Information Rough Communication And Its Characteristics

People use a great deal of information to reason and make decision, and their knowledge which is used to analyze and solve problems has its granulation. In real world, people's cognition of many things is uncertain, imprecise and incomplete owing to the limitation of their knowledge. Rough sets theory is a new mathematical tool to deal with imprecision, uncertainty and vagueness. The main advantage of the theory over other techniques, such as probability and statistics, evidence theory and fuzzy set, is that it does not need any preliminary or additional information about analyzed data. Rough sets theory provides an important theoretical tool to study rough information and its characteristics.The dissertation consists of six chapters. It studies rough communication and its characteristics under two practical situations of information communication. It includes static and dynamic rough communication of a classical concept, dynamic fuzzy rough communication of a fuzzy concept, an uncertainty measure for rough sets and numerical characteristics of variation rough sets.In chapter one, we introduce the basic concepts and development of rough sets, variation rough sets and two-direction S-rough sets.In chapter two we discuss static rough communication. We propose two static rough communication models using Z.Pawlak rough sets theory, discuss their properties and applications, obtain rough communication information invariability theorems, a rough communication information loss theorem , a rough communication information gain theorem, and give methods to improve accuracy of rough communication. The main results are Theorem 2.3.5-2.3.6, Theorem 2.4.5-2.4.6 and Definition 2.4.1. The main results are as follows:Theorem 2.3.5 Let(U,R₁),(U,R₂),…,(U,R_n)be n knowledge bases, where R₁,R₂,…,R_n are the knowledge of A₁, A₂,…,A_n, respectively. Let X(?)U and the information flow path be X→A₁→A₂→…A_n. If U/ind (R₁) (?)U/ind(R₂)(1) (G₁^-,G₁^-)=(G₂⁺,G₂^-)=…=(G_n⁺,G_n^-),(2) Lossd _{Ai-1→Ai}= 0 , i = 2,3,…,n.Where (G_i⁺ ,G_i^-) is the information which A₁ obtains from A_i-1 according to his knowledge R_i, Lossd _{Ai-1→Ai} is the information loss degree when information is communicated from A_i-1 to A_i, i= 2,3,…,n.Theorem 2.3.6 Let (U,R₁),(U,R₂),…,(U,R_n) be n knowledge bases, where R₁,R₂,…,R_n are the knowledge of A₁, A₂,…,A_n, respectively. Let X(?) U and the information flow path be X→A₁→A₂→…→A_n. Then(1) (G₁⁺,G₁^-)(?)(G₂⁺,G₂^-)(?)…(?)(G_n⁺,G_n^-),(2) Lossd_{Ai-1→Ai}≥0, i = 2,3,…,n.If U / ind( R₁) (?) U / ind(R₂)(?)…(?)U / ind(R_n), and comparing U/ind (R_i-1) with U/ind(R₁), if the blocks which are repartitioned in U / ind (R_i-1) are neither the positive region nor the negative region of X in (U,R_i-1, i = 2,3,…,n, then(3) (G₁⁺,G₁^-)(?)(G₂⁺,G₂^-)(?)…(?)(G_n⁺,g_n^-),(4) Lossd _{Ai-1→Ai} > 0 , i = 2,3,…,n.In chapter three we discuss dynamic rough communication. In fact, practical information communication is always dynamic. On one hand the agents continuously absorb new knowledge, and get rid of useless knowledge with more cognition, on the other hand information source absorbs much useful information, and deletes meaningless information, too. Using two-direction S-rough sets theory, we propose two dynamic rough communication models, discuss their properties and applications, and obtain the conditions which cause information to remain invariable or cause information to be lost or gained. Basing on the properties, we get methods of improving accuracy of dynamic rough communication. The main results are Definition 3.3.1 and Definition 3.4.1, Theorem 3.3.6-3.3.11, Theorem 3.4.6-3.4.11. The main results are as follows:Theorem 3.4.9 Let(U,R₁),(U,R₂) ,…,(U,Rn)be n knowledge bases, where R₁,R₂,…,R_n are the knowledge of A₁, A₂,…,A_n, respectively. Let X^* (?) U and theinformation flow path be X^*→A₁→A₂→…→A_n. If the knowledge of A_i hasbeen changed into R_i∪α_i^f\β_i^f|- from R_i, where the meanings of a_i^f andβ_i^f|- are the same as that in Theorem 3.3.3, i= 1,2,…,n, satisfying U/ind(R₁∪α₁^f\β₁^f|-) (?) U/ind(R₂∪α₂^f\β₂^f|-)(?)