In this paper, we have developed the multi-item inventory model in the fuzzy environment. Here we considered the demand rate is constant and production cost is dependent on the demand rate. Set-up- cost is dependent on average inventory level as well as demand. Lead time crashing cost is considered the continuous function of leading time. Limitation is considered on storage of space. Due to uncertainty all cost parameters of the proposed model are taken as generalized trapezoidal fuzzy numbers. Therefore this model is very real. The formulated multi objective inventory problem has been solved by various techniques like as Geometric Programming (GP) approach, Fuzzy Programming Technique with Hyperbolic Membership Function (FPTHMF), Fuzzy Nonlinear Programming (FNLP) technique and Fuzzy Additive Goal Programming (FAGP) technique. An example is given to illustrate the model. Sensitivity analysis and graphical representation have been shown to test the parameters of the model.