In this study, we consider a fuzzy inventory model of type (s,S) with random demands having an inverse Gaussian distribution. We first show the monotonicity of the renewal function with respect to mean parameter. Thus we obtain the membership function of the fuzzy renewal function when the amount of demands is a random variable having an inverse Gaussian distribution with a fuzzy mean parameter by using the monotonicity property of renewal function. Making use of the membership function of the renewal function, we obtain the membership function of the fuzzy ergodic distribution of this process. We also present some numerical results obtained by using this membership function.