1.
Integrated Intelligent Research(IIR) International Journal of Business Intelligent
Volume: 03 Issue: 01 June 2014,Pages No.4-9
ISSN: 2278-2400
4
Using New Triangular Fuzzy Cognitive Maps
(TRFCM) to Analyze Causes of Divorce in Family
M.Clement Joe Anand1
, A.Victor Devadoss2
1
Ph.D Research Scholar, Department of mathematics, Loyola College, Chennai- 34, India.
2
Head & Associate Professor, Department of mathematics, Loyola College, Chennai- 34, India.
E-mail: arjoemi@gmail.com , hanivictor@ymail.com
Abstract-Our main objective of this paper is to find out the
new fuzzy tool called Triangular Fuzzy Cognitive Maps to
analyze the social problem. Usually in FCM we analyze the
causes and effects of the relationships among the concepts to
model the behavior of any system. But this new model gives
the causes and effect of the relationships among the concepts to
model behavior with ranking of any system. In this paper, we
analyze the divorce problem using Triangular Fuzzy Cognitive
Maps, it has five sections. In first section, we give the brief
introduction to Fuzzy Cognitive Maps (FCM), Section two
gives the basic definitions of FCM. In section three we derive
the definitions for Triangular Fuzzy Cognitive Maps (TrFCM)
and Hidden pattern of the dynamical system. In Fourth section
we analyzed the concept of the problem using Triangular
Fuzzy Cognitive Maps (TrFCM).In Final section we give the
conclusion based on our study.
Keywords: Fuzzy Cognitive Maps (FCMs), Triangular Fuzzy
Numbers, Divorce, Family.
I. INTRODUCTION
Lotfi. A. Zadeh (1965) has introduced a mathematical model
called Fuzzy Cognitive Maps. After a decade, Political
scientist Axelord (1976) used this fuzzy model to study
decision making in social and political systems. Then Kosko
(1986, 1988 and 1997) enhanced the power of cognitive maps
considering fuzzy values for the concepts of the cognitive map
and fuzzy degrees of interrelationships between concepts.
FCMs can successfully represent knowledge and human
experience, introduced concepts to represent the essential
elements and the cause and effect relationships among the
concepts to model the behavior of any system. It is a very
convenient simple and powerful tool, which is used in
numerous fields such as social economical and medical etc.
Usually we analyze the number of attributes ON-OFF position.
But the thing is here, this gives the weightage of the attributes
we call ranking of the attributes. Now we see the basic
definitions for FCMs to develop the Triangular Fuzzy
Cognitive Maps (TrFCM).
II. PRELIMINARIES
In this section, some concepts and methods used in this paper
are briefly introduced.
2.1. Fuzzy Set theory
The fuzzy set theory is to deal with the extraction of the
primary possible outcome from a multiplicity of information
that is expressed in vague and imprecise terms. Fuzzy set
theory treats vague data as probability distributions in terms of
set memberships. Once determined and defined, sets of
memberships in probability distributions can be effectively
used in logical reasoning.
2.2. Triangular Fuzzy number and the Algebraic
Operations
2.2.1 Triangular Fuzzy number
It is a fuzzy number represented with three points as follows:
 
1 2 3
, ,
A a a a

a1 a2 a3
1

The membership function defined as
1
1
1 2
2 1
3
2 3
3 2
3
0
( )
0
A
for x a
x a
for a x a
a a
x
a x
for a x a
a a
for x a



 
  
 

 

  
 




2.2.2. Operation of Triangular Fuzzy Number
The following are the four operations that can be performed on
triangular fuzzy numbers: Let  
1 2 3
, ,
A a a a
 and  
1 2 3
, ,
B b b b

then,
(i) Addition (+): 1 1 2 2 3 3
( , , )
A B a b a b a b
    
(ii) Subtraction (-): 1 3 2 2 3 1
( , , )
A B a b a b a b
    
(iii) Multiplication (  ) : (a)
1 2 3
( , , ), , 0,
k A ka ka ka k R k
   
(b) 1 2 1 2 1 2 1 2
( , , ), 0, 0
A B a a bb c c a a
    .
(iv) Division (  ):
1 1
1 1 1 1
1 1 1
1 1 1
( ) ( , , ) , , , 0
A a b c a
c b a
   
  
 
 
,
1 1 1
1 2
2 2 2
, , , 0, 0.
a b c
A B a a
c b a
 
   
 
