粗决策规律与粗规律挖掘
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摘要
本论文针对多属性多目标决策中的不确定现象,利用粗集理论处理不确定性的优势,在文献提出的粗决策的基础上,将S-粗集和函数S-粗集理论渗透其中,对粗决策以及粗决策规律作了较为深入的研究。尤其是从数学结构上,对粗决策理论作了进一步完善,为规律挖掘和规律辨识提供了理论基础。同时,还利用命题逻辑的知识,对决策规律推理和规律挖掘作了研究与讨论。全文共分六章。主要研究内容和创新成果如下:
(1)对粗集的研究成果做了详尽的综述。给出了S-粗集,函数S-粗集的基本概念,数学结构以及基本性质。
(2)从Pawlak粗集入手,给出了粗决策的概念。Pawlak粗集是一个静态粗集,因此基于它生成的粗决策是一个静态决策,并不能反映管理系统决策的真实面貌。S-粗集改进了Pawlak粗集,体现了集合的动态性,基于它生成的粗决策反映了决策因素的动态变化。对于决策因素集X,利用Pawlak粗集,可生成粗决策(μ′_i,μ″_j).而当决策因素集X是一个S-集合的时候,利用S-粗集,我们将会得到一个粗决策序列。利用粗决策序列,文中进一步给出了粗决策规律的生成方法,并对生成的粗决策规律分成三种情况:单向S-粗决策规律,单向S-对偶粗决策规律,双向S-粗决策规律,作了深入讨论.为了实现上决策规律与下决策规律的分离,提出了平凡粗决策规律的概念;此后又给出了粗决策规律带,粗决策规律核,粗决策规律壳等概念,并讨论了它们的主要性质和在实际当中的意义,给出了规律挖掘的基本准则,最后以示例说明之。
(3)从函数粗集的观点来看,系统(?)的函数集是一个R-函数等价类。文中给出了粗规律的概念,以及基于R-函数等价类[u(x)]的规律生成方法,即基于[u(x)]可生成系统规律p(x)。属性集α={α_1,α_2,…,α}在元素迁移族(?)的作用下发生变动,导致R-函数等价类[u(x)]具有动态变化的特性,这种变化又导致了系统规律p(x)的变化.文中给出了属性扰动度的概念,并以此为基础讨论了规律的变化,给出了粗规律F-分解和(?)-分解的概念,并讨论了粗规律F-分解和(?)-分解的性质。
(4)针对函数S-粗集生成的粗规律,给出了规律能量的概念,用于作为粗规律的度量。利用这个概念讨论了F-分解粗规律在二维平面上的度量问题,给出了一系列关于粗规律分解与合成的定理,并指出了其实际的应用背景和意义,为规律挖掘和识别奠定了理论基础。
(5)将命题逻辑推理引入粗规律研究中。给出了规律分离度和规律依赖度的概念;基于这两个概念和粒度的概念,讨论了系统的属性干扰与系统规律之间的逻辑推理关系,以及规律之间的分离依赖关系,为规则推理提供了理论基础。
(6)给出了关于决策规律挖掘和识别的实例研究。
最后对全文进行了总结,并对下一步的研究工作进行了展望。
论文的主要创新工作:
(1)发展和完善了动态粗决策理论。提出了粗决策序列,粗决策规律,粗决策规律带,粗决策规律核等重要概念,给出了规律挖掘的基本准则。
(2)针对函数S-粗集生成的决策粗规律,提出了粗规律F-分解和(?)-分解的概念;提出了粗规律度量的问题,并给出属性干扰度和规律能量的概念,用于讨论粗规律度量,给出了一系列定理和结论,为粗规律挖掘和识别奠定了基础。
(3)将命题逻辑引入规律推理,提出规律隐藏度和规律依赖度的概念,基于此讨论了系统规律之间的隐藏依赖推理关系。
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= {α_1,α_2,...,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.
(1)对粗集的研究成果做了详尽的综述。给出了S-粗集,函数S-粗集的基本概念,数学结构以及基本性质。
(2)从Pawlak粗集入手,给出了粗决策的概念。Pawlak粗集是一个静态粗集,因此基于它生成的粗决策是一个静态决策,并不能反映管理系统决策的真实面貌。S-粗集改进了Pawlak粗集,体现了集合的动态性,基于它生成的粗决策反映了决策因素的动态变化。对于决策因素集X,利用Pawlak粗集,可生成粗决策(μ′_i,μ″_j).而当决策因素集X是一个S-集合的时候,利用S-粗集,我们将会得到一个粗决策序列。利用粗决策序列,文中进一步给出了粗决策规律的生成方法,并对生成的粗决策规律分成三种情况:单向S-粗决策规律,单向S-对偶粗决策规律,双向S-粗决策规律,作了深入讨论.为了实现上决策规律与下决策规律的分离,提出了平凡粗决策规律的概念;此后又给出了粗决策规律带,粗决策规律核,粗决策规律壳等概念,并讨论了它们的主要性质和在实际当中的意义,给出了规律挖掘的基本准则,最后以示例说明之。
(3)从函数粗集的观点来看,系统(?)的函数集是一个R-函数等价类。文中给出了粗规律的概念,以及基于R-函数等价类[u(x)]的规律生成方法,即基于[u(x)]可生成系统规律p(x)。属性集α={α_1,α_2,…,α}在元素迁移族(?)的作用下发生变动,导致R-函数等价类[u(x)]具有动态变化的特性,这种变化又导致了系统规律p(x)的变化.文中给出了属性扰动度的概念,并以此为基础讨论了规律的变化,给出了粗规律F-分解和(?)-分解的概念,并讨论了粗规律F-分解和(?)-分解的性质。
(4)针对函数S-粗集生成的粗规律,给出了规律能量的概念,用于作为粗规律的度量。利用这个概念讨论了F-分解粗规律在二维平面上的度量问题,给出了一系列关于粗规律分解与合成的定理,并指出了其实际的应用背景和意义,为规律挖掘和识别奠定了理论基础。
(5)将命题逻辑推理引入粗规律研究中。给出了规律分离度和规律依赖度的概念;基于这两个概念和粒度的概念,讨论了系统的属性干扰与系统规律之间的逻辑推理关系,以及规律之间的分离依赖关系,为规则推理提供了理论基础。
(6)给出了关于决策规律挖掘和识别的实例研究。
最后对全文进行了总结,并对下一步的研究工作进行了展望。
论文的主要创新工作:
(1)发展和完善了动态粗决策理论。提出了粗决策序列,粗决策规律,粗决策规律带,粗决策规律核等重要概念,给出了规律挖掘的基本准则。
(2)针对函数S-粗集生成的决策粗规律,提出了粗规律F-分解和(?)-分解的概念;提出了粗规律度量的问题,并给出属性干扰度和规律能量的概念,用于讨论粗规律度量,给出了一系列定理和结论,为粗规律挖掘和识别奠定了基础。
(3)将命题逻辑引入规律推理,提出规律隐藏度和规律依赖度的概念,基于此讨论了系统规律之间的隐藏依赖推理关系。
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= {α_1,α_2,...,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.
引文
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