The Study of Symptoms of Tuberculosis Using Induced Fuzzy Coginitive Maps (IFCMS)

Integrated Intelligent Research (IIR) International Journal of Data Mining Techniques and Applications
Volume: 02 Issue: 02 December 2013 Page No.51-54
ISSN: 2278-2419
51
The Study of Symptoms of Tuberculosis Using
Induced Fuzzy Coginitive Maps (IFCMS)
K. Ponnivalavan , P. Pathinathan
Department of Mathematics, Loyola College, Chennai, India.
Abstract- Tuberculosis or TB is a common, infectious disease
caused by various strains of mycobacterium usually called as
mycobacterium Tuberculosis. Tb attacks the lungs but can also
affect other parts of the body. Most infections are
asymptomatic and latent, but about one in ten latent infections
eventually progresses to active disease which, if left untreated,
kills more than 50% of those so infected. Hence, this paper
analysisthes y m p t o m s o f Tuberculosis using Induced
Fuzzy Cognitive Maps (IFCMs). IFCMs area fuzzy-graph
modeling approach based on expert’s opinion. This is the non-
statistical approach to study the problems with imprecise
information.
Keywords - Induced fuzzy Cognitive Maps
(IFCMS),Tuberculosis, symptoms.
I. INTRODUCTION
Tuberculosis is a common and an infectious disease which is
caused by bacteria called "Mycobacterium tuberculosis". It was
first isolated in 1882 by a German physician named "Robert
Koch" who received the Nobel Prize for this discovery.
Tuberculosis most commonly attacks the lungs but can also
affect the central nervous system, the lymphatic system, the
circulatory system, the genitourinary system, bones, joints and
even the skin. It spreads through the air when people who have
an active TB infection cough, sneeze, or otherwise transmit
their saliva through the air.TB infection usually occurs initially
in the upper part (lobe) of the lungs. The body's immune
system, however, can stop the bacteria from continuing to
reproduce. Thus, the immune system can make the lung
infection inactive (dormant). On the other hand, if the body's
immune system cannot contain the TB bacteria, the bacteria
will reproduce (become active or reactivate) in the lungs and
spread elsewhere in the body.
A. Types of Tuberculosis
a) Active Tuberculosis
Active TB means the bacteria are active in the body. The
immune system is unable to stop these bacteria from causing
illness. People with active TB in their lungs can pass the
bacteria on to anyone they come into close contact with. When
a person with active TB coughs, sneezes or spits, people
nearby may breathe in the tuberculosis bacteria and become
infected.
b) Inactive Tuberculosis
Inactive TB infection is also called latent TB. If a person has
latent TB, it means their body has been able to successfully
fight the bacteria and stop them from causing illness. People
who have latent TB do not feel sick, do not have symptoms
and cannot spread tuberculosis [9].
c) Tuberculosis meningitis
This is caused by the spread of Mycobacterium tuberculosis to
the brain, from another site in the
body.Thesymptomsusuallybegingradually.
d) GenitourinaryTB
In men, genital TB may present as epididymitis or scrotal
mass. In women, genital Tb may mimic pelvic inflammatory
disease. This type of TB causes approximately 10% of sterility
in women worldwide and approximately 1% in industrialized
countries.
e) Gastrointestinal TB
Any site along the gastrointestinal tract may become infected.
Tuberculosis lymphadenitis (scrofula):
The most common site is in the neck along the
sternocleidomastoid muscle. It usually is unilateral. It usually
is unilateral, with little or no pain. Advanced disease may
suppurate and form a draining sinus.
f) Cutaneous TB
Several different types of cutaneous TB exist. Direct infection
of the skin or mucous membranes from an outside source
ofmycobacteria results in an initial lesion called the
tuberculous chancre.
g) Uterus Ovarian TB
Female genital organs are one of the common sites to be
involved in women.It is a chronic disease and bacteria may
remain for long time slowly destroying the organs. The disease
may remain totally symptomless or may lead to pelvic pain,
Infertility may be caused even by early or minimal disease.
h) Osteo-articular Skeletal - Bone - Joint TB
The most common site of a involvement is the spine "Potts
diseases. Symptoms include back pain or stiffness. Lower
extremity paralysis occurs in as many as half the patients with
ndiagnosed Potts disease. Tuberculosis arthritis usually
involves only 1 joint.Although any point may be involved, the
hip of the knee is affected most commonly, followed by the
ankle, elbow, wrist, hip or the knee is affected most commonly,
followed by the ankle, elbow wrist and shoulder[10].Other
types of tuberculosis include:MycobacteriumAvium-
Intracellulare, Mycobacterium Chelonae, Mycobacterium
Fortuitum, Mycobacterium Gordonae, Mycobacterium
Haemophilum, Mycobacterium Kansasii, Mycobacterium
Marinum, Mycobacterium Xenopi.It may take many months
from the time the infection initially gets into the lungs until
symptoms develop.By our interview with Tb patients, we

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gathered their illness and symptoms before and after infection.
