Rough Decision Law And Rough Law Mining

In this dissertation,rough decision and rough decision law are researched by using S-rough sets and function S-rough sets,which have an advantage in processing uncertainty problem in multi-attributes and multi-objects decision.In[17],the concept of rough decision is proposed based on S-rough sets,but the theory of rough decision is not being perfected.This study perfects the theory of rough decision especially in mathematics structure,which provides theoretical foundation with law mining and law identification.Moreover,by using propositional logic,the problem of decision law inference and law mining are discussed.The dissertation includes six chapters.Main contents and creative results are as follows.(1) An elaborate review of research on rough sets is given.Based on concepts of Pawlak rough sets,this dissertation gives the concepts of S-rough sets and function S-rough sets.Their mathematics structure and elementary characteristics are discussed.(2) By using Pawlak rough sets,the concept of rough decision is perfected. Because Pawlak rough sets is static,rough decision is static decision based on it,and it can't reflect the essence of problem.S-rough sets develops Pawlak rough sets, which reflects the dynamic nature of set,so rough decision based on S-rough sets reflects the change of decision-making factors.For decision-making factor set X, by employing Pawlak rough sets,it can generate rough decision(μ_i^′,μ_j^″).When decision-making factor set X is a S-set,by using S-rough sets,we will get a rough decision sequence.Based on the rough decision sequence,the dissertation gives a generation method of rough decision law.Rough decision is divided into three classes:one direction S-rough decision law,one direction S-dual rough decision law, two direction S-rough decision law,which were discussed indepth.In order to separate upper-decision law and lower-decision law,the concept of ordinary rough law is put forward.Later,we give the concepts of rough decision law band,rough decision law kernel,and rough decision hull,moreover,discuss their main characteristics and the meanings of the concepts in practice,and give the elementary criteria of law mining.Finally,an example is given for illustrating the theory.(3) From the point of view of function rough sets,the function set of system,(?) is a R-function equivalence class.The concept of rough law is defined,and the rough law generation method is proposed,which is based on R -function equivalence class[u(x)].R-function equivalence class[u(x)]can generate system law p(x). Attribute setα= {α₁,α₂,...,α_r} changes by the action of element transfer family (?),which results in the dynamic characteristics of R-function equivalence class [u(x)].The law p(x) changes along with[u(x)].We give the concept of attribute disturbance degree,and discuss the changes of law based on this concept. The concepts of rough law F-decompose and(?)-decompose are proposed,and the characters of rough law F-decomposition and(?)-decomposition are discussed.(4) Based on the rough law generated from function S-rough sets,the concept of the law energy is proposed,which is used as measurement of rough law.By using the concept,we discuss the measurement of F -decomposition rough law in two-dimensional plane,and give a series of theorems of decomposition and composition of rough law,and point out its background and significance,which lays a theoretical foundation for law mining and identification.(5) Propositional logic is applied in study of rough law.Based on the new concepts of law separation degree and law dependent degree,we discuss the logical inference relations between attribute disturbance and system law.As well as we discuss the separation-dependent relations between the laws and their separation laws.The research provides a theoretical foundation with rule-based reasoning.(6) The example of rough decision law mining and law identification is given.Finally,we summarize all discussion in the dissertation,and prospect the next work.The main innovative viewpoints of this dissertation are as follows: (1) Dynamic rough decision theory is developed and perfected.A new rough decision law model is proposed.The concepts of rough decision sequence,rough decision law,rough decision law band are defined.The criteria of law mining and application of law mining is given.(2) Based on rough law generated from function S-rough sets,the concept of law energy is proposed,which is used as measurement of rough law.By using of the concept,we discuss the measurement of F- decomposition and(?)- decomposition rough law in two-dimensional plane,and give a series of theorems of decomposition and composition of rough law,and point out its background and significance,which lays a theoretical foundation for law mining and identification.(3) Propositional logic is introduction to law inference,and the concepts of law separation degree and law dependent degree are proposed.Based on these concepts, the separation-dependent relations between the laws and their separation laws are discussed.