J. Biomedical Science and Engineering, 2009, 2, 359-362
doi: 10.4236/jbise.2009.25051 Published Online September 2009 (http://www.SciRP.org/journal/jbise/
Published Online September 2009 in SciRes. http://www.scirp.org/journal/jbise
Applications of fuzzy similarity index method in
processing of hypnosis
Soroor Behbahani1, Ali Motie Nasrabadi2
1Biomedical Engineering Department, Islamic Azad University, Science and Research Branch, Tehran, Iran; 2Biomedical Engineering
Department, Faculty of Engineering, Shahed University, Tehran, Iran.
Email: 1Soroor_Behbahani@yahoo.com; 2nasrabadi@shahed.ac.ir
Received 1 June 2009; revised 10 July 2009; accepted 12 July 2009.
The brain is a highly complex system. Under-
standing the behavior and dynamics of billions
of interconnected neurons from the brain signal
requires knowledge of several signal- process-
ing techniques, from the linear and non-linear
domains. The analysis of EEG signals plays an
important role in a wide range of applications,
such as psychotropic drug research, sleep
studies, seizure detection and hypnosis proc-
essing. In this paper we accomplish to analyze
and explore the nature of hypnosis in Right, Left,
Back and Frontal hemisphere in 3 groups of
hypnotizable subjects by means of Fuzzy Simi-
larity Index method.
Keywords: Fuzzy Similarity Index; Hypnosis; Left-
Right; Frontal-Back Hemisphere; Higuchi; Entropy;
Energy; Frequency Band
The analysis of EEG signals plays an important role in a
wide range of applications, such as psychotropic drug
research, sleep studies, seizure detection and hypnosis
processing. Still it is unclear that what happens in the
brain during hypnosis. Changes in different EEG fre-
quencies have already been reported in association with
hypnosis; however, it is difficult to compare different
studies with each other because of methodological dif-
ferences as well as different criteria when selecting sub-
jects for experiments. EEG during pure hypnosis would
differ from the normal non hypnotic EEG [1].
Various EEG analysis methods have been proposed in
the literature, and some of these methods achieved good
results in specific applications [2].
Today’s Fuzzy theory is one of principal method of
researches. A number of basic concepts and methods
already introduced in the early stages of the theory have
become standard in the application of fuzzy-theoretic
tools to medical artificial intelligence subjects [3].
The notion of similarity involves an elaborate cogni-
tive whenever the assessment of similarity should re-
produce the judgment of a human observer based on
qualitative features, it is appropriate to model it as a
cognitive process that simulates human similarity per-
Among the various knowledge representation formal-
isms that have been proposed as ways of reasoning in the
presence of uncertainty and imperfect knowledge, a
situation typical to the human cognitive processes, fuzzy
logic has very important features because:
• Fuzzy set theory has been proved a plausible tool for
modeling and mimicking cognitive processes, especially
those concerning recognition aspects, and
• Fuzzy set theory is able to handle qualitative no nu-
merical descriptions, approximate class memberships
and possibility reasoning [4,5].
In this study we propose to explore the nature of hyp-
nosis in Right, Left, Back and Frontal hemisphere in 3
groups of hypnotizable subjects by means of Fuzzy
Similarity Index method.
To identify the change state of a system, one of the sim-
plest methods is to compare the feature sets of the pre-
sent state and ones of the previous states. If the both
states are very similar, then it means that the feature sets
does not show a large change. After the feature extrac-
tion process, a fuzzy membership function can be used
to transfer the present and previous features as two fuzzy
sets. The parameters of the fuzzy membership function
can be determined by the features. Fuzzy sets can be
obtained from the feature sets of the signals under study
by repeating the fuzziness process. Suppose two fuzzy
sets A and B and each set includes N features
, a reliable and simple method can be used to
compute the similarity between the two fuzzy sets, A and
B as follows:
xxx ,...,, 21
360 S. Behbahani et al. / J. Biomedical Science and Engineering 2 (2009) 359-362
SciRes Copyright © 2009 JBiSE
where )()(1 iBiA xx
 can be regarded as the simi-
larity degree of fuzzy sets A and B on the features xi. S
(A, B) is the average of the similarity degree of fuzzy
sets A and B, called fuzzy similarity index. The range of
is from 0 to 1, which corresponds to the dif-
ferent similarity degree. , means the two
signals are identical; otherwise there exist a difference
between the two signals [5].
),( BAS
1),( BAS
Decision making is performing in two stages: feature
extraction by computing the entropy and energy of each
signal and computing fuzzy similarity index of feature
sets between the reference EEG signals and the other
classes of EEG signals.
