Research On Threshold Method And Uncertainty Of Probabilistic Rough Sets

Rough sets model is a typical method to obtain decision rules from knowledge system.It has been widely applied in fault diagnosis,knowledge acquisition,approximate reasoning,fuzzy clustering and so on.Probabilistic rough sets model is an extension of Pawlak's rough sets model,which has better fault-tolerance and practicability.However,there is not any mature theory of probabilistic rough sets in the study of uncertainty research.In this paper,based on the latest research of probabilistic rough sets,we mainly study the the method of learning the thresholds in probabilistic rough sets model and the uncertainty of the probabilistic rough sets.This thesis studies from the following two aspects:(1)First of all,for three-way decision-theoretic rough sets model,we propose a new way to learn thresholds in three-way decision-theoretic rough sets model.It is a stochastic optimization algorithm to get smaller risk cost without way prior knowledge.We analysis the experiments from different data sets and compare with the existing methods.It has achieved a faster run-time and smaller cost.These results are important to further enrich and improve the thresholds method of probabilistic rough sets.(2)Based on uncertainty of Pawlak's rough sets,we propose a method for measuring the uncertainty of probabilistic rough sets and discuss the changing rules of uncertainty in multi-granulation knowledge spaces.The uncertainty theory of probabilistic rough sets is more complete than Pawlak's rough sets.We also discuss the uncertainty of the probabilistic rough sets in three regions: positive region,negative region and boundary region,and prove the conclusion.In Pawlak's rough sets model,the uncertainty of target concept in the boundary region will decrease monotonically when equivalence class is subdivided.The uncertainty of target concept in probabilistic rough sets model is more complex,we analysis and prove the related conclusion.