Optical Character Recognition Using Automatically Generated Fuzzy Classifiers

tealackingΤεχνίτη Νοημοσύνη και Ρομποτική

8 Νοε 2013 (πριν από 3 χρόνια και 9 μήνες)

199 εμφανίσεις

Fonseca, Jose Manuel; Rodrigu
es, Nuno Miguel; Mora, Andre Damas; Ribeiro, Rita Almeida; , "Optical character recognition
using automatically generated Fuzzy classifiers,"
Fuzzy Systems and Knowledge Discovery (FSKD), 2011 Eighth International
Conference on

, vol.1, no., pp.448
-
452, 26
-
28 July 2011


Optical Character Recognition Using
Automatically
Generated
Fuzzy Classifiers


José Manuel Fonseca

Nuno Miguel Rodrigues

André Damas Mora

Rita Almeida Ribeiro

Departamento de Engenharia Electrotécnica

Faculdade de Ciências e Tecnologia da Universidade No
va de Lisboa

Lisbon, Portugal

Email: jmf@uninova.pt


Abstract



Character recognition using Fuzzy classifiers
has been
showing
very promising results. However, the definition of the
membership functions together with the design of the
classifi
cation rules

is a challenging task even considering just

the
10 digits
and 23 characters

of the Roman alphabet
. In this paper
we present a solution for
the semi
-
automatic design of a Fuzzy
classifier for letters and digits
to be applied on the automatic
recognition of

cars license plates on unstructured conditions.
Based on a training set of fuzzified examples
of measures
,

taken
from digital images of single characters,
the CART algorithm
learns the rules that regulate the design of the different
characters and generat
es fuzzy rules that implement the fuzzy
classifiers in a completely automatic way.
After,
a fuzzy inference
engine
executes the rules
to obtain the

characters classification.
T
o take advantage of syntactical correction, a

hierarchical
classifier with two l
ayers of classifiers

is proposed
: one classifier
distinguish
es between

letters
or
digits
;

the second

layer classif
ies

either the

letters
or the
digits.
T
he performance
achieved by
the
two
-
layer

classifier
is

shown and discussed.


Keywords:
Fuzzy Logic, Fuz
zy
Classifiers
, Image processing
,
Optical Character Recognition

I.


I
NTRODUCTION

Fuzzy Logic
is nowadays

a popular and successful solution
for a multitude of projects and applications in numerous fields
.

W
e can find

a
large number

of real applications in diff
erent
fields such as

embedded systems

[
2
]
, data clustering [3] or
image processing [4] among many others
.
There are also a
great number of commercial products available that take
advantage of Fuzzy techniques with thousands of patents
announced [1].
Despit
e
many

original theoretical papers on
fuzzy methods dealt with knowledge representation and
reasoning [
5
],
most

of the developed ap
plications have been in
control [
6
, 7
, 8
].

Optical character recognition
is

nowadays of common use
in many different
applicat
ions

from PDAs to license plate
recognition systems for traffic control.
Several papers
from

pattern and/or formula
-
related fuzzy
procedures
to fuzzy
applications developed to pre
-
classify, pos
-
classify, or
complement the classificati
on underdone by anothe
r method
[
9,
10]
.

A comparison between our proposal and other works
concerning Fuzzy Logic Optical Character Recognition (OCR)

[11, 12, 13]

reveals some similarities. The
classifier

used by
William Gowan [
14
] also deals with single
-
font characters, but
it
concerns only fourteen specific and exclusive characters. For
strictly fuzzy based recognition there is a good effort reported
in [
15
], which allows also multi
-
font, but it concerns only to
numerals, not to letters. In [
16
] there are similarities with this

project, although it concerns handwriting instead of font
characters and limited to a very small subset of characters. It
also
proposes

an automatic
solution

for generating the rules,
making the system simple and effective. Important work has
also been de
veloped on the area of fuzzy classification [
17, 18
]
but
usually
more focused on the creation of new algorithms for
induction of fuzzy decision trees than on the use of standard
algorithms such

as CART

[21]

for the generation of standard
fuzzy rules. Anoth
er interesting work is presented on [
9
]
where

the goal is focused on the automatic extraction of mathematical
formulas
rather
than on the recognition of the individual
characters.

II.

M
ETHODOLOGY

The goal of this work
is

to create a system
that
could
identify
single font characters based on their images captured
by
low cost

digital image cameras. These systems are useful on
a multitude of applications from automatic bank check
numbering to cars license plate recognition [
19
]. In this work
we
focus on
images con
taining single characters
, from an
historic set of standard license plates (2 letters, and 2 sets of 2
digits)
.

