基于屬性集信息粒的信息系統(tǒng)結(jié)構(gòu)及同態(tài)研究
發(fā)布時間：2018-11-24 07:34
【摘要】：互聯(lián)網(wǎng)時代大規(guī)模復(fù)雜信息的涌現(xiàn),帶來處理(計算)復(fù)雜性的高度增加。大數(shù)據(jù)作為繼云計算、物聯(lián)網(wǎng)之后IT產(chǎn)業(yè)又一次重要的技術(shù)變革,正在驅(qū)動管理領(lǐng)域的新變革。粒計算是由美國控制論專家Zadeh提出的計算智能研究領(lǐng)域中解決復(fù)雜問題的新方法和有效工具,對大數(shù)據(jù)處理中面臨的主要挑戰(zhàn)有著十分積極的作用,特別是在降低數(shù)據(jù)規(guī)模方面,很多粒計算研究都認(rèn)為使用信息�？梢詫崿F(xiàn)數(shù)據(jù)壓縮。信息系統(tǒng)(也稱為知識表示系統(tǒng))是粒計算研究中重要的數(shù)學(xué)模型之一,具有屬性集和對象集兩個維度,能夠描述數(shù)據(jù)對象具有某些屬性特征。當(dāng)前對于信息粒的研究,主要集中于信息系統(tǒng)數(shù)據(jù)對象集的�；�、粒結(jié)構(gòu)及其性質(zhì)和應(yīng)用等方面。本文以信息系統(tǒng)的屬性集為研究對象,將粒計算理論與方法、關(guān)系數(shù)據(jù)庫中的函數(shù)依賴?yán)碚�、現(xiàn)代數(shù)學(xué)中的序、格理論結(jié)合起來,利用屬性上的語義信息,對信息系統(tǒng)屬性集的�；�、粒結(jié)構(gòu)及其性質(zhì)和應(yīng)用做了研究,主要的工作和結(jié)論如下:(1)建立了基于集合論的信息系統(tǒng)屬性集信息粒計算模型。提出了信息系統(tǒng)屬性集信息粒的概念并給出了其語義解釋,研究了屬性集信息粒的基本性質(zhì)及粒與粒之間的關(guān)系;利用屬性集信息粒定義了信息系統(tǒng)屬性粒結(jié)構(gòu)及結(jié)構(gòu)復(fù)雜度的概念,研究了屬性粒結(jié)構(gòu)的數(shù)量性質(zhì);證明了信息系統(tǒng)全部屬性粒可以由其基本粒的交生成,利用這些基本�？梢詫崿F(xiàn)信息系統(tǒng)結(jié)構(gòu)的簡化表示;研究了當(dāng)屬性或函數(shù)依賴變化時,信息系統(tǒng)結(jié)構(gòu)的動態(tài)變化規(guī)律;從系統(tǒng)結(jié)構(gòu)復(fù)雜度變化最小的角度定義一種新的屬性約簡,并給出相應(yīng)的計算方法。(2)應(yīng)用分治的思想實現(xiàn)了信息系統(tǒng)屬性粒結(jié)構(gòu)的有效計算。定義了信息系統(tǒng)結(jié)構(gòu)的可分離性,給出了可分離性的充要條件,并證明了如果一個信息系統(tǒng)是可分離的,則該系統(tǒng)的粒結(jié)構(gòu)可分解為該系統(tǒng)的子系統(tǒng)粒結(jié)構(gòu)的笛卡爾乘積(分解定理),利用分解定理給出了可分離信息系統(tǒng)結(jié)構(gòu)的計算方法;研究了在已知信息系統(tǒng)屬性粒結(jié)構(gòu)的條件下,增加新的語義信息時,粒結(jié)構(gòu)的變化規(guī)律,證明了信息系統(tǒng)結(jié)構(gòu)增量定理;利用分解定理和增量定理給出了計算不可分離信息系統(tǒng)屬性粒結(jié)構(gòu)的算法;給定兩個構(gòu)成信息系統(tǒng)屬性集覆蓋的屬性子集,將原系統(tǒng)分解為兩個子系統(tǒng),分別計算兩個子系統(tǒng)的屬性粒結(jié)構(gòu);然后,根據(jù)兩個屬性子集的交集,在每個子系統(tǒng)的屬性粒結(jié)構(gòu)上建立一個等價關(guān)系,證明了兩個子系統(tǒng)屬性粒結(jié)構(gòu)中相對應(yīng)的等價類乘積的并集就是原信息系統(tǒng)的屬性粒結(jié)構(gòu)(覆蓋分解定理);利用覆蓋分解定理給出了信息系統(tǒng)屬性粒結(jié)構(gòu)的覆蓋分解算法。與直接計算不可分離信息系統(tǒng)的粒結(jié)構(gòu)相比,該計算方法可將復(fù)雜度由指數(shù)運算相乘降低為相加。理論分析和實例計算表明,以上所提計算方法是可行的。(3)應(yīng)用現(xiàn)代數(shù)學(xué)中的序論,研究了信息系統(tǒng)屬性同態(tài)的性質(zhì)。定義了信息系統(tǒng)屬性同態(tài)的概念,利用屬性同態(tài)可以誘導(dǎo)出信息系統(tǒng)結(jié)構(gòu)上的并同態(tài);定義了信息系統(tǒng)理想同態(tài)的概念,利用屬性等價關(guān)系誘導(dǎo)出了信息系統(tǒng)屬性理想同態(tài),應(yīng)用信息系統(tǒng)屬性理想同態(tài)實現(xiàn)了信息系統(tǒng)屬性集的無損壓縮�，F(xiàn)有度量方法只能度量屬性集相同的信息系統(tǒng)結(jié)構(gòu)間的距離,通過引入與原信息系統(tǒng)屬性集相同并且與像信息系統(tǒng)同構(gòu)的中間系統(tǒng),得到了任意信息系統(tǒng)結(jié)構(gòu)間距離的度量方法。通過比較原信息系統(tǒng)與同態(tài)像信息系統(tǒng)的距離,給出了度量任意屬性同態(tài)理想程度的方法。(4)應(yīng)用從特殊到一般的歸納思想,通過具體實例,研究了信息系統(tǒng)的分解及�；�,屬性同態(tài)構(gòu)造,不同信息系統(tǒng)間的比較等內(nèi)容。為了得到性質(zhì)良好的分解,定義了信息系統(tǒng)分解均衡度的概念,以此為基礎(chǔ),對已有的算法進行了改進,使得信息系統(tǒng)分解更為均衡合理。利用分解的結(jié)果,給出了構(gòu)造信息系統(tǒng)屬性同態(tài)的方法。對于誘導(dǎo)出的同態(tài)像系統(tǒng),可以根據(jù)實際處理需要,遞歸執(zhí)行該方法以獲得更粗粒度的同態(tài)像系統(tǒng),直到得到某個適合處理的信息系統(tǒng)粒度。進一步地,利用兩個不同結(jié)構(gòu)的信息系統(tǒng)的同態(tài)像系統(tǒng)之間的關(guān)系來研究它們本身之間的關(guān)系,并給出了一般結(jié)論。
[Abstract]:The emergence of large-scale complex information in the Internet era brings about an increase in the complexity of processing (calculation). Big data is another important technological change in IT industry after cloud computing and Internet of Things, and is driving new changes in the field of management. the particle calculation is a new method and an effective tool for solving complex problems in the field of computing intelligent research by the American cybernetics expert Zadeh, and has a very