The lack of available historical data resulting from increasing market turbulence and very short product life cycles means that the demand in an inventory system varies non-stochastically and must therefore be subjectively determined. This paper investigates the economic production lot size inventory problem, in which a positive lead time and shortages are allowed, with fuzzy demands and an unknown explicit membership function. An analysis method based on an <inline-formula><tex-math notation="LaTeX">\alpha </tex-math></inline-formula>-cut representation and fuzzy ranking is proposed to derive the optimal inventory policy. In addition, the necessary and sufficient conditions for the optimal inventory policy are determined. The merits of the proposed approach include the ability to obtain a numeric and precise optimal policy rather than a fuzzy policy and no requirement for explicit forms of the membership functions of the fuzzy demands, which increases the generality of the proposed model. Additionally, practical insights are provided.