In the changing scenario of market, inventory system have become important for all researchers and fuzzy set theory mainly deals with quantitative analysis of uncertainty and imprecision. In this paper the inventory system for deteriorating items with price sensitive demand under fuzzy logic has been developed. This system is allowed shortage which is completely backlogged. Due to uncurtaining in the market fuzzy set theory is used to deal with the imprecise data. Therefore demand rate, deterioration rate and holdings cost taken as pentagonal fuzzy numbers and graded mean representation method (GMRM) has been used to defuzzify the total inventory cost (TC) function made from this model. The purpose of this work is to minimise the total inventory cost. We have illustrated the model by numerical example along with graphical illustration and sensitivity analysis is finally depicted to understand this model based on real life scenario.