using different optimization methods. A full fuzzy model is by using different optimization methods. A fully fuzzy model is developed where the input parameters and the decision variables are fuzzified. The optimal policy for the developed model is determined are fuzzified. The optimal policy for the developed model is determined by using the Lagrangean conditions after the defuzzification of the cost function with the graded mean integration method. The proposed method finds the optimal lotsize for both the vendor and buyer in an integrated two stage supply chain. Numerical examples are provided to highlight the difference between crisp and the fuzzy cases.