Research On Fuzzy Covering-based Rough Sets And Their Extensions

As an excellent generalization of Pawlak's rough set,covering-based rough set plays an important role for data pre-process and attribute reduction in incomplete information systems.Fuzzy coverings are a natural extension of the coverings by replacing crisp sets with fuzzy sets.Then the research of fuzzy covering-based rough set provide the theoretical support for data pre-process and attribute reduction in fuzzy information systems.This thesis is mainly devoted to the study of fuzzy covering-based rough set and its extensions based on some definitions and properties of fuzzy covering approximation space.The main work of in this thesis are listed as follows.(1)We study some basic concepts and properties of fuzzy covering approximation space.First,some basic definitions of fuzzy covering approximation space are defined by generalizing some definitions on covering such as neighborhood system,minimal description and maximal description.Second,some fuzzy neighborhood operators based on fuzzy covering are defined by using some operations on fuzzy sets and their properties and relationship are investigated.Moreover,some fuzzy coverings are derived by using these fuzzy neighborhood operators.Naturally,we consider the relationship between the fuzzy covering and corresponding derived fuzzy covering,respectively.Finally,we consider the issue under what conditions two fuzzy cover-ings generate the same fuzzy minimal description(resp.fuzzy maximal description,fuzzy neighborhood system)of an element on the universe.(2)We define a new type of fuzzy covering-based rough set model based on fuzzy minimal description.First,some properties of this fuzzy covering-based rough set model are studied.Then,the matrix representations and axiomizations of the fuzzy covering-based approximation operators are the vital problems we investigate in this chapter.It is an important issue that the redundancy of fuzzy covering blocks should be solved.Then we consider the necessary and sufficient conditions under what two fuzzy coverings generate the same fuzzy covering-based approximation operators.Finally,we generalize this fuzzy covering-based rough set models to fuzzy lattices.(3)We define some types of fuzzy covering-based rough set models by using fuzzy neigh-borhood operators.First,we study some properties of these fuzzy covering-based rough set models.Then,the matrix representations and axiomizations of these fuzzy covering-based approximation operators are given.Moreover,we consider the necessary and sufficient conditions under what two fuzzy coverings generate the same fuzzy covering-based approximation operators.Especially,the relationship among these fuzzy covering-based rough set models is investigated.(4)We study the fuzzy covering-based rough set on two different universes.First,we present a new type of fuzzy covering-based rough set on two different universes by using Zadeh's extension principle and investigate the properties of this model.Sec-ond,the matrix representation of fuzzy covering-based approximation operators are given.Moreover,we consider the necessary and sufficient conditions under what two fuzzy coverings generate the same fuzzy covering-based approximation opera-tors.Notably,this model can be used for attribute reduction of a kind of multiple criteria decision making problem.Information acquisition and communication play an important role in the field of information technology.Then we consider the communication between fuzzy information systems by using fuzzy covering-based rough set over two universes.(5)We consider some generalizations of fuzzy covering-based rough set on residuated lattices.Residuated lattices is an important mathematical stucture and plays a vital role in multivalued reasoning.Then the generalizations of fuzzy covering-based rough sets to residuated lattices axe necessary in theory.First,we generalize fuzzy covering-based rough set to residuated lattices and study their properties.Second,the matrix representation,axiomizations and interdependency of these L-fuzzy covering-based approximation operators are investigated.