 
2.2.3 Degrees of the Triangular Fuzzy Number
The linguistic values of the triangular fuzzy numbers are
Very Low (0, 0, 0.25)
Low (0, 0.25, 0.50)
Medium (0.25, 0.50, 0.75)
High (0.50, 0.75, 1)

2.
Integrated Intelligent Research(IIR) International Journal of Business Intelligent
Volume: 03 Issue: 01 June 2014,Pages No.4-9
ISSN: 2278-2400
5
Very High (0.75, 1, 1)
2.3. Fuzzy Cognitive Maps (FCMs)
Fuzzy Cognitive Maps (FCMs) are more applicable when the
data in the first place is an unsupervised one. The FCMs work
on the opinion of experts. FCMs model the world as a
collection of classes and causal relations between classes.
2.3.1 Definition
When the nodes of the FCM are fuzzy sets then they are called
as fuzzy nodes.
2.3.2. Definition
FCM with edge weights or causalities from the set {-1, 0, 1}
are called simple FCM.
2.3.3. Definition
An FCM is a directed graph with concepts like policies, events
etc, as nodes and causalities as edges, It represents causal
relationships between concepts.
2.3.4. Definition
Consider the nodes/concepts C1, C2,…,Cn of the FCM.
Suppose the directed graph is drawn using edge weight eij∈ {-
1, 0, 1}. The matrix E be defined by E = (eij) where eij is the
weight of the directed edge CiCj. E is called the adjacency
matrix of FCM, also known as the connection matrix of the
FCM. It is important to note that all matrices associated with
an FCM are always square matrices with diagonal entries as
zero.
2.3.5. Definition
Let C1, C2,…,Cn be the nodes of an FCM. A= (a1, a2,…,an)
where eij∈ {-1, 0, 1}. A is called the instantaneous state vector
and it denotes the on-off position of the node at an instant. ai=
0 if ai is OFF and ai= 1 if ai is ON for i = 1, 2,…, n.
2.3.6. Definition
Let C1, C2,…,Cn be the nodes of and FCM. Let
1 2 2 3 3 4
, , ,..., i j
C C C C C C C C be the edges of the FCM (i≠j).
Then the edges form a directed cycle. An FCM is said to be
cyclic if it possesses a directed cycle. An FCM is said to be
acyclic if it does not possess any directed cycle.
2.3.7. Definition
An FCM is said to be cyclic is said to have a feedback.
2.3.8. Definition
When there is a feedback in an FCM, i.e, when the causal
relations flow through a cycle in a revolutionary way, the FCM
is called a dynamical system.
2.3.9Definition
Let 1 2 2 3 3 4 1
, , ,..., n n
C C C C C C C C
 be a cycle. When Ci is
switched on and if the causality flows through the edges of a
cycle and if it again causes Ci, we say that the dynamical
system ges round and round. This is true for any node Ci for
i =1,2,…,n. The equilibrium state for this dynamical system is
called the hidden pattern.
2.3.10. Definition
If the equilibrium state of a dynamical system is a unique state
vector, then it is called a fixed point. Consider a FCM with C1,
C2,…,Cn as nodes. For example let us start the dynamical
system by switching on C1. Let us assume that the FCM settles
down with C1 and Cn on i.e., in the state vector remains as (1,
0, 0,…, 0) is called fixed point.
2.3.11. Definition
If the FCM settles down with a state vector repeating in the
form A1→A2→…→Ai→A1 then this equilibrium is called a
limit cycle.
2.4. METHOD OF DETERMINING THE HIDDEN
PATTERN OF FUZZY COGNITIVE MAPS (FCMs)
Let C1, C2,…,Cn be the nodes of an FCM, with feedback, Let E
be the associated adjacency matrix. Let us find the hidden
pattern when C1 is switched on. When an input is given as the
vector A1 = (1, 0,…, 0), the data should pass through the
relation matrix E. This is done by multiplying Ai by the matrix
E. Let AiE = (a1, a2,…, an) with the threshold operation that is
by replacing ai by 1 if ai> k and ai by 0 if ai< k ( k is a suitable
positive integer). We update the resulting concept; the concept
C1 is included in the updated vector by making the first
coordinate as 1 in the resulting vector. Suppose AiE→ A2 then
consider A2E and repeat the same procedure. This procedure
is repeated till we get a limit cycle or a fixed point.
III. PROPOSED TRIANGULAR FUZZY
COGNITIVE MAPS (TrFCMs)
Triangular Fuzzy Cognitive Maps (TrFCM) are more
applicable when the data in the first place is an unsupervised
one. The TrFCM works on the opinion of three experts.
TrFCM models the world as a collection of classes and causal
relations between classes. It is a different process when we
compare to FCM. Usually the FCM gives only the ON-OFF
position. But this Triangular Fuzzy Cognitive Maps is more
precise and it gives the ranking for the causes of the problem
by using the weightage of the attribute it is main advantage of
the new Triangular Fuzzy Cognitive Maps.
3.1. BASIC DEFINITIONS OF TRIANGULAR
FUZZY COGNITIVE MAPS
3.1.1. Definition
When the nodes of the TrFCM are fuzzy sets then they are
called as fuzzy triangular nodes.
3.1.2. Definition
Triangular FCMs with edge weights or causalities from the set
{-1, 0, 1} are called simple Triangular FCMs.
3.1.3. Definition
An TrFCM is a directed graph with concepts like policies,
events etc, as nodes and causalities as edges, It represents
causal relationships between concepts.
3.1.4. Definition
Consider the nodes/concepts TrC1, TrC2,…,TrCn of the Triangular
FCM. Suppose the directed graph is drawn using edge weight
Treij∈ {-1, 0, 1}. The triangular matrix M be defined by Tr(M)
= (Treij) where Treij is the triangular weight of the directed edge