The license plate detection and

segmentation
are

out of
the scope of this paper.



Figure 1.

Example of single character images

taken from cars license p
lates
.

The initial idea was to build a fuzzy classifier that, based on
the asymmetries of the objects, could correctly identify the
characters. The first
image
-
processing

step is the binarization
of the image using the Otsu
method [
20
].

After the binariza
tion the images are normalized to a
standardized size (keeping their original proportions) in order
to make them comparable.

Th
ese

pure black & white images
are too complex to be directly classified

and some strategy was
required to reduce the complexity
of the classifier input
.

I
t was

then

decided to use the geographical distribution of the
Fonseca, Jose Manuel; Rodrigu
es, Nuno Miguel; Mora, Andre Damas; Ribeiro, Rita Almeida; , "Optical character recognition
using automatically generated Fuzzy classifiers,"
Fuzzy Systems and Knowledge Discovery (FSKD), 2011 Eighth International
Conference on

, vol.1, no., pp.448
-
452, 26
-
28 July 2011


characters and base the classification on
the

balance or
unbalance between the different sub
-
areas
of the

image.



Figure 2.

Example of th d
ivision of
two

binarized

characte
r
es

on the 16 sub
-
areas.

For classification proposes,
16 asymmetric sub
-
areas where
defined
(see
in
Figure 2

the digits 0 and 1
)
, corresponding to a
matrix of uneven size cells of 4*4
.
To ensure relative balance
we used 2 small horizontal and vertical
sub
-
areas

(where most
of the character is concentrated)
, surrounded by one larger area
in each side of the smaller areas

(double in size)
. With this
balanced approach and u
sing the
number
of
pixels in
each sub
-
area
,

it is possible to identify the characters us
ing simple
concepts

(i.e. metrics)

such as horizontal or vertical
balance
.

After several tests about the number of variables to use for
the characters classification it was concluded that eight
metrics

were necessary to achieve a good discrimination betwe
en all
the characters
: a) DVDM
-
vertical unbalance right
-
middle; b)
DVME
-

vertical unbalance left
-
middle; c) DVDE
-

vertical
unbalanced right
-
left; d) DVPCT


vertical unbalance borders
-
center; e) DHBC
-

horizontal unbalance bottom
-
up; f) DHMC
-

horizontal unb
alance top
-
center borders; g) DHPBC
-

horizontal
unbalance middle
-
top
-
middle
-
bottom; h) DHBM
-

horizontal
unbalance bottom
-
center.
If we use a simple
sequential number
for each
sub
-
area (
a
i
j

cell
)

of the asymmetric 4*4 matrix (1 to
16),

t
he above sub
-
areas are

depicted in Figure 3
:









Figure 3.

Calculation of the
membership values for the
eight

linguistic
variables
of
the Fuzzy Classifier.

After defining the metrics we moved to
the
definition of the
linguistic variables

[1]
, correspond
ing

to each metric
. We The
membership functions were determined experimentally
,
resulting in the

5 membership functions for each linguistic
variable

shown in Figure 4
.
The adjustment of the membership
functions was a

simple

interactive process that took g
reat
advantage of the autom
atic classifier of Fuzzy rules

used,

because we were allowed to change the membership functions
and immediately test their influence on the final classifier
by
automatically
generating new rules and testing the
ir

performance of t
he resulting classifier. F
ive membership
functions (VL
-
very low, L
-
low, M

me
dium, H
-
high and VH
-
very high) were

thus

adopted for all the
eight linguistic
variables expressing different levels of geometrical balance or
unbalance.

0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
0
1
1
DHBC
VL
L
M
H
VH

0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
0
1
1
DHEM
VL
L
M
H
VH

0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
0
1
1
DHPBC
VL
L
H
VH
M
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
0
1
1
DHMC
VL
L
M
H
VH

0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
0
1
1
DVDM
VL
L
M
H
VH

0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
0
1
1
VL
L
M
H
VH
DVME

0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
0
1
1
DVDE
VL
L
M
H
VH

1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0
1
1
DVPCT
VL
L
M
H
VH
9.0

Figure 4.

Membership
functions for the diferent variables.

