Information Structure And Uncertainty Measurement In Fuzzy β-cover Information System

As a new technology that simulates the natural mode of human thinking,granular computing has attracted the attention of many scholars.The main idea is to granulate complex data,select appropriate information granules instead of samples as the basic unit of calculation,and further describe,reason and solve actual problems from different angles and levels.The reasoning and solving of the problem in granular computing is actually carried out by accessing the granular structure of the information system.At this stage,the research on granular computing has made great progress,but there are still many problems to be solved further.This dissertation takes the fuzzy β-covering information system as the research object,trying to establish the granular structure representation of the fuzzy β-covering information system and the uncertainty measurement based on information entropy.Based on the related theories of rough set and fuzzy set,the fuzzy β-covering information system is discussed and researched,and the granular computing theory and method of fuzzy β-covering information system is further enriched and perfected.The main work of this dissertation is as follows:(1)The information structure and its attributes in β-covering information systems are studied.From the perspective of granular computing,the fuzzy β-neighborhood is regarded as the information granule generated by the point set from the database.All these information granules form a vector,and this vector forms an information structure in the fuzzy β-covering information system caused by this attribute subset.Further,in order to study the relationship between the information structure in the fuzzy β-covering information system,two research directions of dependence and separation are proposed.The dissertation that exist between two given information structures in the same fuzzy β-covering information system are obtained.Finally,a brief discussion of the difference and change of information distance of information structure in a fuzzy covering information system when β is set to 1 in a fuzzyβ-covering information system.(2)A homomorphism among fuzzy β-covering information systems is proposed.Through the expansion principle of fuzzy sets proposed by Zadeh,a fuzzy mapping model of fuzzy β-covering compatibility is established.Further obtain the relationship between the information structure of the fuzzy β-covering information system and the information structure of the homomorphic image information system.Finally,by calculating the information structure of an information system with a small amount of data,a method is obtained that homomorphism can transform and compress the original information system while maintaining certain data structures.(3)The uncertainty measurement of fuzzy β-covering information system is established.The uncertainty measurement of fuzzy β-covering information system is established by introducing the concepts of information entropy,rough entropy and information volume.By researching the important properties and discussing the measurement relationship of the uncertainty measurement.It can be obtain that both the granularity measure and rough entropy in the fuzzy β-covering information system decrease monotonically with the increase of coverage,that is,the uncertainty of the fuzzyβ-covering information system increases with the increase of the number of coverage.Finally,from a statistical point of view,the effectiveness of the uncertainty method of the β-covering information system is analyzed,and the feasibility of the proposed uncertainty measurement method is verified.These results will help understand the nature of uncertainty in fuzzy β-covering information systems.In summary,this dissertation mainly starts from the point of view of granular computing,uses rough set as the main research tool,and adopts the method of combining theoretical research and data calculation.In-depth research on the theory and methods of granular computing and knowledge acquisition of fuzzy coverage information systems.These results will be very helpful for establishing a framework for granular computing in information systems.