Measurement And Attribute Reduction Based On Covering Rough Set

Rough set theory is a method of soft computing to deal with uncertainty information. The main idea of the theory is that by using the lower and upper approximations in rough sets, the knowledge hidden in information systems may be discovered and expressed in the form of decision rules. The equivalence relation and partition can be viewed as the basis of the theory due to the lower and upper approximations are defined with the equivalence relation and the partition of the universe. Since attributes only in the datasets where each object only can take a unique discrete value for every attribute can induce a partition of the universe, and this limits the application of classical rough sets. To overcome this issue, many scholars consider generalizing rough set theory and Zakowski was the first to established covering rough sets by relaxing partitions of a universe to coverings. From then on, the research mainly focus on the study of covering approximations and a lot of definitions of lower and upper covering approximations are proposed, while the uncertainty measurement and attribute reduction of covering rough sets are less concerned. For this case our paper made the following research.(1) Summarize various covering approximations and define the uncertainty measurement for covering rough sets. Firstly, we found that dozens of covering approximations can be summarized as five kinds of lower covering approximation and ten kinds of upper covering approximation. Secondly, due to the uncertainty of covering rough sets results from the size of the boundary region of covering rough sets and the roughness of covering knowledge granularity, in this paper we defined the uncertainty measurement of covering rough sets.(2) Belief and plausibility functions in evidence theory are used to measure covering approximations. As mass function, belief function and plausibility function can be determined with each other, and belief function and the plausibility function satisfy dual property, so it is naturally that the pairs of approximation operators with no duality definitely cannot be measured by belief and plausibility functions simultaneously. Then we try to point out whether or not the pairs of approximation operators with duality which are summarized in Chapter Ⅲ can be measured by belief and plausibility functions.(3) Develop new algorithms for attribute reduction in covering decision systems. Firstly we define the relative discernibility relation of covering decision systems. Secondly we develop algorithms to find the minimal elements of covering decision systems by using the correspondence between the minimal elements and sample pairs. Finally, we give algorithms of finding a reduct for covering decision system by applying the relative discernibility relations respectively.