In this paper we have formed an inventory system for a single decaying item with two distinct storage facilities and in which demand is inventory dependent. Shortage is permitted and is partially backlogged. It is considered that the holding cost of the rented warehouse is higher than that of owned warehouse.  As demand, holding- cost, shortage, lost- sale, decaying- rate are uncertain in nature, we assume them as triangular fuzzy numbers and formed the model for fuzzy total cost function and is defuzzied by using Signed Distance and Centroid methods. In order to show the model, we contrast the results of crisp and fuzzy models through a numerical example and depend on the example the effect of different variable have been exactly considered by sensitivity analysis taking one variable at a time keeping the other variables unchanged.