This paper deals withthe s y m p t o m s a n d r e m e d y
f o r Tuberculosis using Induced Fuzzy Cognitive Maps
(IFCMs).Section two presents the basic definitions and section
three Presents the analysis using theIFCMS model. In fourth
section we draw the conclusions from our study and
proposedremedial measures.
II. BASIC NOTION AND DEFINITIONS
We proceed to state the definitions of IFCMS model.
A. Definition
Fuzzy Cognitive Maps (FCMs) are digraphs that capture the
cause/effect relationship in a system. Nodesofthegraphstand
for the concepts representing the key factors and attributes of
the modeling system, such asinputs, variable states,
components factors ,events, actionsof any
system.Signedweightedarcs describe the casual relationships,
which exists among concepts and interconnect them, with a
degree of causality. The constructed graph clearly shows how
concepts influence each otherandhow much the degree of
influenceis. Cognitive Maps (CMs) were proposed for decision
making by Axelrod [10] for the firsttime. Using two basic
types of elements;concepts and casual relationship, the
cognitive map canbeviewed asasimplified mathematical model
of a belief system.FCMs wereproposed with the extension of
the fuzzified casual relationships. Kosko[3] ,introduced FCMs
as fuzzygraph structures for representing casual
reasoning.When then odeso f the FCM are fuzzy sets then they
are called fuzzy nodes.FCMs with edge weights or causalities
from the set{-1,0, 1} are called simple FCMs.Consider then
odes/concepts P1,P2, P3,…,PnoftheFCM. Suppose the directed
graph is drawn using edge weight eijfrom {-1,0,1}.
B. Definition
Thematrix Mbedefined byM= (eij) whereeijisthe weightof the
directed edgePiPj.Mis called the adjacency matrix of the
FCM,also known as connection matrix.The directed edgeeij
from thecasua lconcept Pito concept
PjmeasureshowmuchPicausesPj.Theedgeeijtakesvaluesintherea
linterval[−1,1].
eij =0indicatesnocasuality.
eij>0indicatescasualincrease/positivecasuality.
eij<0indicatescasualdecrease/negativecasuality.
Simple FCMs provide quick first-hand information to an
expert’s stated casual knowledge. Let P1,P2, P3,…,Pnbe the
nodesof FCM. Let A=(a1,a2, …,an) iscalledastate vector
whereeitherai=0or1.Ifai=0,theconceptaiintheOFFstate
andifai=1, theconceptaiintheONstate,fori=1,2, …,n. LetP1P2,
P2P3, …,PiPj.betheedgesoftheFCM(i ≠ j).
Thentheedgesformadirectedcycle.
C. Definition
An FCM is said to be cyclic ifitpossessesadirectedcycle.
AnFCMwithcyclesis saidtohaveafeedback,whenthereisa
feedbackinanFCM,i.e.,whenthecasualrelationsflowthrough
acycleinarevolutionary way,theFCMiscalledadynamical
system.Theequilibriumstateforthedynamicalsystemiscalled
thehiddenpattern.Iftheequilibrium stateofadynamical state isa
uniquestatevector,itiscalledafixedpointorlimitcycle. Inference
from the hidden patterns summarizes the joint effects of al
linteracting fuzzy knowledge.
D. Algorithmic Approach in IFCM
Even though IFCM is an advancement of FCM it follows the
foundation of FCM ,it has a slightmodificationonlyin
Algorithmic approaches. Toderiveanoptimistic solutiontothe
problem with anunsupervised data,the following steps tobe
followed:
Step 1:Forthegivenmodel(problem),collecttheunsupervised
datathatisindeterminantFactorscallednodes.
Step 2: According to the expert opinion, draw the directed
graph.
