Study On Information System Structure And Homomarphism Based On Attribute Set Information Granules

The emergence of large-scaled complex information in the Internet Age Greatly increased the complexity of processing(computing).Big data as another important technological changes in the IT industry,is driving new changes in the field of management after the cloud computing and Internet of things.Granular computing(GrC)proposed by Professor L.A.Zadeh is a new method and effective tool for solving complex problems in the field of Computational Intelligence Research.It has very positive effect for the main challenges of the big data processing,especially in reducing data size.A lot of granular computing research revealed that using information granule can reduce the amount of data or realize data compression.Information system(also known as knowledge representation system)is one of the important mathematical models in the research of granular computing.It has two dimensions of attribute set and object set and can describe data objects with certain properties.The extant research on the information granule is mainly on granulation,granular structure of the data object set of information system and its properties and applications.Taken the attribute set of information systems as research objective,this paper combined the theory and method of granular computing,the function dependency theory in relational database,the partial ordered set and the lattice theory of modern mathematics,and studied the granulation,granular structure of information system attribute set as well as its properties and applications on the basis of functional dependency relation between information system attributes.The main work and research result are as follows:(1)An information granular computing model of information system attribute set based on set theory was established.In this paper,the concept of information granules of information system attribute set was proposed and its semantic interpretation was given,basic properties and relationship between granules was studied and then the concepts of information system attribute granule structure and structure complexity was defined based on information granules of information system attribute set.Quantitative properties of attribute granule structure of information system were studied.It was proved that every attribute granule of information system can be generated by the intersection of some basic granules,which can be used to realize the simplified representation of information system structure.The dynamic change regularity of attribute granule structure of information system with the change of attributes or function dependencies was studied.A new concept of attribute reduction was presented and effective calculation method was put forward.(2)The idea of divide-and-conquer was adopted to achieve effective calculation of information system attribute granule structure.Firstly,the separability of information system was defined,and it was proved that if an information system is separable,the structure of attribute granule of the system can be decomposed into the Cartesian product of the structure of attribute granules of its sub-systems(decomposition theorem),then the method to judge the separability of an information system and the decomposition algorithm of separable information system were given.A computation method for calculating the structure of attribute granule of a separable information system was proposed based on decomposition theorem.Secondly,the rule that how the structure of attribute granule of an information system change when new functional dependency was added to the functional dependency set of an information system was studied and the increment theorem of information system structure was proved.Afterwards,the algorithm to calculate the structure of attribute granule of inseparable information system was given by using increment theorem and decomposition theorem.Thirdly,given two attribute subsets that constitute the cover of attribute set of an information system,the original system was decomposed into two subsystems and the attribute granule structure of these two subsystems was calculated.After that,equivalence relations were built up upon the attribute granule structure of each subsystem based on the intersection of the two attribute subsets.It was proved that the union of the products of the corresponding equivalence class of the attribute granule structure of the two subsystems is the attribute granule structure of the original system(cover decomposition theorem).A decomposition computation method based on cover decomposition theorem was proposed to compute the attribute granule structure of inseparable information systems.Analysis results showed that the method reduced the complexity from the multiplication of the exponent arithmetic to the addition of the exponent arithmetic compared with the direct computation of the attribute granule structure of inseparable information systems.The theoretical analysis and example demonstrate that the computation methods above are feasible.(3)In this paper,the properties of the information system attribute homomorphism were investigated based on the partial ordered set theory of modern mathematics.The concepts of attribute homomorphism for information system was defined,which can be used to induce the join-homomorphism over information system structure.The concepts of information system deal isomorphism was defined,which can be induced by using the attribute equivalence to achieved lossless compression for information system.Existing measurement method can only measure distance between two information systems with the same attribute sets,distance between any two information systems can be obtained by introducing intermediate system which has the same attribute set with the original system and be isomorphic with image information system.Finally,a method was proposed to measure the ideal level of any attribute homomorphism by comparing distance between the original system and the image information system.(4)The decomposition and granulation of information system,construction of attribute homomorphism,and the comparison between different information systems were studied with concrete examples applying the thinking from special to general.In order to get a good decomposition,the concept of the information system decomposition equilibrium degree was defined,and the existing algorithm was improved,which made the information system decomposition more balanced and reasonable.Using the result of decomposition,the method of constructing attribute homomorphism of information system was given.For the induced homomorphism image system,the method can be executed recursively according to the actual processing needs to obtain a more coarse-grained image system until a suitable processing information system granularity was obtained.Further,the relationship between two different-structured information systems was studied using the relationship between their homomorphism image systems,and general conclusions were given.