Research On Structured Tolerance Rough Set Model

Rough set theory is a mathematical theory method for dealing with incomplete information and inaccurate data.Compared with other methods(such as fuzzy set theory,probability theory,etc.)to deal with data,the main idea of rough set is to use a pair of upper and lower approximation sets to represent a given concept.In recent years,the theoretical method has been widely used in many scientific fields such as data mining,machine learning,pattern recognition,decision analysis,image processing,data analysis and so on.The classical rough set theory is established on the basis of the indiscernibility relation,which satisfies reflexivity,symmetry,and transitivity,and its essence is an equivalence relation.This relationship is too harsh for many practical problems,the accuracy of the data is also very high,and the structural information cannot be retained in the final classification.Aiming at the problem of preserving structural information,this paper replaces equivalence relations with tolerance relations,and proposes several structured tolerance rough set.The main research contents of this dissertation include:Firstly,discussing several rough set models and the structural theoretical basis and development status of structured rough set.Secondly,we propose several new rough set models: structured variable precision rough set and structured variable precision probabilistic rough set,the upper and lower approximations of structured variable precision rough set and structured variable precision probabilistic rough set are defined respectively,and can give the related properties of the structured variable precision rough set and structured variable precision probabilistic rough set,enhance the ability of data classification,the above model is a promotion of the structured rough set in incomplete information systems.Thirdly,in incomplete information systems,and combine with the structural theory of rough set,replace tolerance relations with equivalence relations,the structured tolerance rough set,structured probabilistic tolerance rough set,and structured variable precision tolerance rough set are proposed.By research the upper and lower approximate definitions of these models,the relevant properties of the structured tolerance rough set,the structured probabilistic tolerance rough set,and the structured variable precision tolerance rough set can be given,analyze these structured rough set through examples finally,the superiority of the model makes it better to play a better role in incomplete information systems.