…(?) U/ind(R_n∪α_n^f\β_n^f|-),then(1) (DB₁⁺,DB₁^-)=(DB₂⁺,DB₂^-)=…=(D)B_n⁺,DB_n^-),(2) DGaind_{Ai-1→AI}=0, i = 2,3,…,n.Where (DB_i⁺,DB_i^-) is the infonnation which A_i obtains from A_i-1 according to his new knowledge R_i∪α_i^f\β_i^f|-, DGaind_{Ai-1→Ai} is the information gain degree when information is communicated from A_i-1 to A_i, i=2,3,…,n.Theorem 3.4.11 Let(U,R₁),(U,R₂),…,(U,R_n)be n knowledge bases, where R₁,R₂,…,R_n are the knowledge of A₁, A₂,…,A_n, respectively. Let X^* (?) U and theinformation flow path be X^*→A₁→A₂→…→A_n. If the knowledge of A_i hasbeen changed into R_i∪α_i^f\β_i^f|- from R_i, where the meanings of a_i^f andβ_i^f|-are the same as that in Theorem 3.3.3, i= 1,2,…,n, then(1) (DB₁⁺,DB₁^-)(?)(DB₂⁺,DB₂^-)(?)…(?)(DB_n⁺,DB_n^-),(2) DGaind_{Ai-1→Ai}≥0, i = 2,3,…,n.IF U/ind(R₁∪α₁^f\β₁^f|-)(?) U/ ind(R₂∪α₂^f\β₂^f|-) (?)…(?)U/ ind(R_n∪α_n^f\β_n^f|-), and comparing U/ind{R_i-1∪α_i-1^f\β_i-1^f|-} with U/ind{R_i∪α_i^f\β_i^f|-}, if the blocks which are repartitioned in U/ind{R_i-1∪α_i-1^f\β_i-1^f|-} are neither the positive region nor the negative region of X^* in (U, R_i-1∪α_i-1^f\β_i-1^f|-), i = 2,3,…,n, then(3) (db₁⁺,db₁^-)(?)(db₂⁺,db₂^-)(?)…(?)(db_n⁺,db_n^-),(4) DGaind_{Ai-1→Ai}＞0, i = 2,3,…,n.In chapter four we propose two-direction S-rough fuzzy sets, and discuss dynamic rough communication of a fuzzy concept. In order to discuss the dynamic fuzzy rough communication, static rough fuzzy sets proposed by Dubios and Prade is generalized to dynamic rough fuzzy sets, two-direction S-rough fuzzy sets and its cut set are put forward. The properties of the two-direction S-rough fuzzy sets are discussed. Using two-direction S-rough fuzzy sets, we propose two dynamic fuzzy rough communication models, discuss their properties, and give their applications in risk investment management system. The main results are Definition 4.2.4, Definition 4.5.1 and Definition 4.6.1, Theorem 4.5.6-4.5.11 and Theorem 4.6.6-4.6.11. The main results are as follows:Theorem 4.5.6 Let (U,R₁)and (U,R₂)be two knowledge bases, where R₁, and R₂ are the knowledge of A₁ and A₂, respectively. Let two-direction S-fuzzy set (X|～)^*∈F (U) and the information flow path be (X|～)^*→A₁→A₂ . If U/ind(R₁) (?) U/ind(R₂) , and at least there exist a R₂ -equivalence class [x]_R2 and an element y in [x]_R2, satisfying and Then the fuzzy information loss quantity and loss degree will be decreased by means of enriching the knowledge of A₂.Theorem 4.6.11 Let(U,R₁),(U,R₂),…,(U,R_n) be n knowledge bases, where R₁,R₂,…,R_n are the knowledge of A₁, A₂,…,A_n, respectively. Let (X|～)∈F(U) andthe information flow path be (X|～)→A₁→A₂→…→A_n. If the knowledge of A_i hasbeen changed into R_i Uα_i^f\β_i^f|- from R_i, where the meanings ofα_i^f andβ_i^f|- are the same as that in Theorem 3.3.3, i = 1,2,…,n, thenIf U/ind (R₁ Uα₁^f\β₁^f|-) (?)U/ind (R₂ Uα₂^f\β₂^f|-) (?)