A Simple Method to Extract Fuzzy Rules by Measure
implement the fuzzy rules system.
First, we extract fuzzy rules from different class
region which was named as
Second, when the activation hyper
overlapped, a recursive process are applied to
additive activation hyper
in these uncertainty
Third, the stop criterion for the recursive process
by measure of fuzziness.
Relation between activation hyper
overlap regions by 2
Measure of fuzziness for a fuzzy set.
Measure of fuzziness of a fuzzy rule in a fuzzy
Compare our method with other methods.
To extract more efficiently fuzzy rules from
numerical information data in classification
To save computation cost
To get available rules and cancel redundant
Human can always collect the knowledge to
discriminate the uncertainty or ambiguous
data by their experience.
But computer still can’t be dealt perfectly in
So, many methods are still proposed to
improve the performance of classification
The methods of classification problem are
divided into four groups:
1) Statistical method:
It is not practical in solving classification
problem in a real world.
2) Neural network:
It is a system that is constructed to make
use of some organizational principles like
human brain. It is good for many application.
3)Fuzzy inference engine:
By querying experts’ experience or other
techniques directly from training data to build
fuzzy rule database.
It combines the fuzzy inference and neural
network theory to computer
Hong and Lee
, proposed a method based on
the fuzzy clustering technique to setup the
. But they need to determine
the scaling it usually takes
Hong and Chen
, they propose the other
method to decrease the computation time,
but it still
generates many rules
much computation process
, when the training
Wu and Chen
have a fuzzy learning algorithm
base on the
induce the fuzzy rule
and reaches a
higher average classification
. But we don
t know how to
setup the fuzzy rules by an
contraction, it usually generated
too many hyper
box that mean
rules to be concerned
S. Abe and M
extract the fuzzy rules
by resolving overlaps, it can
. But there some
in following points:
1)It needs more computation time to resolve
overlaps when the data include many classes.
2)It can’t be resolved in some critical
3)It generate many meaningless fuzzy rules
as the data are chaos.
Our propose is to decrease the computation
time and to extract more efficient fuzzy rule,
the method is described in the following steps:
1)Find the activation hyper
2)Find uncertainty overlap.
3)Extracts fuzzy rules .
4)Construct an easy and efficient neural
network by measure of fuzziness.
Measure of Fuzziness of a Fuzzy
To measure uncertainty of vagueness .
Measure of fuzziness is a function
satisfies the following axioms:
(A)=0 if only if A is a crisp set.
: If A B, then
A B denotes that A is shaper than B.
(A) assumes the maximum
value if and only if A is maximally fuzzy
Degree of fuzziness of fuzzy
Normalized measure of
Measure of Fuzziness of a Fuzzy
Rule in a Fuzzy System
In this section, we define a classification system by a
sequence of multi
output fuzzy rules as
n is the number of attribute of the classification
c is the number of class of the system
is the linguistic label, i=1,2,…n,
can be rewrote by the T
norm operator with min
operation in the following:
The membership value of this rule R
We can define the measure of fuzziness of the
in the fuzzy rule system as:
According to the formula (3)
We can decide the rule R
is worth to exist in
based system or not necessary.
If the rule have high measure of fuzziness of
a rule, it means too much uncertain for this
Neural Network Structure
A variable structure
We will leave the rule which is very efficient
and useful, so the number of nodes in the
second layer are variable.
We will reduce the cost, because the
redundant second layer nodes are eliminated.
Second layer includes two Sub
the first sub layer is configured by the hyper
box nodes which are created from our
the second sub
layer is a maximum
node, which takes the maximum values of
inputs from the first sub
Step1: set level = 1.
Step2: Set up the hyper
membership function for each class.
Step3: Find the overlap among the activation
boxes of level l ,then l=l+1.
Step4:Extract activation hyper
boxes and set
up feature as in step 1.
Step5:Calculate the measure of fuzziness for
each extracted fuzzy rule. If it is bigger than
threshold, we discard this rule.
Step6:If none of hyper
box exist in Step 4,
then stop the process, else go to Step 2.
Step7:Build up the fuzzy
structure by these extracted fuzzy rules
We use Fisher’s iris data, there are three
kinds of flowers, four kinds of attributes.
Setosa Versicolor Verginica
Sepal length Sepal width Petal length Petal
Original Iris Data
Randomly generated area
By this proposed method, we can find more efficient
It generates fewer fuzzy rules than other methods
It avoids a huge matrix computation  so its
computation time decreases.
It provides a simple recursive process and stopping
criteria to extract the fuzzy rules in the uncertainty
overlap region. Thus, the network structure is simple
and easy to implement.
The classifier can be generated even for a large
scale of data pattern.