The Study of Symptoms of Tuberculosis Using Induced Fuzzy Coginitive Maps (IFCMS)
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Indo-Bhutan International Conference On Gross National Happiness Vol 02, October 2013
Pages: 237-241
The Study of Symptoms of Tuberculosis Using Induced Fuzzy Coginitive
Maps (IFCMS)
Ponnivalavan.K .,Pathinathan.T
Department of Mathematics, Loyola College, Chennai-34, 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 analysis the s y m p t o m s o f Tuberculosis using Induced Fuzzy
Cognitive Maps (IFCMs). IFCMs are a 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.
1. Introduction successfully fight the bacteria and stop them
Tuberculosis is a common and an infectious from causing illness. People who have latent
disease which is caused by bacteria called TB do not feel sick, do not have symptoms
"Mycobacterium tuberculosis". It was first and cannot spread tuberculosis [9].
isolated in 1882 by a German physician named Tuberculosis meningitis:
"Robert Koch" who received the Nobel Prize This is caused by the spread of
for this discovery. Tuberculosis most Mycobacterium tuberculosis to the brain, from
commonly attacks the lungs but can also affect another site in the body. The symptoms
the central nervous system, the lymphatic usually begin gradually.
system, the circulatory system, the Genitourinary TB:
genitourinary system, bones, joints and even In men, genital TB may present as
the skin. It spreads through the air when epididymitis or scrotal mass. In women,
people who have an active TB infection genital Tb may mimic pelvic inflammatory
cough, sneeze, or otherwise transmit their disease. This type of TB causes approximately
saliva through the air. 10% of sterility in women worldwide and
TB infection usually occurs initially in the approximately 1% in industrialized countries.
upper part (lobe) of the lungs. The body's Gastrointestinal TB:
immune system, however, can stop the Any site along the gastrointestinal tract may
bacteria from continuing to reproduce. Thus, become infected.
the immune system can make the lung Tuberculosis lymphadenitis (scrofula):
infection inactive (dormant). On the other The most common site is in the neck along the
hand, if the body's immune system cannot sternocleidomastoid muscle. It usually is
contain the TB bacteria, the bacteria will unilateral. It usually is unilateral, with little or
reproduce (become active or reactivate) in the no pain. Advanced disease may suppurate and
lungs and spread elsewhere in the body. form a draining sinus.
1.1. Types of Tuberculosis: Cutaneous TB:
Active Tuberculosis: Active TB means the Several different types of cutaneous TB exist.
bacteria are active in the body. The immune Direct infection of the skin or mucous
system is unable to stop these bacteria from membranes from an outside source of
causing illness. People with active TB in their mycobacteria results in an initial lesion called
lungs can pass the bacteria on to anyone they the tuber culous chancre.
come into close contact with. When a person Uterus Ovarian TB:
with active TB coughs, sneezes or spits, Female genital organs are one of the common
people nearby may breathe in the tuberculosis sites to be involved in women. It is a chronic
bacteria and become infected. disease and bacteria may remain for long time
Inactive Tuberculosis: Inactive TB infection slowly destroying the organs. The disease may
is also called latent TB. If a person has latent remain totally symptomless or may lead to
TB, it means their body has been able to
International Journal of Data Mining Techniques and Applications (IJDMTA) 237
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Pages: 237-241
pelvic pain, Infertility may be caused even by map can be viewed as a simplified
early or minimal disease. mathematical model of a belief system.
Osteo-articular Skeletal - Bone - Joint TB: FCMs were proposed with the extension of
The most common site of a involvement is the the fuzzified casual relationships. Kosko[3],
spine "Potts diseases. Symptoms include back introduced FCMs as fuzzy graph structures
pain or stiffness. Lower extremity paralysis for representing casual reasoning. When the
occurs in as many as half the patients with nodes of the FCM are fuzzy sets then they
ndiagnosed Potts disease. Tuberculosis are called fuzzy nodes. FCMs with edge
arthritis usually involves only 1 joint.Although weights or causalities from the set {-1, 0, 1}
any point may be involved, the hip of the knee are called simple FCMs. Consider the
is affected most commonly, followed by the nodes/concepts P1, P2, P3, …, Pn of the FCM.
ankle, elbow, wrist, hip or the knee is affected Suppose the directed graph is drawn using
most commonly, followed by the ankle, elbow edge weight eij from {-1,0,1}.
wrist and shoulder[10]. 2.2. Definition: The matrix M be defined by
Other types of tuberculosis M = (eij) where eij is the weight of the
include:Mycobacterium Avium-Intracellulare, directed edge P i P j. M is called the adjacency
Mycobacterium Chelonae, Mycobacterium matrix of the FCM, also known as connection
Fortuitum, Mycobacterium Gordonae, matrix.