In applications such as cars license plate recognition,
syntactical verification represents a useful correction tool that
sometimes improves significantly the final classifier
performance. In this type of applications
there are rules that
regulate how license plates are build that can be used to
improve the correctness of the classification. Imag
ine

for
example, that license plates are forme
d by three groups of two
letters, two groups of letters composed by digits and o
ne group
by letters. If the single digit classification identifies DD
-
LD
-
DD (where L means Letter and D means Digit) it is highly
probable that there is a mistake on the third digit that should
instead be a letter to get the combination DD
-
LL
-
DD. In order
15
14
11
10
7
6
3
2
16
12
8
4











DVDM
13
9
5
1
15
14
11
10
7
6
3
2











DVME
4
3
2
1
16
15
14
13







DHBC
12
11
10
9
8
7
6
5
16
15
14
13












DHBM
14
13
10
9
6
5
2
1
16
15
12
11
8
7
4
3















DVDE
4
3
2
1
12
11
10
9
8
7
6
5











DHMC
8
7
6
5
4
3
2
1
16
15
14
13
12
11
10
9















DHPBC
15
14
11
10
7
6
3
2
16
12
8
4
13
9
5
1















DVPCT
9
10
5
1
6
2
13
14
11
7
3
15
12
8
4
16
Fonseca, Jose Manuel; Rodrigu
es, Nuno Miguel; Mora, Andre Damas; Ribeiro, Rita Almeida; , "Optical character recognition
using automatically generated Fuzzy classifiers,"
Fuzzy Systems and Knowledge Discovery (FSKD), 2011 Eighth International
Conference on

, vol.1, no., pp.448
-
452, 26
-
28 July 2011


to allow this type of correction it was decided to build an
hierarchical classifier as shown on

Figure 5
.

Letter
/
Digit
classifier
Letter
classifier
Digit
classifier
A B C D E … Z
Digit
1 2 3 4 5 6 7 8 9 0
Letter

Figure 5.


Hierarchcal classifier

structure
.

With this classifier structure it is possible to correct wrong
classifications that violate the syntactical rules
. In cases such as
the one previously explained, there is a high probability of
wrong Letter/Digit decision by the first level classifier and it is
possible to force a better decision by imposing the syntactical
restrictions by changing the first level dec
ision. This approach
has the additional advantage of reduc
ing

the complexity of the
classifiers but the disadvantage of requiring several classifiers
(in this case three) instead of a single one. Note
that the first
classifier

has to deal with the 33 chara
cters but has a simple
yes/no decision
, while

the second level classifiers have 23 and
10 possible decisions instead of the initial 33. However,
the
design of the rules for
recognition of
th
is

number of

different
noisy symbols
,

based on their geometric bal
ance/unbalance
,

is
an

overwhelming task if taken without any aid from automatic
inference tools.

In fact, as the number of rules increases the
complexity of its verification becomes extremely hard
,

particularly

if we take into account the necessity of adju
stment
of the membership functions in order to make them enough
discriminative.

To
overcome

this pr
oblem we decided to use
CART [
21
]

tree induction software

for the rule generation
.
CART is a well
-

known recursive partitioning method that
builds classific
ation
and regression trees for predicting continuous dependent
variables (regression) and categorical predictor variables
(classification).

We used this software for automatic induction
of fuzzy rules based on a training set built from a set of
example cha
racters. In order to achieve this,
a
set of 23*15
alphabetic characters plus 10*15 numeric characters was used.
For fuzzy rule
-
based inference we selected the simple
Mamdani maxmin model

[2]
, where for
AND

we use

the
min

operator and for both
OR

and infer
ence scheme we use

the
max
operator
.

TABLE I.

E
XAMPLE OF CHARACTERS

MEASURES AND CORRESP
ONDENT
MEMBERSHIP

Character
1
4,03
VH
1,30
M
3,97
VH
0,70
L
0,91
L
0,68
L
1
3,77
VH
1,18
M
4,64
VH
0,71
L
0,95
L
0,66
VL
1
3,69
VH
1,36
M
4,27
VH
0,75
L
0,95
L
0,70
L
2
1,15
H
0,91
L
1,39
H
1,18
H
1,84
VH
0,65
L
DHMC
DVDE
DVDM
DVME
DHBC
DHBM

It can be easily checked
,

taking as example the first row of
Table I corresponding to character “1” and referring to the
membership functions presented on Fi
gure 4, that the value
DVDE=4,03 is a VH value, DVDM=1,30 is M and so forth.
Using the training set of 4
95 examples 495 seven component

vectors (the six variables values and the class that is the
original character) was built and used as input for the CART

induction of the Letter/D
igit classifier. A subset of these
examples

containing only the numeric characters was used for
the induction of the Digits classifier and the remaining
examples for the construction of the Letter classifier. The
resulting decisio
n tree for Digits classifier is presented on
Figure 6.

