This paper has analyzed fuzzy EOQ model through fractional back order for inventory system. Here, under function principle, fuzzy entire behavior cost of the model is calculated. The ideal EOQ is derived through median rule. This approach can be very helpful when the precise data of Fuzzy variables is unavailable. In this paper for recommended fuzzy EOQ model, the ideal resolution for the proposed fuzzy EOQ model is slightly greater than the economic order quantity (EOQ) in crisp value because of the scarcity of data. Partial backorder of fuzzy system, Setup and interrelated mechanism for implementation of fuzzy set for inventory system with partial backorder, A numerical example and conclusion are described in different sections.