Research On The Uncertainty Measure Based On Covering Rough Sets

Rough set theory is a new mathematical tool to deal with the uncertainty problem, and is also an important branch of granular computing. In the study of the rough set theory, the solving of attribute significance, attribute core and attribute reduction is the main issue, while uncertainty measure is the key problem in these issues, so the study of the uncertainty measure in rough sets is very necessary. The classic rough set theory is based on the domain of the equivalence relation or divided, however, in real application, there is intersection or overlap phenomenon in the concept of knowledge, and all the concepts constitute the domain of covering, such as by the general binary relation or the neighborhood system of knowledge systems are belonged to this category. The equivalence relation or divided is limit the further application of rough set theory, especially for covering. Therefore, rough set theory is needed to be further extension, covering rough set theory is the extension of the classical rough sets, it has a broad application prospects in the field of knowledge discovery, so it is necessary to study uncertainty measure based on covering rough sets, the main content of this paper is to study uncertainty measure based on covering rough sets, specific research work is shown as follows:Fist of all, the uncertainty of measure has been researched based on the fourth type of covering rough sets. The fourth type of covering rough sets is one type of the covering rough set models, it is a comprehensive model based on the first, the second and the third type of covering rough sets, and it’s a reasonable model in covering rough sets, the study of uncertainty measure is the aspects of covering rough sets. This paper has analyzed the fourth type of covering rough set model; we define the rough membership function based on the fourth type of covering rough sets, and subsequently define the fuzziness based on the proposed rough membership function. A specific example is illustrated to explain the fuzziness. These research results extend the uncertainty measures based on the covering rough sets, and it provides a theoretical basis for knowledge reduction based on the fourth type of covering rough sets.Secondly, we analyze the uncertainty measure from the first to the fourth type of covering rough sets, and compare with the fuzziness relationship between the first and the fourth type of covering rough sets. We found the irrationality of the fuzziness based on the third type of covering rough sets; we amended the fuzziness and put forward a reasonable rough membership function.Thirdly, from the view of knowledge granularity, according to analyze the existent measures of uncertainty based on covering rough sets, it is revealed that they all bear some irrationality under specified situations. Here a concept of relative knowledge granularities based on covering rough sets is defined, and we propose an uncertainty measure of covering rough sets based on knowledge granularities-C-improved roughness. Analysis has proven that the uncertainty measuring approach solves the irrationality of former approaches, so it provides a new method for measuring the uncertainty of covering rough sets.In summary, this paper mainly study the uncertainty of covering rough sets, and these conclusions can provide ideas for solve the related problem of covering rough sets. At the same time, this model has better knowledge expression ability, it can be applied to the area of the data mining, machine learning and pattern recognition, and it has an important theoretical significance and potential application value.