Function S-rough Sets Research Articles

Dynamic Fuzzy (λ,η)–Function Rough Sets

By learning function S-rough sets, we find that transfer functions play the roles in practice are that define which elements into the set Q and which elements left the set Q. But the changed elements have been mapped into what kinds of elements that are not very important, so it is not necessary to intensive study the transfer functions. Thus we can defines a dynamic fuzzy sets in the set D to reconsider the fates of the elements of Q. By using function S-rough sets and dynamic fuzzy sets, the new definition of dynamic fuzzy (λ,η)–function rough sets are given, then the mathematical structure and characteristics of dynamic fuzzy (λ,η)–function rough sets are discussed. The structural relations of dynamic fuzzy (λ,η)–function rough sets and function S-rough sets are deeply deliberated. Dynamic fuzzy (λ,η)–function rough sets are the general form of function S-rough sets, then function S-rough sets are the special cases of dynamic fuzzy (λ,η)–function rough sets. Dynamic fuzzy (λ,η)–function rough sets are the new direction in the study of rough sets. In terms of practical application, dynamic fuzzy (λ,η)–function rough sets can achieve some better results than the other methods.

F-model generated by function S-rough sets

By employing function S-rough set, the researchers generate the $$f$$ -model of R-function equivalence class $$[u(x)]$$ and the $$f$$ - $$t$$ dynamic model as well as the corrective concept, generate F-model and F-dynamic model as well as the corrective concept, and propose the order relation theorem and dynamic separation theorem of the F-dynamic model. The dynamic characteristics of F-model rely on attribute $$\alpha$$ complement set. The generation principle and application of the model are given on the basis of the above discussion.

Function S-Rough Sets Over-Dual-Universes and Law Identification

This paper studies function S-rough sets over-dual-universes and the identification law in information system, describing the basic conceptions and properties of function S-rough sets over-dual-universes, its law feature and generating method, criterions to identify its law and the corresponding identification theorem and applications of law identification.

Function S-Rough Sets and Image <i>F</i>-Exterior Packet

Function S-rough sets is defined by employing -function equivalence class. A function is a curve. Function S-rough sets has curve characteristics and dynamic character- istics. By employing function S-rough sets, the concept of image -exterior packet is defined; the theorem of image -exterior packet and the recognization criteria of image -exterior packet are proposed. Function S-rough sets is a new theory and new tools for image processing.

Function S-rough sets and security-authentication of hiding law

Function S-rough sets are defined by R-function equivalence class, which have dynamic characteristic. Function S-rough sets have dynamic characteristic, law characteristic and law-hiding characteristic. Function S-rough sets can generate f-hiding law and \( \bar f \)-hiding law. By engrafting, crossing, and penetrating between the information security theory and function S-rough sets, the security hiding and the authentication of f-hiding law and \( \bar f \)-hiding law are given respectively in this paper. The fusion and share between function S-rough sets and information security theory is a new research direction of the application of information law in information system.

Function S-rough sets and law identification

By introducing element equivalence class that proposes dynamic characteristic into Pawlak Z rough sets theory, the first author of this paper improved Pawlak Z rough sets and put forward S-rough sets (singular rough sets). S-rough sets are defined by element equivalence class that proposes dynamic characteristic. S-rough sets have dynamic characteristic. By introducing the function equivalence class (law equivalence class) that proposes dynamic characteristic into S-rough sets, the first author improved S-rough sets and put forward function S-rough sets (function singular rough sets). Function S-rough sets have dynamic characteristic and law characteristic, and a function is a law. By using function S-rough sets, this paper presents law identification, law identification theorem, and law identification criterion and applications. Function S-rough sets are a new research direction of rough sets theory, and it is also a new tool to the research of system law identification.

-Law collision and system state recognition

Using dual function one direction S-rough sets, this article gives the ▪-law, the ▪-law, law distance and the concept of system law collided by the ▪-law. The characteristics presented by the system law collided by the ▪-law, the recognition of these characteristics and recognition criterion are also proposed. The dual function one direction S-rough sets is one of the basic forms of function S-rough sets. Its basic theory and application in the study of system law collision are reviewed.

F-Law collision and system state recognition.

Using function one direction S-rough sets (function one direction singular rough sets), f-law and F-law and the concept of law distance and the concept of system law collided by F law are given. Using these concepts, state characteristic presented by system law collided by F law and recognition of these states characteristic and recognition criterion and applications are given. Function one direction S-rough sets is one of basic forms of function S-rough sets (function singular rough sets).Function one direction S-rough sets is importance theory and is a method in studying system law collision.

Function S-rough sets and mining-discovery of rough law in systems

Function S-rough sets (function singular rough sets) is defined on α -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives rough law generation model of α -function equivalence class, discussion on law mining and law discovery in systems, and application of law mining and law discovery in communication system. Function S-rough sets is a new theory and method in law mining research.

Function S-Rough sets and its applications

Based on S-rough sets (singular rough sets), this paper presents function S-rough sets (function singular rough sets) and its mathematical structures and features. Function S-rough sets has two forms: function one direction S-rough sets (function one direction singular rough sets) and function two direction S-rough sets (function two direction singular rough sets). This paper advances the relationship theorem of function S-rough sets and S-rough sets. Function S-rough sets is the general form of S-rough sets, and S-rough sets is the special case of function S-rough sets. In this paper, applications of function S-rough sets in rough law mining-discovery of system are given. Function S-rough sets is a new research direction of rough sets and rough system.