基于属性集信息粒的信息系统结构及同态研究
[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.
【学位授予单位】:西北工业大学
【学位级别】:博士
【学位授予年份】:2016
【分类号】:TP18;TP311.13
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