The development of information technology brings the challenge of data redundancy and data shortage to information fusion. Based on the dynamic boundary characteristics of p-set, this paper analyzes the structure and generation of p-augmented matrix, and then analyzes the dynamic generation of information equivalence class, and then proposes an intelligent acquisition algorithm of information equivalence class based on matrix reasoning. In addition, this paper analyzes two types of information fusion, namely information redundancy fusion and information supplement fusion. Then, the relationship among redundant information fusion, supplementary information fusion, and information equivalence classes is analyzed. Finally, this paper presents the application of intelligent acquisition of information equivalence class in information retrieval.

Big data sets are composed of many records with various attributes. In order to extract information from big data sets, this paper researched a $V$ -type big data which satisfied the logical characteristics of “attribute disjunction”. Based on the inverse packet set theory, this paper put forward some new concepts of big data block, such as matrix, element of block. Using these concepts, this paper presented two structures of block reasoning, and then presented three theorems for block element, such as intelligent separation theorem, intelligent retrieval the-orem, and equivalence class theorem; Based on the separation and retrieval criteria of block element, this paper presented the separation and retrieval algorithm of block element. Finally, this paper researched the application of big data intelligent retrieval in credit default.