Step 3: Obtain theconnectionmatrix, M,from the directed graph
(FCM). Herethenumber ofrowsinthegivenmatrix =
numberofstepstobeperformed.
Step 4: Consider thestatevector S(X1).by setting 1
c
inONposition thatisassigningthefirst
componentofthevectortobe1andthe rest of thecomponents as
0.Find S(X1) × M.The state vector isupdated and threshold at
eachstage.
Step 5: Threshold value is calculated by assigning 1 for the
values>0and0forthevalues<1.Thesymbol‘↪’represents
thethresholdvaluefortheproductoftheresult.
Step 6:Now eachcomponent in theC1vectoris taken
separatelyand productof the givenMatrixis calculated. The
vector which has maximum number of one’sis found. The
vectorwithmaximumnumberof one’swhichoccursfirstis
consideredasC2.
Step7:Whenthesamethresholdvalueoccurstwice.Thevalue
isconsideredasthefixedPoint.Theiterationgetsterminated.
Step8:ConsiderthestatevectorC1bysettingC2inONstatethatisassi
gningthesecondcomponentofthevectortobe1andthe rest of
thecomponents as 0.Precedethe calculations
discussedinSteps4to6.
Step9:ContinueStep9forallthestatevectorsandfindhidden
pattern.
III. ANALYSIS USING IFCMS MODEL WE TAKE
THE FOLLOWING ATTRIBUTES IN THE
CASE OF SYMPTOMS
C1-Pain in breathing, chest pain and shortness of breath, all
these together make the breathing difficult.
C2- coughwith thick, cloudy and sometimes bloody mucus
from the lungs for more than two weeks.
C3-Increased speed in heartbeat, chillness of the body and night
sweats..
C4-Fever and continuous cough gives irritating mood to the
patient, also gives headacheand mental stress.
Table 1

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C5-continuous cough gives throat pain, dryness in the tongue
and also creates abdominal pain.
C6-Immunity of the body decreases, body become weak and it
results in weight loss..
C7- Back pain, overall sensation of feeling unwell, pain in
joints, kidney pain etc.,
C8- Patient becomes tired, feels sleepy and fatigue.
An expert, a lady doctor, according to her opinion on the same
set of 8 attributes has been converted into a connection matrix
M.
[ ]
Analysis using IFCMS:
Step 1:
Let C1 (1 0 0 0 0 0 0 0)
C1 M= (0 0 1 1 0 0 1 1) = C1
’
C1
’
M≈
(0 0 1 0 0 0 0 0)M= (1 0 0 0 0 0 0 1)
(0 0 01 0 0 0 0)M= (0 0 0 0 1 0 0 1)
(0 0 0 0 0 0 1 0)M= (1 1 1 0 1 0 0 1) = C2
(0 0 0 0 0 0 0 1)M= (0 0 1 0 1 1 0 0)
C2 M = (1 1 1 0 1 0 0 1) M = (3 1 3 2 2 1 3 4)
↪ (1 1 1 1 1 1 1 1 ) = C2
’
C2
’
M≈
(1 0 0 0 0 0 0 0)M= (0 0 1 1 0 0 1 1)
(0 1 0 0 0 0 0 0)M= (1 0 0 1 1 0 1 1)
(0 0 1 0 0 0 0 0)M= (1 0 0 0 0 0 0 1)
(0 0 0 1 0 0 0 0)M= (0 0 0 0 1 0 0 1)
(0 0 0 0 1 0 0 0)M= (1 1 1 0 0 1 1 1) = C3
(0 0 0 0 0 1 0 0)M= (0 0 1 0 1 0 0 1)
(0 0 0 0 0 0 1 0)M= (1 1 1 0 1 0 0 1)
(0 0 0 0 0 0 0 1)M= (0 0 1 0 1 1 0 0)
C3M = (1 1 1 0 0 1 1 1)M = (3 1 4 2 4 1 2 5)
↪ (1 1 1 1 1 1 1 1 ) = C3
’
C3
’
M ≈
(1 0 0 0 0 0 0 0)M= (0 0 1 1 0 0 1 1)
(0 1 0 0 0 0 0 0)M= (1 0 0 1 1 0 1 1)
(0 0 1 0 0 0 0 0)M= (1 0 0 0 0 0 0 1)
(0 0 0 1 0 0 0 0)M= (0 0 0 0 1 0 0 1)
(0 0 0 0 1 0 0 0)M= (1 1 1 0 0 1 1 1) = C3
(0 0 0 0 0 1 0 0)M= (0 0 1 0 1 0 0 1)
(0 0 0 0 0 0 1 0)M= (1 1 1 0 1 0 0 1)
(0 0 0 0 0 0 0 1)M= (0 0 1 0 1 1 0 0)
(1 1 1 0 0 1 1 1) is the fixed point and the triggering pattern is
C1→ C7 → C5→C5whenThe first attribute is kept in on state. The
following table gives the triggering patterns when other
attributes are kept in ON state consecutively.
