الفهرس 
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Abstract
This Thesis consists of five chapters: In Chapter 1, a survey for rough set approximation is introduced. The aim of Chapter 2 is to show the different generalized rough sets First we discussed rough set based on any binary relation, Second generalized rough set based on any relation, Finally discussed Covers and Covering generalized rough sets . Chapter 3 is devoted to present several probabilistic extensions of the rough set model. Moreover, based on the probabilistic definition by using the prior and posterior probabilities, Kilany (2007) proposed two probabilistic rough set models, namely, modified rough set model (MRS) and modified variable precision Bayesian rough set model (MVPBRS). Chapter 4 The idea of rough random variable, rough expectation and rough variance have been defined and discussed. Introduced a new discrete rough distribution and there codes with scientific math program Maple. Some of the results established in this chapter are published in Journal of Egyptian and Statistical Society. The main concern of Chapter 5 is the methods of data reduction to make the best decision. A brief presentation of some methods for data reduction using independence rough set is given. The main results of this chapter are published in Journal of Egyptian and Statistical Society.