ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS’’, Bangkok, May 23-25, 2001 
138 
In Eq.6, (jc) stands for the reference value or actual value 
of affiliation degree of pixel X to class l. 
The cross-entropy value indicates the difference between 
the fuzzy classification result and supposed actual fuzzy 
classification result. So the higher the cross-entropy value is, the 
lower the classification precision is, which may be explained the 
same way as the distance value. 
We take the Bayesian classifier as an example. In the 
routine training, the data analysis need gather enough, 
reasonably distributed and representative objects in order to 
calculate the spectral feature values of the various selective 
classes. The fully fuzzy classification requires that it could 
involve the fuzzy characteristics in the process of training, that is 
to say, it could deal with a group of training samples described in 
fuzzy form. 
THE NEURAL NETWORK REALIZATION OF FULLY FUZZY 
SUPERVISED CLASSIFICATION 
The neural network (NN) has been a big hit in recent 
studies. It can be simply regarded as a complicated function 
equation transforming the import to output. Its solution can be 
calculated by means of learning and generalizing some samples. 
Once it is definite after learning, it can be used to calculate the 
unrecognized objects and finally recognize them. 
As far as the structure is concerned, a NN is a multi-layer 
system made up of several mutually linked nodes. Every link 
corresponds to a function equation and every node is a process 
unit corresponding to the import with weight from other nodes. A 
typical NN structure is shown in Fig. 1. 
Fig. 1. The structure of a multi-layer NN 
The nodes in the import layer correspond to all the 
elements of object’s eigenvectors, such as the radiation values 
of all bands in the remote sensing multi-spectral image. The hide 
layer receives the signals from the import layer. The nodes in the 
export layer correspond to all the elements of output vectors. As 
for processing the image classification, the nodes in the export 
layer correspond to every category of a classification system for 
the number of the nodes is equal to the whole categories. 
In a NN, a node receiving signals from the anterior linked 
nodes sums them up with their weights. And it is processed by a 
response function as follows. 
netj = Yj Mji 0 , ’ °j = f( net j) (Eq- 7 ) 
In Eq.7, CO- stands for the weight of the link from node / to 
j . Oj is the import from node i and O ■ is the export of 
node j . The function f is generally a nonlinear response 
function. 
The principal procedure of the BP net is as follows. The 
training samples are respectively provided for the net, Eq.7 used 
for forward propagation. The export of the net is compared to the 
their actual values. At the same time, the errors are propagated 
backward. The weights of the corresponding links are rectified 
according to the following equation. 
Aco- (n + \) = rj(S J O i ) + aAco jt (n) (8) 
In Eq.8, n + 1, n stand for the present and former rectification 
to weights respectively. 7/ is the value of learning speed. 8 ■ 
is the variation speed index of errors. (X is the momentum 
parameter. The processes of transferring signals forward and 
propagating errors backward are repeated and iterated until the 
whole error of the net decreases to the minimum or an allowed 
value. 
The export from all the nodes in the net export layer is 
called activation level, which is equal to or between 0 and 1. It is 
natural to make the activation level become the fairy ideal direct 
or indirect candidate for fuzzy number. Moreover, the NN can be 
expanded to the fuzzy classifier. 
During the training of the net, some known samples or 
examples correspond to its export layer. Since the export of the 
net is originally fuzzy numbers, the training samples may also be 
fuzzy. That is to say, the fuzzy characteristics can be involved in 
the training. Actually, the samples in non-fuzzy form that are 0 or 
1 are a typical example of fuzzy samples. This feature makes 
the fuzzy training fit for all the training samples in various forms