Table 3.1 Induced Patterns for M by IFCM
Merging all these induced graphs on a single graph, we obtain
the following graph.
Fig 1: Induced graphs on a merged graph
The interrelationship between the attributes
revealsthatC5[continuous cough gives throat pain, dryness in
the tongue and also creates abdominal pain] isthe
terminalnodeand C2[A cough with thick, cloudy and
sometimes bloody mucus from the lungs for more than two
weeks]plays
theroleofintermediarynode.Thelimitpointcorresponding
toC5(11100111)highlightstheattributesandC1 ,
C2,C3,C6,C7,C8whichseems to be major symptoms of
Tuberculosis.
.
IV. CONCLUSION
In all the diseases, prevention is must than curing it. So to
reduce the illness after the infection of tuberculosis, the patient
has to follow certain remedial measures inorder to have a
happy surrounding for him and also to others by not spreading
it.The corporation has to maintain some safety measures and
follow some steps to overcome this problem.We suggest the
following remedial measures.Covering of mouth by a mask
will prevent from spreading of the diseases.Increase the
immunity by performing regular exercise everyday and good,
undisturbed sleep will also strengthens the immune
system.Taking healthy foods and get tested regularly with
doctor will give you a better improvement.A drug called
Isoniazed(INH) can be used as a preventive therapy for those
who are at high risk of becoming infected with tuberculosis.
REFERENCES
[1]Klir, G.J. and Folger,T.A., Fuzzy Sets, Uncertainty and Information,
Prentice Hall, Englewood, Cliffs. N.J.1988.[2]Pathinathan,T. Thirusangu.K.
and John M.Mary“On causes for school dropouts- A fuzzyanalysis”.(Accepted
for publication in ActaCienciaIndica).
[3] Kosko, B., January, “Fuzzy CognitiveMaps”, International journal of man-
machine studies, pp.62-75, (1986).
[4]Vasantha, W.B., .Pathinathan,T. and John M.Mary, “ School environment:
A cause for
increase in School Dropouts – Fuzzy Analysis”,Proc. of the State Level
Seminar on IndustrialMathematics, pp.127-136, Nov.2005.
[5]Vasantha,W.B., and Pathinathan,T., “LinkedFuzzy Relational maps to study
the relation
between migration and school dropouts in TamilNadu”. Ultra. Sci.17, 3(M),
Dec., pp. 441-465,2005.
Number Attribute ON state Triggering pattern
Step1 C1; (10 0 0 0 0 0 0 ) C1→ C7 → C5→C5
Step2 C2;(0 1 0 0 0 0 0 0) C2 → C5→C5
Step3 C3;(0 0 1 0 0 0 0 0) C3→ C1 → C5→C5
Step4 C4;(0 0 0 1 0 0 0 0) C4 → C5→C5
Step5 C5;(0 0 0 0 1 0 0 0) C5→ C2 → C5
Step6 C6;(0 0 0 0 0 1 0 0) C6→ C5→C5
Step7 C7;(0 0 0 0 0 0 1 0) C7 → C5→C5
Step8 C8;(0 0 0 0 0 0 0 1) C8 → C5→C5

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[6]Donald D. Spilegelburg, New topics in tuber culosis research.,Novea
science publishers, New York, 2007
[7]Barry R.Bloom., TuberculosesPathogenes, Protection and
control.,American Society Microbiology, Washington 1994.
[8]Axelrod. R., Structure of Decision, the cognitive maps of Political Elites,
Princeton, NJ:Princeton University Press, (1976).
[9]http://www.emedicinehealth.com/tuberculosis/page3_em.htm.
[10]http://library.thinkquest.org/C0126375/types%20of%20%20tb.htm.
[11]http://www.cdc.gov/tb/publications/factsheets/testing/TB_Factsheet.pdf.

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