Research On Uncertainty Measurement And Attribute Reduction In Generalized Fuzzy Information Systems

With the rapid development of the Internet,the data accumulated by people in various fields has increased rapidly,and the internal relationship of data has become more complex,which makes the uncertainty of the data more significant and also leads to the generation of a large number of redundant or irrelevant information.How to analyze and deal with these vague,imprecise and incomplete information and extract effective information has become an increasingly important issue.As a mathematical tool developed in recent years,rough set theory has unique advantages in quantitative analysis of uncertain information such as vagueness,imprecision and incompleteness.In rough set theory,data exist in the form of information tables(information systems).As the core research contents of information sys-tems,uncertainty measurement and attribute reduction have become the current research hotspots and research directions.Uncertainty measurement can provide effective measure-ment indexes for the uncertainty of information systems,help to understand the essence of the uncertainty of information systems,and provide ideas for its uncertainty reasoning.At-tribute reduction can extract important information in information systems,so as to reduce the dimension of data,compress and denoise data,in order to simplify the data presentation,improve the data quality and greatly simplify data processing in later stage.In information systems,the uncertain data are often presented in a fuzzy form,i.e.,fuzzy information systems.However,the information values in fuzzy information systems are still uncertain sometimes.This prompts us to study the extension of fuzzy information systems—generalized fuzzy information systems.The generalized fuzzy information sys-tem is one of the existing forms of complex fuzzy data,and it can describe the imprecise and uncertain information in a deeper level.At present,the research on generalized fuzzy infor-mation systems are relatively few.In order to explore complex fuzzy data and improve the effect of data processing,this paper focuses on the uncertainty measurement problem and attribute reduction method of generalized fuzzy information systems.Taking the interval-valued fuzzy information system,type-2 fuzzy information system and intuitionistic fuzzy information system contained in generalized fuzzy information system as examples,the gen-eralized fuzzy relations describing the differences between objects are constructed,so as to establish the uncertainty measurement model based on the idea of granularity and entropy.The attribute reduction methods based on positive domain in rough set theory and based on uncertainty measurement indexes are designed.The experimental analysis and comparative analysis of the actual data sets and the data sets in the UCI Machine Learning Repository are carried out to verify the feasibility and effectiveness of the measurement indexes and the reduction methods.The main work of this paper is listed as follows:(1)The similarity degree of interval form is defined in interval-valued fuzzy information systems to better describe the simi-larity differences between objects;the interval-valued fuzzy granular structures based on the interval-valued fuzzy granules are given and the relationships between the interval-valued fuzzy granular structures are considered;the measurement indexes are proposed from two aspects of granularity measurement and entropy measurement;the attribute reduc-tion method based on interval-valued fuzzy rough sets,the unsupervised attribute reduction methods based on granularity and entropy,and the supervised attribute reduction methods based on granularity and entropy are constructed respectively;the unsupervised and super-vised attribute reduction methods are experimentally analyzed.(2)The fuzzy T_cos-similarity relation is constructed based on Gaussian kernel in type-2 fuzzy information systems;the fuzzy information structures are defined and the dependence between them is discussed;the measurement indexes of rough granularity and rough entropy are studied by combining roughness to distinguish two type-2 fuzzy information systems effectively;the effective-ness of rough entropy measurement index is analyzed by experiments;the attribute reduc-tion methods based on positive region,rough granularity and rough entropy are proposed respectively.(3)The intuitionistic fuzzy dominance relation is given in intuitionistic fuzzy information systems and the intuitionistic fuzzy information structure is studied;the intu-itionistic fuzzy dominance entropy and its expansions are defined to measure uncertainty;the attribute reduction methods based on intuitionistic fuzzy dominance rough sets and based on intuitionistic fuzzy dominance entropy are constructed respectively;the attribute reduction method based on intuitionistic fuzzy dominance mutual information is given when consid-ering the redundancy between attributes;and the performance of attribute reduction method based on mutual information is evaluated by numerical experiments.The research in this paper will enrich and expand the rough set theory,contribute to the understanding of generalized fuzzy data,enrich the theory and connotation of uncer-tainty measurement,provide theoretical basis for the application of measurement tools and attribute reduction methods,and help to construct and evaluate the knowledge discovery algorithms in generalized fuzzy data.