DVDE
1
DVME
DHBC
0
DVME
DVDE
DHMC
DVDE
DVDM
DHBC
4
2
3
9
6
5
8
7
VH
VL, L,M,H
L,M,H,VH
VL
L,M,H,VH
VL
H,VH
VL,L,M
M,H
VL,L
L,VH
M,H
H
L,M
VL,L,M,VH
H
M
L

Figure 6.

Numeric characters classifier tree.

Due
to their complexity, the decision trees for the three
classifiers are presented on the annex of this paper as tables for
better understanding.
Briefly inspecti
ng the decision tree
presented on Figure 6 we can analyze for example the
classification rule for character “1” and try to understand what
the induction algorithm automatically produced

based on
images such as those presented on Figure 2
. The classificatio
n
of a character as a “1” simply requires that the balance left
-
right (DVDE variable) is very high. It is quite understandable
once that, due to its geometry, the digit one is the most
unbalanced digit we can find since it gets all its “body” on the
right
with only a very small portion of it on the right side of the
image. Looking at the characterization of the character “
0
” we
can see that it requires DVDE

not VH and DVME very low. It
means that
the


0
” is
most unbalanced between the center and
the left ar
eas character we can find in the digits set
.

It must be
noted that all the system was developed in real
scenario conditions using pictures from license plates taken on
an unstructured environment with limited
resolution
. The noise
shown on Figure 7
is resu
lting from the binarization of the
images and has a natural influence on the behavior of the
algorithms. The unavoidable variation of all the measurements
that can be done on these scenarios was in fact the main
motivation for the adoption of fuzzy techniq
ues and the results
confirm their robustness to this kind of perturbations.

Fonseca, Jose Manuel; Rodrigu
es, Nuno Miguel; Mora, Andre Damas; Ribeiro, Rita Almeida; , "Optical character recognition
using automatically generated Fuzzy classifiers,"
Fuzzy Systems and Knowledge Discovery (FSKD), 2011 Eighth International
Conference on

, vol.1, no., pp.448
-
452, 26
-
28 July 2011


III.

R
ESULTS

The ultimate goal of this work was to produce a character
classifier that could achieve an acceptable accuracy on the
recognition of characters captured from real
-
world ima
ges
containing considerable levels of noise and the typical
distortion introduced by low cost image acquisition systems
such as consumer SLR cameras.

In order to develop the system, 200 digit images (20 of each
digit) and 345 letters images (15 of each let
ter) were collected.
In order to achieve a fair evaluation of the resulting classifier
performance, the image sets were divided on training and test
set with10 images of each character on the training set and the
remaining images on the test set.

Using thi
s data, the results achieved by the classifier are
presented on Table
II
.

TABLE II.

R
ESULTS OBTAINED BY T
HE FUZZY CLASSIFIER

Total
number
Correctly
classified
Sucess rate
Letter/Digit classifier
150
150
100,0%
Letter classifier
230
230
100,0%
Digit classifier
380
379
99,7%
Trainning set

Total
number
Correctly
classified
Sucess rate
Letter/Digit classifier
50
49
98,0%
Letter classifier
115
113
98,3%
Digit classifier
165
160
97,0%
Test set

As it can be seen on Table II, the classification performance
with the training set is very close to 100% correctness.
However, this valu
e clearly optimistic and with reduced
significance.
T
he
results obtained with the test set are also very
good with the lowest score of 97% correctness obtained on the
classification of digits. It is important to remember that all the
tests were done using
images taken on an unstructured
environment using a low cost camera.

IV.

C
ONCLUSIONS

T
he methodology adopted for the automatic generation of
fuzzy rules shown to be adequate producing understandable
and effective rules for a complex problem such as optical
ch
aracter recognition of 33 different characters. The
performance of the resulting classifier was very acceptable and
demonstrat
ed

the correctness of the automatically generated
rules. This methodology also facilitates considerably the tuning
of the membersh
ip functions by allowing a straightforward test
of their influence on the resulting classifier once that after any
change on the membership functions it is possible to generate
new rules and test their effectiveness without any human
intervention.
Moreover
,

the

methodology presented in this
paper is easily transposed to other fields of application
,

where
the design of Fuzzy rules is complex, which often limits
its
applicability
.

