The Applied Study Of Generalized Neighborhood System In Rough Set Theory

The theory of rough set is a mathematical tool for dealing with uncertain information and knowledge.The mathematical basis of its theory and application is a pair of approximation operators.Generally,there are two methods to study the pair of approximation operators,the constructive way and the axiomatic way.In the constructive method,the researchers often consider binary relations,covering and(generalized)neighborhood systems on the universe of discourse as primitive notions,and then use them to construct and study rough approximation operators.On the other hand,in the axiomatic method,the scholars usually consider the abstract approximation operators as primitive notions,and then use a set of axioms to characterize the approximation operators that are defined by the constructive method.Fuzzy set theory is another mathematical tool to deal with uncertain problems.It has strong complementarity with rough set theory,and fuzzy rough set is the combination of the two theories.In recent years,topological methods have been widely used in the study of(fuzzy)rough set theory.In addition,the(generalized)neighborhood system is a fundamental tool to study topology.Our objective of this paper is to apply the generalized neighborhood system in the study of(fuzzy)rough set theory.The contents of the study mainly includes the following four aspects:In the first chapter,we study the basic properties and give the axiomatic characterization on two types of rough approximation operators based on generalized neighborhood system.In the second chapter,we apply the two types of rough approximation operators based on generalized neighborhood system in the research of incomplete information system.In particular,with the help of the approximation operators,we dig up the truly decision rules from the decision table.In the third chapter,we introduce the concept of lattice-valued fuzzy generalized neighborhood system,then define a pair of rough approximation operators based on it.We also study the basic properties of the pair of rough approximation operators.In the fourth chapter,we present an axiomatic study on lattice-valued fuzzy generalized neighborhood system-based approximation operators,which are defined in thethird chapter.The main contribution of this paper is to establish a mathematical foundation for the theory of rough set based on(lattice-value fuzzy)generalized neighborhood system.We prove that some well-known rough approximation operators can be regarded as special cases of our defined rough approximation operators,and so these rough approximation operator can be included into one framework for discussion.This makes the research of rough approximation operators based on(lattice-valued fuzzy)generalized neighborhood system has more general significance.