…(?)U/ind (R_n∪α_n^f\β_n^f|-), and at least there exist a R_it∪α_i^f\β_i^f|- -equivalence class and an elementy_i, in satisfying and DB; , i = 2,3,…n, thenWhere is the fuzzy information which A_i obtains from A_i-1 according to his new knowledge R_I, Uα_i^f \β_i^f, FGaind _{Ai-1→Ai} is the fuzzy information gain degree when fuzzy information is communicated from ,A_i-1 to A_i, i = 2,3,…,n.In chapter five, we study numerical characteristics of rough sets and variation rough sets. We propose a new uncertainty measure by combining traditional roughness with knowledge capacity measure. The new uncertainty measure not only calculates easily but also has properties of other measures.Using the concepts of variation rough sets and variation knowledge, we present some numerical characteristics of variation rough sets and variation knowledge [α/R]. It is convenient for us to study rough properties of system and data mining using these numerical characteristics. The main results are as follows:Definition 5.2.3 Let K = (U,R)be a knowledge base. Let X (?)U andU/R ={X₁,X₂,…X_n}.callRough_g(X)=ρ_R(X)(1-I(R))the R-improved roughness of X.CallD_R(X)=1-Rough_R(X)the R-improved accuracy of X.Variation knowledge filter-separation principleLet [α/R] = {[α/R,]|i =1,2,…,s; GRD([α/R_p]) =GRD([α/R_q]) ,p≠q, and p, q∈(1,2,…,m)} be a variation knowledge family on V. If there exists a disturbance (f|-)∈F to variation knowledge, thenthe variation knowledge [α/R_k ] which is disturbed by (f|-) is filtered and separated from [α/R]. Where GRD([α/R)k]) is the granulation degree of [α/ R_k].Variation knowledge filter surplus-separation principleLet [α/R] = {[α/R_I]|i = 1,2,…,s; GRD([α/R_p]) =GRD([α/R_q]) ,p≠q, and p, q∈(1,2,…,m)} be a variation knowledge family on V . If there exists a disturbance f∈F to variation knowledge, then the variation knowledge [α/ R_λ] which is disturbed by f is filtered and separated from [α/R]. Where FID([α/R_λ]) is the filter degree of [α/ R_λ].In chapter six, we give conclusion and expectation of the dissertation.The innovative viewpoints of this dissertation are as follows:1. A new rough communication model, i.e. the upper approximation rough communication model is proposed. The concepts of information loss quantity, gain quantity, information loss degree, gain degree are defined. The conditions which cause information to remain invariable or cause information to be lost or gained are obtained. Methods to improve accuracy of rough communication are given. The applications of the two rough communication models are given, and rough communication principles are obtained.2. Two dynamic rough communication models, i.e. the two-direction S-lower and upper approximation dynamic rough communication models are proposed. Their properties are discussed, and the conditions which cause information to remain invariable or cause information to be lost or gained are obtained. Methods to improve accuracy of dynamic rough communication are given. The applications of the two dynamic rough communication models are given, and the dynamic rough communication principles are obtained.3. The concepts of two-direction S-rough fuzzy sets and its cut sets are defined, and its structure and properties are given. Two dynamic fuzzy rough communication models are proposed. The concepts of fuzzy information loss quantity, gain quantity, fuzzy information loss degree, gain degree are defined. Relationships between knowledge and information invariability, knowledge and information loss, knowledge and information gain are obtained. The applications of the two models are given.4. A new uncertainty measure for rough sets is given, i.e. R -improved accuracy D_R (X) and R -improved roughness Rough_R (X) . Significance degree, granulation degree and filter degree of variation knowledge [α/R] are defined, and properties of variation knowledge and variation knowledge family are discussed. The concepts of granulation degree and filter degree of variation rough sets (X_a,X^-(a)) are proposed, and its granularity characteristics and filter characteristics are analyzed. It is convenient for us to study rough properties of system and data mining using these numerical characteristics.