Following this work, we plan to
devise ways to automate the
construction of fuz
zy sets and fuzzy rules, by using specialized
learning and optimization algorithms (e.g. neural networks),
thus improving the robustness
and autonomy
of the approach
.

R
EFERENCES

[1]

Zimmerman, H. J. “Fuzzy set theory and its applications”,
Kluwer
Academic Pub
lishers
, 2001.

[2]

Ibrahim, A. H. “Fuzzy Logic for Embedded Systems Applications”,
Elsevier, 2004.

[3]

Oliveira, J. V. and Pedrycz (Eds) “Advances in Fuzzy Clustering and its
Applications”, Wiley, 2007.

[4]

Krishnan

M. H. and
Viswanathan
, R.

“Applications of Advanced
Fuzzy
Logic Techniques in Fuzzy Image”, Processing SchemeAdvances in
Fuzzy Mathematics, ISSN 0973
-
533X Volume 5, Number 1 (2010), pp.
71

76.

[5]

Zadeh L.A.; Fuzzy
S
ets,
Information and Control, 8(3), pp. 338
-
353.

[6]

Passino, K. M. and
Yurkovich
, S. “Fuzzy Control
”, Addison
-
Wesley,
1998
.

[7]

Sugeno

M.
. 1985. Industrial Applications of Fuzzy Control. Elsevier
Science Inc., New York, NY, USA.

[8]

Kosko, B. and Isaka S. “Fuzzy Logic”, Scientific American, July 1993,
pp. 76
-
81.


[9]

Kacem

A., Belaïd A., Ben Ahmed

M. “
Automatic ext
raction of printed
mathematical formulas using fuzzy logic and propagation of context
”.
International Journal on Document Analysis and Recognition, Volume 4,
Number 2, 97
-
108.

[10]

N. M. Noor, M. Razaz, P. Manley
-
Cooke, "Global Geometry Extraction
for Fuzzy Log
ic Based Handwritten Character Recognition," Pattern
Recognition, International Conference on, pp. 513
-
516, 17th
International Conference on Pattern Recogni
tion (ICPR'04)
-

Volume 2,
2004

[11]

zbay, E. en o lu, M.T
, “
Load frequency control for small hydro
power plants using adaptive fuzzy controller
”,
2010 IEEE International
Conference on Systems Man and Cybernetics (SMC),

10
-
13 October
2010, Istanbul, Turkey.

[12]

Fitzgerald

J. A.
, Geiselbrec
htinger

F.
, Kechadi

T.
.Application of Fuzzy
Logic to Online Recognition of Handwritten Symbols. In Proceedings of
the Ninth International Workshop on Frontiers in Handwriting
Recognition (IWFHR '04). IEEE Computer Society
, Washington, DC,
USA, 395
-
400.

[13]

Sur
esh R. M., Arumugam S. “Fuzzy Technique Based Recognition of
Handwritten Characters”

Fuzzy Logic and Applications. Lecture Notes
in Computer Science, 2006, Volume 2955/2006, 297
-
308

[14]

Gowan
W.

A.,

Optical Character Recognition Using Fuzzy Logic

,
Microproce
ssors and Microsystems, Elsevier, Volume 19, Issue 7,
September 1995, Pages 423
-
434.

[15]

Madasu V. K., Hanmandlu M., Yusof M. “
Fuzzy Based Approach to the
Recognition of Multi
-
Font Numerals
”,
Proceedings of the Second
National Conference on Document Analysis a
nd Recognition
,
Mandya,
India
,
11
-
12 July, 2003
, 118
-
126.

[16]

Marsala, C. “
Application of Fuzzy Rule Induction to Data Mining
”.
Springer.

Proceedings of the 3rd Int, Conf, FQAS'98 pp.
260

271
.

[17]

Hühn

J. and
Hüllermeier

E.

´”FURIA: an algorithm for unordered fuzz
y
rule induction”. Springer.
Data Min
ing

and
Knowl
edge

Disc
overy

(2009) 19:293

319
.

[18]

Ranawana

R.
, Palade

V.,
Bandara

. “
An Efficient Fuzzy Method for
Handwritten Character Recognition
”. Knowledge
-
Based Intelligent
Information and Engineering Systems. Lectu
re Notes in Computer
Science, 2004, Volume 3214/2004, 698
-
707.

