On The Key Technologies Of Covering-Based Rouch Sets

Intelligent information processing technology (IIPT) has become a popular issue inartificial intelligence, machine learning and data mining. As an important IIPT, roughset theory is especially successful in processing vague and uncertain data. It hasattracted much researcher’s interests all over the world. With the development of datamining applications, people are trying to mine information from complex and diversedata. The classical rough set theory is not suitable in this case. Hence people proposeddifferent extensions of rough set theory. Covering-based rough sets extend the partitionin rough sets to the covering. In this way, rough sets are enriched from both theory andapplication in terms of more complicated data.With the development of covering-based rough sets, there are many needs to mineessential characteristics of a covering, construct more extensions of the theory, andexplore the algebra structure and the axiomatization of the theory. This dissertationtakes an extensive study on key technologies of these issues. An approach to refining acovering is proposed. Three extension models of coving-based rough sets areconstructed. The matroid theory is introduced to study rough sets. The matroidalstructures of rough sets are established from different viewpoints. The matroid basedreduction algorithms are designed. The main contributions of this work are listed asfollows:(1) An approach to refining a covering is proposed to improve the approximateability of covering approximations. An element is a determinate element if it belongs toseveral different covering blocks, otherwise it is an indeterminate element. Alldeterminate elements of a covering block possess certain characteristics of the block.With these characteristics, we combine the determinate and indeterminate elements ofeach covering block to form some new blocks. In this way, the refinement of eachcovering block is obtained. Six types of covering-based rough set models before andafter the refinement operation are compared. It is shown that the refinement of acovering improves the approximate ability effectively.(2) A new type of covering-based rough fuzzy set model is established. The relationship between each element and its minimal description is studied. Themembership of each element in the given fuzzy set is investigated. Based on the aboveanalysis, the concept of fuzzy covering rough membership is proposed. At the sametime, a new type of covering-based rough fuzzy set model is established. Comparedwith three existing models, the new one provides a more comprehensive description tothe given fuzzy set. Experimental results validate the analysis further.(3) One type of covering vague set model is established. Vague sets provide richerinformation than fuzzy sets while describing the fuzziness of some object. The uncertainrelationships between the covering lower/upper approximations and each element in theuniverse are studied. With these relationships, a covering-based vague set of the objectis constructed. It provides a new perspective to describe the relationships between anelement and the target set. This description is more concise than the one in classicalcovering-based rough sets. That is, elements in the covering lower approximation of atarget set do not always belong certainly to the set, yet elements in the negative regionof a target set may belong to the set to some extent.(4) One type of covering-based soft rough set model is established.Characteristics of soft sets and covering-based rough sets are compared. Based on thesecomparisons, the soft covering approximation space is constructed through thecomplementary parameter. Then a covering-based soft rough set model is built. Theconditions that different soft covering approximation spaces have the same approximateoperations are studied. A parametric reduction approach is proposed to removeredundant subsets in the soft covering approximation space. For any subset of theuniverse, its soft lower/upper approximations based on a soft covering approximationspace will not change after the space is reducted.(5) Matroid theory is introduced to study rough sets. Three types of matroidstructures of rough sets are constructed and matroid based methods of knowledgereduction are proposed. Matroid theory is a mathematical tool with perfect axiomaticsystems. It provides a new way to the axiomatic study of rough sets or covering-basedrough sets. Three types of matroidal structures for rough sets are established by usinguniform matroid, complete graph, and cycle, respectively. The upper and lowerapproximations in rough sets are characterized equivalently by using matroids. In thisway, some new properties of rough sets are found. The relationships between two matroid structures induced respectively by a complete graph and a cycle are analyzed.Results show that the two matroid structures are dual. Furthermore, matroid basedknowledge reduction algorithms are designed. This provides a concise and efficientapproach to the attribute reduction and the attribute value reduction.To sum up, this dissertation studies some critical issues of covering-based roughsets and proposes some key technologies to deal with them. Three extension models ofcovering-based rough sets are established by using fuzzy sets, vague sets and soft sets,respectively. An approach to refining a covering is proposed. The matroid theory isintroduced to study rough sets. Three types of matroidal structures of rough sets areconstructed and some algorithms of attribute reduction are designed with matroidalapproaches. From the theoretical viewpoint, covering-based rough sets are enrichedthrough fundamental investigation of basic concepts and connection with matroids.From the application viewpoint, more types of real-world data can be processed throughthese technologies.