positive effect on the main challenges in the large data processing, in particular in the aspect of reducing the data size, Many of the particle-based computational studies are of the view that data compression can be achieved using information particles. The information system (also known as the knowledge representation system) is one of the important mathematical models in the particle calculation research, and has two dimensions of the attribute set and the object set, and can describe the characteristic of the data object. At present, the research on the information particles mainly focuses on the granularity, the grain structure, the properties and the application of the data object set of the information system. The paper takes the attribute set of information system as the research object, and combines the particle calculation theory with the method, the function-dependent theory in the relational database, the order of the modern mathematics and the lattice theory, and uses the semantic information on the attribute to make the granularity of the information system attribute set. The grain structure and its properties and application have been studied. The main work and conclusion are as follows: (1) The information system attribute set information particle calculation model based on set theory is established. The concept of information system attribute set information is put forward and its semantic interpretation is given. The basic properties of the attribute set information particles and the relation between the particle and the particle are studied. The concept of the structure and the structure complexity of the information system attribute set is defined by the attribute set information. The quantitative property of the attribute grain structure is studied, and it is proved that all the attribute particles of the information system can be generated by the intersection of the basic particles, and the simplified representation of the information system structure can be realized by using the basic particles, and the dynamic change rule of the information system structure when the property or the function is dependent on the change is studied. In this paper, a new attribute reduction is defined from the angle of minimum structural complexity variation, and a corresponding calculation method is given. (2) The effective calculation of the structure of the information system's attribute is realized by the idea of dividing and treating. the separability of the information system structure is defined, the sufficient and sufficient condition for separability is given, and it is proved that if an information system is separable, the grain structure of the system can be decomposed into a cartesian product (decomposition theorem) of the subsystem particle structure of the system, The calculation method of the structure of the separable information system is given by using the decomposition theorem. Under the condition of the structure of the known information system attribute, the rule of the grain structure is increased, and the increment theorem of the structure of the information system is proved. using the decomposition theorem and the increment theorem, an algorithm for calculating the attribute particle structure of the non-separable information system is given; given