The author utilizes the concepts of fuzzy logic and gives the basic ideas of the nearest rule and the closeness function (approximation function). The author introduces the augmented ordered fuzzy subset for a property, which lets the nearest rule become a more powerful derivation and retrieval mechanism in the FOODB environment. After introducing the augmented ordered fuzzy subset, the author defines three memberships for the FOODB which are membership of an object in the class, membership in the single inheritance and membership in the multiple inheritances. Two algorithms to implement the nearest rule and closeness function in FOODB are also provided. It makes the complex multiple inheritance processing much easier. The author also distinguishes the differences between the complex object and the compound object which have not been made clear in other papers.