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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.

Rescuers and search dogs must enter the disaster area within the golden rescue time. Design meets the mission needs to increase efficiency. The IOT device and package performs better communication and increases productivity. Other sensors record the status of the dog (heartbeat, temperature and GPS positioning). When the temperature is high, the system reminds the dog to prevent heat stroke. Rescuers click the recall button, and the remote device sends a signal to direct the dog to return.

Inverse packet sets is a set model with dynamic characteristics, which is got by introducing dynamic characteristics into Cantor set $$ X $$ and improving Cantor $$ X $$ . By using inverse packet sets to improve the concept of ordinary augmented matrix, the structure of internal inverse packet augmented matrix, outer inverse packet augmented matrix and inverse packet augmented matrix are given. Internal inverse packet augmented matrix reasoning, outer inverse packet augmented matrix reasoning, inverse packet augmented matrix reasoning and reasoning model are given. Finally intelligent dynamic separating-acquisition of information is given. By using these theoretical results, the application of intelligent dynamic separating-acquisition of educational information is given. Inverse packet matrix reasoning provides a new theory and new method for mining and acquisition of dynamic educational information. This is also a successful teaching demonstration on the research of matrix Teaching.

Function packet set is a dynamic model of information law, which introduces function concept into packet set and improves it; function packet set is a function set pair composed of function internal packet set $$ S^{{\bar{F}}} $$ and function outer packet set $$ S^{F} $$ ; or, $$ (S^{{\bar{F}}} ,S^{F} ) $$ is a function packet set. Packet reasoning is a dynamic reasoning generated from packet set, and it’s composed of internal packet reasoning and outer packet reasoning. This paper introduces function into packet reasoning, improves packet reasoning and gives packet information law reasoning; by cross-penetration of function outer packet set with outer packet information law reasoning, the studies on intelligent fusion of outer packet information law and its outer separating are given. The generating of outer packet information law reasoning of intelligent fusion of outer packet information law, intelligent fusion of outer packet information law with attribute conjunctive reduction theorem, outer separating and reducing of intelligent fusion of outer packet information law and outer separating of intelligent fusion of outer packet information law with discovery-application of unknown information law are given in this paper.

Function packet sets (P-sets) is a novel model with law and dynamic characteristics, which is composed of function internal P-set $$S^{{\bar{F}}}$$ and function outer P-set $$S^{F}$$ . Using the structure, law and dynamic characteristic of function P-sets, we present the concepts of P-information law and band information law and their generation. Subsequently, the attribute theorem of P-information, the hiding and hiding theorem of P-information in band information law and the recovery theorem of information law are studied. Based on the above theory results, an application example of information law hiding is given and validated.

Firstly by improving inverse P-sets, inverse P-data model is proposed, it consists of internal and external inverse P-data models, and demonstrates dynamic characteristics; then the expansion-contraction generations of attribute disjunctive normal form for inverse P-data model are shown, and inverse P-data reasoning is proposed; finally intelligent data separation-discovery is given, and verified by an application.

By improving function inverse P-sets, inverse P-information law model and its structures are proposed. Then attribute disjunctive expansion-contraction generations of inverse P-information law models are presented. Furthermore, inverse P-information reasoning and reasoning structures are proposed Finally intelligent generating theorems of information law are proposed, the reality-camouflage intelligent transformations of information image and their intelligent generations and applications are also given.

Using S-rough sets, this paper gives the concepts of f -heredity knowledge and its heredity coefficient, and f -variation coefficient of knowledge; presents the theorem of f -attribute dependence of variation coefficient and the relation theorem of heredity-variation. The attribute dependence of f -variation coefficient and the relation of heredity-variation are important characteristics of S-rough sets. From such discussion, this paper puts forward the heredity mining of f -knowledge and the algorithm of heredity mining, also gives its relative application.