two attribute subsets covered by the attribute set of the information system, the original system is decomposed into two sub-systems, and the attribute grain structure of the two subsystems is respectively calculated; and then, according to the intersection of the two attribute subsets, a unitary relation is established on the attribute particle structure of each subsystem, and the product of the equivalent class corresponding to the two sub-system attribute particle structures is proved to be the attribute particle structure (covering decomposition theorem) of the original information system; The overlay decomposition algorithm of the information system attribute particle structure is given by using the overlay decomposition theorem. The calculation method can reduce the complexity by the exponential operation to be added as compared with the grain structure of the direct-calculation non-separable information system. The theoretical analysis and the calculation of the case show that the above-mentioned calculation method is feasible. (3) The nature of the attribute homomorphism of information system is studied by using the sequence theory in modern mathematics. The concept of information system attribute homomorphism is defined, and the homomorphism of the information system structure can be induced by using the attribute homomorphism, the concept of the ideal homomorphism of the information system is defined, the ideal homomorphism of the information system property is induced by using the attribute homomorphism, The application information system attribute ideal homomorphism implements the lossless compression of the information system attribute set. The existing measurement method can only measure the distance between the same information system structure of the attribute set, and obtains the measurement method of the distance between the information system structures by introducing the intermediate system which is the same as the original information system attribute set and is isomorphic to the image information system. By comparing the distance between the original information system and the homomorphic image information system, a method to measure the ideal degree of any attribute homomorphism is given. (4) From the special to the general induction thought, through the concrete example, this paper studies the information system's decomposition and granularization, the property homomorphism and the comparison among different information systems. In order to get good property, the concept of information system decomposition equilibrium is defined. Based on this, the existing algorithm is improved, so that the decomposition of information system is more balanced and reasonable. Using the result of the decomposition, the method of constructing the attribute homomorphism of the information system is given. For the induced homomorphic image system, the method can be recursively executed to obtain a more coarse-grained homomorphic image system according to the actual processing requirement until an information system granularity suitable for processing is obtained. Further, the relationship between the homomorphic image systems of the information systems with two different structures is used to study the relationship between them, and the general conclusions are given.
