Information (data) mining and applications are the important branch of theoretical and application research in information (data) system and information (data) engineering. Information (data) mining is a dynamic process. For a given source information ( Deleting some redundant information elements Supplementing some information elements Deleting some redundant information elements
Deleting some redundant information elements
Supplementing some information elements
Deleting some redundant information elements
I-III are the three different concepts of information (data) mining. A number of authors are studying the dynamic characteristics of I–III to find a mathematical method. In Ref. , the concept of P-sets with dynamic characteristics is proposed by improving the finite common element set (Conter set). In Refs. [2,3,4,5,6,7,8,9,10], the application of P-sets in dynamic information system is shown. In Ref. , P-matrix (P-augmented matrix) is obtained by using the structure and dynamic characteristics of P-sets. P-matrix reasoning (p-augmented matrix reasoning) is a new reasoning structure with dynamic characteristics generated by P-sets. In this paper, the basic theory and application of information (data) intelligence mining are discussed using the structure and dynamic characteristics of P-sets and P-matrix reasoning.
Conter set Supplementing some attributes in Deleting some attributes in Supplementing some attributes in The dynamic characteristics (1–3) of P-sets are the same as those of the information mining concepts I–III. If
Supplementing some attributes in
Deleting some attributes in
Supplementing some attributes in
The dynamic characteristics (1–3) of P-sets are the same as those of the information mining concepts I–III. If
This paper gives the structures and characteristics of P-sets and P-matrix (P-augmented matrix), gives three new concepts of information mining, proposes P-matrix reasoning (P-augmented matrix reasoning) and reasoning theorems, presents the information (data) intelligent mining method under the condition of P-matrix reasoning and gives the simple application of information (data) intelligent recursive mining. All the results given in this paper are new.
In Ref. , P-sets and its structure are presented as follows: Conter set
The set pair which is composed of internal packet set
From Eq. (3),
The dynamic characteristic of Eq. (1) are the same as the dynamic characteristics of down-counter The dynamic characteristic of Eq. (4) are the same as the dynamic characteristics of accumulator
The dynamic characteristic of Eq. (1) are the same as the dynamic characteristics of down-counter
The dynamic characteristic of Eq. (4) are the same as the dynamic characteristics of accumulator
Take an example:
In Ref. , the structure and generation of p-augmented matrix are proposed as follows: Conter set
Here: in Eqs (15)–(17),
The matrix pair composed of
It should be noted that: In Ref. , by using the structure and dynamic characteristic of P-sets, they improved the definition of augmented matrix in classical mathematics, proposed internal P-augmented matrix
The internal P-augmented matrix
If internal P-matrix
If outer P-matrix
By Eqs (20)–(22), we get:
By Eqs (15) and (16) in Section 3, we get:
Since the proof of Theorem 2 is similar to the proof of Theorem 1, the proof is omitted. By Theorems 1 and 2, we get Theorem 3.
Assumption: For simple and without losing generality, in this section only the application of internal P-information intelligent recursive mining under the condition of internal P-matrix reasoning is given. The application of outer P-information intelligent recursive mining under the condition of outer P-matrix reasoning and the application of P-information intelligent recursive mining under the condition of P-matrix reasoning are omitted.
Source of information (
Under the condition of internal P-matrix reasoning:
By using internal P-matrix reasoning family Eq. (23),
Special note: Examples in this section are taken from the computer information image intelligent recognition system. Matrix
The cross and penetration of P-sets and P-matrix reasoning is a new research field of information intelligent dynamic mining. In this paper, the basic theory and application of information (data) intelligent mining are given by using the intersection of P-sets and P-matrix reasoning. This paper discusses information intelligent recursive mining and mining methods, and gives its application in information image intelligent mining and recognition. Several new concepts are discussed, and a new reasoning method (intelligent method) is proposed. Ref.  gives the dual form of inverse P-sets of P-sets, and Ref.  presented inverse P-matrix, which is the dual form of P-matrix. In Refs. [14,15,16,17,18], inverse P-sets and inverse P-matrix have been applied in the dynamic discovery of unknown information and the intelligent fusion and separation of information laws. P-sets, inverse P-sets, P-matrix and inverse P-matrix provide new mathematical theories and methods for information intelligent mining, and become a new tool to study dynamic information system.
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