Granularity analysis and measurements for complex data environment are important tools to describe the essential attributes of the granular computing model(GCM). Firstly, based on fuzzy multiple relations, this paper difines a multi-fuzzy granular structure, and studies the hierarchical characteristics and relates mathematical conclusions of the four fuzzy multiple partial-order relations on the structure; Secondly, the measurement method of multi-fuzzy information granularity is proposed, and its properties of measurements are analyzed; Finally, the axiomatic definition of multi-fuzzy information granularity and its properties are discussed.