【學(xué)位授予單位】：西北工業(yè)大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TP18;TP311.13
本文編號：2352806
[Abstract]:The emergence of large-scale complex information in the Internet era brings about an increase in the complexity of processing (calculation). Big data is another important technological change in IT industry after cloud computing and Internet of Things, and is driving new changes in the field of management. the particle calculation is a new method and an effective tool for solving complex problems in the field of computing intelligent research by the American cybernetics expert Zadeh, and has a very positive effect on the main challenges in the large data processing, in particular in the aspect of reducing the data size, Many of the particle-based computational studies are of the view that data compression can be achieved using information particles. The information system (also known as the knowledge representation system) is one of the important mathematical models in the particle calculation research, and has two dimensions of the attribute set and the object set, and can describe the characteristic of the data object. At present, the research on the information particles mainly focuses on the granularity, the grain structure, the properties and the application of the data object set of the information system. The paper takes the attribute set of information system as the research object, and combines the particle calculation theory with the method, the function-dependent theory in the relational database, the order of the modern mathematics and the lattice theory, and uses the semantic information on the attribute to make the granularity of the information system attribute set. The grain structure and its properties and application have been studied. The main work and conclusion are as follows: (1) The information system attribute set information particle calculation model based on set theory is established. The concept of information system attribute set information is put forward and its semantic interpretation is given. The basic properties of the attribute set information particles and the relation between the particle and the particle are studied. The concept of the structure and the structure complexity of the information system attribute set is defined by the attribute set information. The quantitative property of the attribute grain structure is studied, and it is proved that all the attribute particles of the information system can be generated by the intersection of the basic particles, and the simplified representation of the information system structure can be realized by using the basic particles, and the dynamic change rule of the information system structure when the property or the function is dependent on the change is studied. In this paper, a new attribute reduction is defined from the angle of minimum structural complexity variation, and a corresponding calculation method is given. (2) The effective calculation of the structure of the information system's attribute is realized by the idea of dividing and treating. the separability of the information system structure is defined, the sufficient and sufficient condition for separability is given, and it is proved that if an information system is separable, the grain structure of the system can be decomposed into a cartesian product (decomposition theorem) of the subsystem particle structure of the system, The calculation method of the structure of the separable information system is given by using the decomposition theorem. Under the condition of the structure of the known information system attribute, the rule of the grain structure is increased, and the increment theorem of the structure of the information system is proved. using the decomposition theorem and the increment theorem, an algorithm for calculating the attribute particle structure of the non-separable information system is given; given two attribute subsets covered by the attribute set of the information system, the original system is decomposed into two sub-systems, and the attribute grain structure of the two subsystems is respectively calculated; and then, according to the intersection of the two attribute subsets, a unitary relation is established on the attribute particle structure of each subsystem, and the product of the equivalent class corresponding to the two sub-system attribute particle structures is proved to be the attribute particle structure (covering decomposition theorem) of the original information system; The overlay decomposition algorithm of the information system attribute particle structure is given by using the overlay decomposition theorem. The calculation method can reduce the complexity by the exponential operation to be added as compared with the grain structure of the direct-calculation non-separable information system. The theoretical analysis and the calculation of the case show that the above-mentioned calculation method is feasible. (3) The nature of the attribute homomorphism of information system is studied by using the sequence theory in modern mathematics. The concept of information system attribute homomorphism is defined, and the homomorphism of the information system structure can be induced by using the attribute homomorphism, the concept of the ideal homomorphism of the information system is defined, the ideal homomorphism of the information system property is induced by using the attribute homomorphism, The application information system attribute ideal homomorphism implements the lossless compression of the information system attribute set. The existing measurement method can only measure the distance between the same information system structure of the attribute set, and obtains the measurement method of the distance between the information system structures by introducing the intermediate system which is the same as the original information system attribute set and is isomorphic to the image information system. By comparing the distance between the original information system and the homomorphic image information system, a method to measure the ideal degree of any attribute homomorphism is given. (4) From the special to the general induction thought, through the concrete example, this paper studies the information system's decomposition and granularization, the property homomorphism and the comparison among different information systems. In order to get good property, the concept of information system decomposition equilibrium is defined. Based on this, the existing algorithm is improved, so that the decomposition of information system is more balanced and reasonable. Using the result of the decomposition, the method of constructing the attribute homomorphism of the information system is given. For the induced homomorphic image system, the method can be recursively executed to obtain a more coarse-grained homomorphic image system according to the actual processing requirement until an information system granularity suitable for processing is obtained. Further, the relationship between the homomorphic image systems of the information systems with two different structures is used to study the relationship between them, and the general conclusions are given.
【學(xué)位授予單位】：西北工業(yè)大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TP18;TP311.13
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