2.1. Experimental Data
EEG data used in this study was collected by Ali Moti
Nasrabadi [6]. The data collected from 32 Right hand
subjects, 4 low (below 20 at Stanford scale), 16 medium
(between 20-40) and 12 subjects were high (more than
40) hypnotizable. EEG signals are obtained from sub-
jects using 19 electrodes placed at fp2,fp1,f8,f4, fz,f3,f7,
t4,c4,cz,c3,t3,t6,p4,pz,p3,t5,o2,o1 locations. The elec-
trodes are positioned as per the international 10 -20 sys-
tem illustrated in Figure 1 [7].
The sampling frequency was 256 Hz. To explore the
relation of hypnotizability and similarity of Right–Left
and Frontal-Back hemispheres during the hypnosis
process between the 3 groups of hypnotizable subjects,
16 and 14 channels of electrodes placed at the fp2,fp1,f8,
f4,f3,f7,t4,c4,c3,t3,t6,p4,p3,t5,o2,o1(Right-Left) and fp1,
fp2, f3, f4, fz, pz, p3, p4, f8, f7, t6, t5, o1, o2 (Fron-
tal-Back) locations was chosen respectively.
In this experiment a simple algorithm is used to extract
the features from the EEG signals. Although Similarity
Figure 1. Electrode positions for data
collection (10-20 standard).
Index method is usually perform with two features (en-
ergy, entropy) we decided to find the best features which
could discriminate 3 groups of hypnotizability in Left-
Right and Frontal-Back hemispheres during hypnosis.
We performed the similarity index method wit 3 kinds
of features, at first exam we use the usual features, en-
ergy and entropy, at second we use the entropy, Higuchi
fractal dimension and at third, entropy, Higuchi and fre-
quency band features were used.
3.1. Entropy
An entropy measure (Shannon’s entropy) can be calcu-
lated directly from the EEG data samples by examining
the probability distribution of the amplitudes of the data
 (2)
is the number of bin that the amplitudes of
the EEG are partitioned into and is the probability
associated with the bin.
3.2. Fractal Dimension
Fractal dimension can be used as a feature to show the
complexity and self similarity of the signal. It has a rela-
tion with entropy, and entropy has a direct relationship
with the amount of information inside a signal. Fractal
dimension can be interpreted simply as the degree me-
andering (or roughness or irregularity) of a signal.
Consider be the time sequence to
be analyzed. Construct new time
series as
)(),...,2(),1( Nxxx
)(),...,2( Nxx
kkmN /)mxkmx ((),...,( mxxk
km ,..,2,1
where indicates the initial time value,
indicates the discrete time interval
between points(delay) and means integer part of a.
for each of curves or time series constructed, the
average length is computed as
)( kLm
),...,2(),1( xx
where is the length of time sequence and
/) is a normalize factor. To-
tal average length is computed for all time series
having the same delay but different as:
)()( (4)
This procedure is repeated for each ranging from
S. Behbahani et al. / J. Biomedical Science and Engineering 2 (2009) 359-362 361
SciRes Copyright © 2009
1 to. The total average length for delay , is
proportional to where D is fractal dimension by
Higuchi’s method [8].
kk)( kL
EEG contains different specific frequency components,
which carry the discriminative information. Normally,
most waves in the EEG can be classified as alpha, beta,
theta and delta waves. The definition of the boundaries
between the bands is somewhat arbitrary, however, in
most of applications these are defined as; delta (less than
4 Hz), theta (4-8 Hz), alpha (8-13 Hz) and beta (13-30
Hz). When the awake person’s attention is directed to
some specific type of mental activity, the alpha waves
are replaced by asynchronous, higher frequency beta
waves. Beta waves occur at frequencies greater than 13
Hz. Theta waves have frequencies between 4 and 8 Hz.
They occur normally in parietal and temporal regions in
children, but they also occur during emotional stress in
some adults. Theta waves also occur in many brain dis-
orders, often in degenerative brain states. Delta waves
include all the waves of the EEG with frequencies less
than 4 Hz, and they occur in very deep sleep, in infancy
and in serious organic brain disease. Therefore, EEG
contains different specific frequency components, which
carry the discriminative information [5].
3.3. Frequency Band
In order to reveal any statistically significant differences
between any two conditions, the ANOVA method was
used separately for each type. Statistical significance
was assumed where (only statistically sig-
nificant values are displayed).
In this research we compare the similarity between hypno-
sis in Left-Right and Frontal-Back hemisphere separately
like previous steps and gathered the obtained results.
Furthermore, we evaluated the ability of FSI to dis-
criminate 3 groups of hypnotizability by means of re-
ceiver operating characteristic (ROC) curves. ROC
curve is a graphical representation of the trade-offs be-
tween sensitivity and specificity. Accuracy quantifies the
total number of subjects precisely classified. The area
under the ROC curve is a single number summarizing
the performance. ROC indicates the probability to pre-
dict the hypnosis scale of a randomly selected hypnotiz-
able subject. Although the set of entropy, Higuchi and
frequency band (low and high) could discriminate C3 &
C4 channels in Left-Right hemisphere, ROC curve value
has the acceptable value for discrimination (0.753), and
similar to this result in Frontal-Back hemispheres only
F8 & T6 (0.721) with energy and entropy features has
the acceptable ROC curve value, so there should be a
trade off between features set, ANOVA and ROC curve
Figure 2 represents the ROC curves obtained at
Left-Right and Frontal-Back hemispheres with highest
discrimination. The highest ROC (0.753 for Left-Right
and 0.721 for Frontal-Back hemispheres) values were
achieved in C3 & C4 and F8 & T6 channels respectively.