Mycobacterium Haemophilum, The directed edge eij from the casual concept
Mycobacterium Kansasii, Mycobacterium
Pi to concept P j measures how much Pi
Marinum, Mycobacterium Xenopi.
causes P j .The edge eij takes values in the
It may take many months from the time the
infection initially gets into the lungs until real interval [−1, 1].
symptoms develop. By our interview with Tb eij = 0 indicates no casuality.
patients, we gathered their illness and eij > 0 indicates casual increase / positive
symptoms before and after infection. This casuality.
paper deals with the s y m p t o m s a n d eij < 0 indicates casual decrease / negative
r e m e d y f o r Tuberculosis using Induced casuality.
Fuzzy Cognitive Maps (IFCMs). Simple FCMs provide quick first-hand
Section two presents the basic definitions and information to an expert’s stated casual
section three Presents the analysis using the knowledge. Let P1, P2, P3, …, Pn be the nodes
IFCMS model. In fourth section we draw the of FCM. Let A = (a1, a2, …, an) is called a
conclusions from our study and state vector where either ai = 0 or 1. If ai =
proposedremedial measures. 0, the concept ai in the OFF state and if ai
=1, the concept ai in the ON state, for i = 1,
2. Basic Notion and definitions
2, …, n. Let P1 P 2, P 2 P 3 , …, Pi P j. be the
We proceed to state the definitions of IFCMS
edges of the FCM (i ≠ j). Then the edges
model.
form a directed cycle.
2.1 Definition: Fuzzy Cognitive Maps
2.3. Definition: An FCM is said to be cyclic
(FCMs) are digraphs that capture the
if it possesses a directed cycle. An FCM
cause/effect relationship in a system. Nodes
with cycles is said to have a feedback, when
of the graph stand for the concepts
there is a feedback in an FCM, i.e., when the
representing the key factors and attributes of
casual relations flow through a cycle in a
the modeling system, such as inputs, variable
revolutionary way, the FCM is called a
states, components factors, events, actions of
dynamical system. The equilibrium state for
any system. Signed weighted arcs describe
the dynamical system is called the hidden
the casual relationships, which exists among
pattern. If the equilibrium state of a
concepts and interconnect them, with a degree
dynamical state is a unique state vector, it is
of causality. The constructed graph clearly
called a fixed point or limit cycle. Inference
shows how concepts influence each other and
from the hidden pattern summarizes the joint
how much the degree of influence is.
effects of all interacting fuzzy knowledge.
Cognitive Maps (CMs) were proposed for
2.4. Algorithmic Approach in IFCM
decision making by Axelrod [10] for the first
Even though IFCM is an advancement of
time. Using two basic types of elements;
FCM it follows the foundation of FCM, it
concepts and casual relationship, the cognitive
International Journal of Data Mining Techniques and Applications (IJDMTA) 238
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Pages: 237-241
has a slight modification only in Algorithmic C5- continuous cough gives throat pain,
approaches. To derive an optimistic solution dryness in the tongue and also creates
to the problem with an unsupervised data, the abdominal pain.
following steps to be followed: C6- Immunity of the body decreases, body
Step 1 : For the given model (problem), become weak and it results in weight loss..
collect the unsupervised data that is in C7- Back pain, overall sensation of feeling
determinant Factors called nodes. unwell, pain in joints, kidney pain etc.,
Step 2: According to the expert opinion, draw C8- Patient becomes tired, feels sleepy and
the directed graph. fatigue.
Step 3: Obtain the connection matrix, M, An expert, a lady doctor, according to her
from the directed graph (FCM). Here the opinion on the same set of 8 attributes has
number of rows in the given matrix = been converted into a connection matrix M.
number of steps to be performed.
Step 4: Consider the state vector S(X1).by 00110011
⎡1 0 0 1 1 0 1 1⎤
setting c1 in ON position that is assigning ⎢ ⎥
10000001
the first component of the vector to be 1 and ⎢ ⎥
0 0 0 0 1 0 0 1⎥
the rest of the components as 0. Find S(X1) × =⎢
M. The state vector is updated and threshold ⎢1 1 1 0 0 1 1 1⎥
at each stage. ⎢0 0 1 0 1 0 0 1⎥
⎢ 11 1 0 1 0 0 1 ⎥
Step 5: Threshold value is calculated by
⎣0 0 1 0 1 1 0 0⎦
assigning 1 for the values > 0 and 0 for the
values < 1. The symbol ‘↪’ represents the
threshold value for the product of the result. Analysis using IFCMS:
Step 6: Now each component in the C1 Step 1:
vector is taken separately and product of the Let C1 (1 0 0 0 0 0 0 0)
given Matrix is calculated. The vector which C1 M= (0 0 1 1 0 0 1 1) = C1’
has maximum number of one’s is found. The C1’ M≈
vector with maximum number of one’s which
(0 0 1 0 0 0 0 0)M= (1 0 0 0 0 0 0 1)
occurs first is considered as C2.
