Abstract: A granule is represented as a hyperbox which is composed of the beginning point and the end point. The hyperbox granules with different granularity are formed by the union and decomposition operators between two hyperbox granules. The positive valuation functions are introduced to measure the fuzzy inclusion relation between two hyperbox granules. The hyperbox granule algebraic system is constructed by the hyperbox granule set, fuzzy inclusion measure, union operator and decomposition operator, and is proved as fuzzy lattice, which can guide the design of granular computing algorithms.