[19]

Barroso

P., Amaral

J., Mora

A., Fonseca

J., Steiger
-
ar ão A. “A
Quadtree Based Vehicles Recognition System”. 4th International
Conference on Optics, Photonics, Lasers and Imaging (ICOPLI 2004)
,
14
-
16 January 2004, Taiwan, January.

Fonseca, Jose Manuel; Rodrigu
es, Nuno Miguel; Mora, Andre Damas; Ribeiro, Rita Almeida; , "Optical character recognition
using automatically generated Fuzzy classifiers,"
Fuzzy Systems and Knowledge Discovery (FSKD), 2011 Eighth International
Conference on

, vol.1, no., pp.448
-
452, 26
-
28 July 2011


[20]

Otsu

N.

"A threshold selection method from gray
-
level histograms".
1979.
IEEE Trans. Sys., Man., Cyber. 9 (1): 62

66
.

[21]

Breiman, L, Friedman, J., Olshen. R., & Stone, C. (1984).
"Classification and Regression Trees", Wa
dsworth.



Fonseca, Jose Manuel; Rodrigu
es, Nuno Miguel; Mora, Andre Damas; Ribeiro, Rita Almeida; , "Optical character recognition
using automatically generated Fuzzy classifiers,"
Fuzzy Systems and Knowledge Discovery (FSKD), 2011 Eighth International
Conference on

, vol.1, no., pp.448
-
452, 26
-
28 July 2011


Annex


Fuzzy rules for character classification

TABLE I.

L
ETTER
/D
IGIT CLASSIFICATION
RULES

VL
L
M
H
VH
VL
L
M
H
VH
VL
L
M
H
VH
VL
L
M
H
VH
VL
L
M
H
VH
VL
L
M
H
VH
VL
L
M
H
VH
VL
L
M
H
VH
Rule 1







Digit
Rule 2







Digit
Rule 3











Digit
Rule 4

















Digit
Rule 5














Letter
Rule 6












Letter
Rule 7








Digit
Rule 8







Letter
Rule 9











Letter
Rule 10







Letter
Rule 11






Letter
Rule 12









Digit
Rule 13









Letter
Rule 14















Digit
Rule 15












Digit
Rule 16













Letter
Rule 17










Digit
Rule 18












Digit
Rule 19










Letter
Rule 20













Letter
Rule 21









Letter
DHPBC
Class
DVPCT
DVDE
DVDM
DVME
DHBC
DHBM
DHMC

TABLE II.

D
IGIT CLASSIFICATION
RULES

VL
L
M
H
VH
VL
L
M
H
VH
VL
L
M
H
VH
VL
L
M
H
VH
VL
L
M
H
VH
Rule 1






0
Rule 2

1
Rule 3









2
Rule 4












3
Rule 5









4
Rule 6







5
Rule 7











6
Rule 8








7
Rule 9







8
Rule 10




9
Class
DVDE
DVDM
DVME
DHBC
DHMC

TABLE III.

L
ETTER CLASSIFICATION

RULES

VL
L
M
H
VH
VL
L
M
H
VH
VL
L
M
H
VH
VL
L
M
H
VH
VL
L
M
H
VH
VL
L
M
H
VH
VL
L
M
H
VH
Rule 1












A
Rule 2












B
Rule 3














C
Rule 4












D
Rule 5






E
Rule 6






F
Rule 7
















G
Rule 8












H
Rule 9




















I
Rule 10

J
Rule 11











K
Rule 12
















L
Rule 13












M
Rule 14













N
Rule 15











O
Rule 16













P
Rule 17













Q
Rule 18










R
Rule 19







S
Rule 20













T
Rule 21
















U
Rule 22













V
Rule 23










Z
DHPBC
Class
DVDE
DVDM
DVME
DHBC
DHBM
DHMC


For all the tables the meaning of the abbreviations is: VL


Very Low, L


Low, M

Medium, H


Hig
h and VH


Very High

Taken the first rule (Rule 1) from Table 1 as an example, the tables are to be interpreted as:

Fonseca, Jose Manuel; Rodrigu
es, Nuno Miguel; Mora, Andre Damas; Ribeiro, Rita Almeida; , "Optical character recognition
using automatically generated Fuzzy classifiers,"
Fuzzy Systems and Knowledge Discovery (FSKD), 2011 Eighth International
Conference on

, vol.1, no., pp.448
-
452, 26
-
28 July 2011


If (DHBM=Low or High) and (DHMC=VL or L or VH) and (DVPTC=Low or High) then Classification=Digit