Table 1 and Table 2 shows the features, discriminated
channels, p and ROC value for Left-Right and Frontal-
Back hemisphere respectively.
The differences between three groups were statistically
significant in 19 channels (p < 0.05; ANOVA). Our re-
sults agree with previous studies that have analyzed
electromagnetic brain recordings with different features.
Significant differences were found between the Fron-
tal-Back and Left-Right hemispheres in medium hypno
Figure 2. Roc curves showing the discrimination between Left-Right and Frontal-Back
hemispheres and hypnotizability scale: (a) Left-Right hemisphere (Medium hypnotizability),
(b) Frontal-Back hemispheres (medium hypnotizability).
362 S. Behbahani et al. / J. Biomedical Science and Engineering 2 (2009) 359-362
SciRes Copyright © 2009 JBiSE
Table 1. The features, discriminated channels, p and ROC values for Left-Right Hemispheres.
Features Discriminate channels sig.<0.05 ROC
Energy, Entropy non non non
Entropy, Higuchi non non non
Energy, Entropy, Frequency Band(low) C3&C4 0.011 0.753
Energy, Entropy, Frequency Band(high) C3&C4 0.043 0.518
Energy, Entropy, Frequency Band(low & high) non non non
Table 2. The features, discriminated channels, p and ROC values for Frontal-Back Hemispheres.
Features Discriminate channels sig.<0.05 ROC
Energy, Entropy F8&T6 0.042 0.721
Entropy, Higuchi PZ&FZ 0.036 0.389
Energy, Entropy, Frequency Band(low) non non non
Energy, Entropy, Frequency Band(high) P4&F4-T5&F7 0.016-0.006 0.198-0.389
Energy, Entropy, Frequency Band(low & high) PZ&FZ 0.031 0.555
tizable subjects. The discriminated channels were ana-
lyzed by means of a ROC curve. The highest ROC
(0.753 for Left-Right and 0.721 for Frontal-Back hemi-
spheres) values were achieved in C3 & C4 and F8 & T6
channels respectively.
[1] Fingelkurts, A. A., Kallio, S., and Revonsuo, A. (2007)
Hypnosis induces a changed composition of brain oscil-
lations in EEG. Contemp. Hypnosis, 24(1), 3–18.
[2] Xu, W., Guan, C., Siong, C. E., Ranganatha, S., Thulasi-
das, M. and Wu, J., (2004) High accuracy classification
of EEG signal, Intl. Conference on Pattern Recognition,
[3] Andrzejak, R. G., Lehnertz, K., Mormann, F., Rieke, C.,
David, P., and Elger, C. E., (2001) Indications of nonlin-
ear deterministic and finite-dimensional structures in
time series of brain electrical activity: Dependence on
recording region and brain state. Phys Rev E, 64,
[4] Binaghi, E., Ventura, A. D., Rampini, A., and Schettini, R.
(1993) Fuzzy reasoning approach to similarity evaluation
in image analysis. International Journal of Intelligent
Systems, 8, 749-769.
[5] Tolias, Y. A., Panas, S. M., and Tsoukalas, L. H., (2001)
Generalized fuzzy indices for similarity matching, Fuzzy
Sets and Systems, 120(2), 255-270.
[6] Ali Moti Nasrabadi.
[7] Domenick, D. G. (1998) International 10-20 electrode
placement system for sleep.
[8] Sabeti, a M., Boostani, a R., Katebi, a S. D., and Price, G. W.
(2007) Selection of relevant features for EEG signals classi-
fication of schizophrenic patients. 10.1016/j.bspc.03.003.
[9] Übeyli, E. D. Fuzzy similarity index for discrimination of
EEG signals. EMBS Annual.
[10] Gómez, C., et al. (2008) Use of the Higuchi’s fractal
dimension for the analysis of MEG recordings from Alz-
heimer’s disease patients. Med Eng Phys, doi:10.1016/j.
[11] Stam, C. J. (2005) Nonlinear dynamical analysis of EEG
and MEG: Review of an emerging field. Clin Neuro-
physiol, 116, 2266–301.
[12] Accardo, A., Affinito, M., Carrozzi, M., and Bouquet, F.
( 1997) Use of fractal dimension for the analysis of elec-
troencephalographic time series. Biol Cybern, 77,
[13] Kwang, H. L., Song, Y.-S., and Lee, K.-M. (1994) Simi-
larity measure between fuzzy sets and between elements,
Fuzzy Sets and Systems, 62(3), 291–293.