The upper approximation is defined as the collection of cases whose equivalence classes are at least partially contained in the set of cases we want to approximate. The upper approximation of set X is denoted BX **and is mathematically represented as:** 
BX = {x ∈U : B(x) ∩ X = **Ø} (4)** 
It is through these lower and upper approximations that any rough set is defined. Lower and upper approximations are defined differently in the literature, but it follows that a crisp set is only defined for BX = BX **. It must be noted that for most cases in RST,** 
reducts are generated to enable us to discard functionally redundant information (Pawlak, 1991). 

## Rough Membership Function

The rough membership function is described; : X η A
 U→ **[0, 1] that, when applied to object** 
x, quantifies the degree of relative overlap between the set X **and the indiscernibility set to** 
which x **belongs. This membership function is a measure of the plausibility of which an** 
object x belongs to set X**. This membership function is defined as:** 

$$\eta_{A}^{x}={\frac{\left|[X]_{B}\cap X\right|}{\left[X\right]_{B}}}$$
η = **(5)** 
$$\quad(5)$$

## Rough Set Accuracy

The accuracy of rough sets provides a measure of how closely the rough set is approximating the target set. It is defined as the ratio of the number of objects which can be positively placed in X to the number of objects that can be possibly be placed in X**. In** other words it is defined as the number of cases in the lower approximation, divided by 