where γ is the output, Gx **is the granulisation of the input space into high, low, medium** 
etc, Nr is the number of rules and R **is the rules. So for a given nature of granulisation, the** 
rough set model will be able to give the optimal number and nature of rules and the accuracy of prediction. Therefore, in rough set modeling there is always a trade-off between the degree of granulisation of the input space (which affects the nature and size of rules) and the prediction accuracy of the rough set model. 

## Multi-Layer Perceptron Model

The other component of the neuro-rough model is the multi-layered network. This network architecture contains hidden units and output units and has one hidden layer. The bias parameters in the first layer are weights from an extra input having a fixed value of x0=1**. The bias parameters in the second layer are weights from an extra hidden unit, with** the activation fixed at z0=1**. The model is able to take into account the intrinsic** 
dimensionality of the data. The output of the j th **hidden unit is obtained by calculating the** 
weighted linear combination of the d **input values to give (Bishop, 2006; Marwala, 2001):** 

$$a_{j}=\sum_{i=1}^{d}w_{j i}^{(1)}x_{i}+w_{j0}^{(1)}$$
$\eqref{eq:walpha}$. 
$$({\boldsymbol{8}})$$
 (7)
Here, )1( wji indicates weight in the first layer, going from input i to hidden unit j **while** 
)1( wj0 indicates the bias for the hidden unit j. The activation of the hidden unit j **is obtained** 
by transforming the output aj in equation 7 into zj**, as follows:** 
( ) j **inner** a j z = f **(8)** 
The f*inner* **function represents the activation function of the inner layer and functions such** 
as hyperbolic tangent function may be used (Bishop, 1996; Marwala, 201; Marwala, 