This article deals with an inventory model for deteriorating items where the rate of deterioration follows the two parameters Weibull distribution. Demand rate depends on the price. The shortages are allowed and are fully backlogged. An uncertain cycle time is considered and described by a (symmetric) triangular fuzzy number. The model is developed analytically by maximizing the total profit. The optimum results are defuzzified by a signed distance method. The numerical examples are given to illustrate the developed model and all results are illustrated numerically and graphically.