of large samples of granules for the input space, which in many cases is not computationally efficient. The MCMC creates a chain of granules and accepts or rejects them using Metropolis algorithm. The application of Bayesian approach and MCMC 
rough set, results in the probability distribution function of the granules, which in turn leads to the distribution of the rough set outputs. From these distribution functions the average prediction of the rough set model and the variance of that prediction can be calculated. The probability distributions of the rough set model represented by granules are mathematically described by equation 11. From equation 11 and by following the rules of probability theory, the distribution of the output parameter, y, **is written as** 
(Marwala, 2007): 

$$p(y\,|\,x,D)=\int p(y\,|\,x,M)\,p(M\,|\,D)d M$$
p( y | x,D) = p( y | x,M ) p(M | D)dM **(12)** 
Equation 12 depends on equation 11, and is difficult to solve analytically due to relatively high dimension of granule space. Thus the integral in equation 12 may be approximated as follows: 

$$\stackrel{\mathrm{�}}{y}\equiv\frac{1}{L}\sum_{i=I}^{R+L-1}F(M_{i})$$
$$\quad(12)$$

$$(13)$$
y **(13)**
Here F is the mathematical model that gives the output given the input, ỹ **is the average** 
prediction of the Bayesian rough set model, R **is the number of initial states that are** discarded in the hope of reaching a stationary posterior distribution function described in equation 11 and L **is the number of retained states. In this paper, MCMC method is** implemented by sampling a stochastic process consisting of random variables 
{g1,g2*,…,g*n} through introducing random changes to granule vector {g} **and either** 
accepting or rejecting the state according to Metropolis et al. algorithm given the 