Image Processing Reference
neurons which send their output to the external environment.
The number of hidden neurons is determined by the following inequality (Chiang and
Braun, 2004; Hu, Lin, and Han, 2004).
N hn ≤ N ts ∗T e ∗N f
N f + N o
N hn is the number of hidden neurons, N ts is the number of training samples, T e is the
tolerance error, N f is the number of attributes, and N o is the number of the output.
The output of a rough neuron is a pair of upper and lower bounds, while the output of
a conventional neuron is a single value. Rough neuron was introduced in 1996 by Lingras
(Henry and Peters, 1996). It was defined relative to upper bound (U n ), lower bound (L n ),
and inputs were assessed relative to boundary values.
Rough neuron has three types of
Step 1. Input-Output connection to U n
Step 2. Input-Output connection to L n
Step 3. Connection between U n and L n
DEFINITION 5.1 (Rough neuron) A rough neuron R n is a pair of usual rough neurons
R n = (U n , L n ), where U n and L n are the upper rough neuron and the lower rough neuron,
Let (Ir L n , Or L n ) be the input/output of a lower rough neuron and (Ir U n , Or U n ) be the
input/output of an upper rough neuron. Calculation of the input/output of the lower/upper
rough neurons is given as follows:
Ir L n
w L nj On j
Ir U n
w U nj On j
Or L n
= min(f (Ir L n ), f (Ir U n ))
Or U n
= max(f (Ir L n ), f (Ir U n ))
The output of the rough neuron (O rn ) will be computed as follows:
Or U n −Or L n
avarge(Or U n , Or L n )
O rn =
The basic structure of rough neural network is given in (Aboul Ella and Dominik, 2006).
Classification error estimation and convergence is taken up in the backward runs of the
rough neural network. We estimate an error function for every neuron in a layer, the output
of which is propagated further based on inverse transfer function and weights on the links
(Sandeep and Rene, 2006; Aboul Ella and Dominik, 2006).
A rule importance measure R I was used as an evaluation to study the quality of the
generated rule. It is defined by:
R I =