Step 7: When the same threshold value (0 0 01 0 0 0 0)M= (0 0 0 0 1 0 0 1)
occurs twice. The value is considered as the (0 0 0 0 0 0 1 0)M= (1 1 1 0 1 0 0 1) = C2
fixed Point. The iteration gets terminated. (0 0 0 0 0 0 0 1)M= (0 0 1 0 1 1 0 0)
Step 8: Consider the state vector C1 by C2 M = (1 1 1 0 1 0 0 1) M = (3 1 3 2 2 1 3 4)
setting C2 in ON state that is assigning the ↪ (1 1 1 1 1 1 1 1 ) = C2’
second component of the vector to be 1 and
the rest of the components as 0.Precede the
C2’ M ≈
calculations discussed in Steps 4 to 6.
Step 9: Continue Step 9 for all the state (1 0 0 0 0 0 0 0)M= (0 0 1 1 0 0 1 1)
vectors and find hidden pattern. (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)
3: Analysis using IFCMS model We take (0 0 0 1 0 0 0 0)M= (0 0 0 0 1 0 0 1)
the following attributes in the case of (0 0 0 0 1 0 0 0)M= (1 1 1 0 0 1 1 1) = C3
Symptoms: (0 0 0 0 0 1 0 0)M= (0 0 1 0 1 0 0 1)
C1- Pain in breathing, chest pain and shortness
of breath, all these together make the breathing (0 0 0 0 0 0 1 0)M= (1 1 1 0 1 0 0 1)
difficult. (0 0 0 0 0 0 0 1)M= (0 0 1 0 1 1 0 0)
C2- cough with thick, cloudy and sometimes C3M = (1 1 1 0 0 1 1 1)M = (3 1 4 2 4 1 2 5)
bloody mucus from the lungs for more than ↪ (1 1 1 1 1 1 1 1 ) = C3 ’
two weeks. C3 ’M ≈
C3- Increased speed in heartbeat, chillness of (1 0 0 0 0 0 0 0)M= (0 0 1 1 0 0 1 1)
the body and night sweats..
(0 1 0 0 0 0 0 0)M= (1 0 0 1 1 0 1 1)
C4- Fever and continuous cough gives
irritating mood to the patient, also gives (0 0 1 0 0 0 0 0)M= (1 0 0 0 0 0 0 1)
headache and mental stress. (0 0 0 1 0 0 0 0)M= (0 0 0 0 1 0 0 1)
International Journal of Data Mining Techniques and Applications (IJDMTA) 239
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Pages: 237-241
The interrelationship between the
(0 0 0 0 1 0 0 0)M= (1 1 1 0 0 1 1 1) = C3 attributes reveals that C5 [continuous cough
(0 0 0 0 0 1 0 0)M= (0 0 1 0 1 0 0 1) gives throat pain, dryness in the tongue and
(0 0 0 0 0 0 1 0)M= (1 1 1 0 1 0 0 1) also creates abdominal pain] is the terminal
(0 0 0 0 0 0 0 1)M= (0 0 1 0 1 1 0 0) node and C2 [A cough with thick, cloudy and
(1 1 1 0 0 1 1 1) is the fixed point and the sometimes bloody mucus from the lungs for
more than two weeks] plays the role of
triggering pattern is C1→ C7 → C5→C5 when
intermediary node.
The first attribute is kept in on state. The
The limit point corresponding to C5 (1 1 1 0
following table gives the triggering patterns 0 11 1) high lights the attributes and C1 , C2
when other attributes are kept in ON state ,C3 ,C6 ,C7 ,C8 which seems to be major
consecutively. symptoms of Tuberculosis.
Table 3.1 Induced Patterns for M by IFCM .
4. Conclusion
Number Attribute ON Triggering In all the diseases, prevention is must than
state pattern curing it. So to reduce the illness after the
Step1 C1; (10 0 0 0 0 0 C1→ C7 → infection of tuberculosis, the patient has to
0) C5→C5 follow certain remedial measures inorder to
Step2 C2; (0 1 0 0 0 0 0 C2 → C5→C5 have a happy surrounding for him and also to
0) others by not spreading it.
Step3 C3; (0 0 1 0 0 0 0 C3→ C1 → The corporation has to maintain some safety
0) C5→C5 measures and follow some steps to overcome
Step4 C4; (0 0 0 1 0 0 0 C4 → C5→C5 this problem.
0) We suggest the following remedial measures.
Step5 C5; (0 0 0 0 1 0 0 C5→ C2 → C5 Covering of mouth by a mask will
0) prevent from spreading of the diseases.
Step6 C6; (0 0 0 0 0 1 0 C6→ C5→C5 Increase the immunity by performing
0) regular exercise everyday and good,
Step7 C7; (0 0 0 0 0 0 1 C7 → C5→C5 undisturbed sleep will also strengthens the
0) immune system.
Step8 C8; (0 0 0 0 0 0 0 C8 → C5→C5 Taking healthy foods and get tested
1) regularly with doctor will give you a better
improvement.
Merging all these induced graphs on a single A drug called Isoniazed(INH) can be
graph, we obtain the following graph. used as a preventive therapy for those who are
at high risk of becoming infected with
tuberculosis.
5. References
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Pages: 237-241
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