Ergodic distribution for a fuzzy inventory model of type (s, S) with gamma distributed demands

In this study, a stochastic process (X(t)), which describes a fuzzy inventory model of type (s, S) is considered. Under some weak assumptions, the ergodic distribution of the process X(t) is expressed by a fuzzy renewal function U(x). Then, membership function of the fuzzy renewal function U(x) is obtained when the amount of demand has a Gamma distribution with fuzzy parameters. Finally, membership function and alpha cuts of fuzzy ergodic distribution of this process is derived by using extension principle of L. Zadeh.