3.
Integrated Intelligent Research(IIR) International Journal of Business Intelligent
Volume: 03 Issue: 01 June 2014,Pages No.4-9
ISSN: 2278-2400
6
TrCiTrCj. Tr(M) is called the adjacency matrix of Triangular
Fuzzy Cognitive Maps, also known as the connection matrix of
the TrFCM.
It is important to note that all matrices associated with an
TrFCM are always square matrices with diagonal entries as
zero.
3.1.5. Definition
Let TrC1, TrC2,…,TrCn be the nodes of an TrFCM. A=(a1,
a2,…,an) where Treij∈ {-1, 0, 1}. A is called the instantaneous
state vector and it denotes the on-off position of the node at an
instant.
Instantaneous vector
1 ( )
0
Tr i
Tr i
a Maximum weight
a Otherwise


 


3.1.6. Definition
Let TrC1, TrC2,…,TrCn be the triangular nodes of and TrFCM.
Let 1 2 2 3 3 4
, , ,...,
Tr Tr Tr Tr Tr Tr Tr i Tr j
C C C C C C C C be the edges of
the TrFCM (i≠j). Then the edges form a directed cycle. An
TrFCM is said to be cyclic if it possesses a directed cycle. An
TrFCM is said to be acyclic if it does not possess any directed
cycle.
3.1.7. Definition
An TrFCM is said to be cyclic is said to have a feedback.
3.1.8. Definition
When there is a feedback in an TrFCM, i.e, when the causal
relations flow through a cycle in a revolutionary way, the
TrFCM is called a dynamical system.
3.1.9. Definition
Let 1 2 2 3 3 4 1
, , ,...,
Tr Tr Tr Tr Tr Tr Tr n Tr n
C C C C C C C C

be a cycle.
When TrCi is switched ON and if the causality flows through the
triangular edges of a cycle and if it again causes Ci, we say
that the dynamical system goes round and round. This is true
for any triangular node TrCi fori =1,2,…,n. The equilibrium
state for this dynamical system is called the hidden pattern.
3.1.10. Definition
If the equilibrium state of a dynamical system is a unique state
vector, then it is called a fixed point. Consider a TrFCM with
TrC1, TrC2,…,TrCn as nodes. For example let us start the
dynamical system by switching on TrC1. Let us assume that the
TrFCM settles down with TrC1 and TrCn ON i.e., in the state
vector remains as (1, 0, 0,…, 0) is called fixed point.
3.1.11. Definition
If the TrFCM settles down with a state vector repeating in the
form A1→A2→…→Ai→A1 then this equilibrium is called a
limit cycle.
3.2. METHOD OF DETERMINING THE HIDDEN
PATTERN OF TRIANGULAR FUZZY COGNITIVE
MAPS (TrFCMs)
Step 1: Let TrC1, TrC2,…,TrCn be the nodes of an TrFCM, with
feedback, Let Tr(M) be the associated adjacency matrix.
Step 2: Let us find the hidden pattern when TrC1 is switched
ON. When an input is given as the vectorA1 = (1, 0,…, 0), the
data should pass through the relation matrix M. This is done
by multiplying Ai by the triangular matrix M.
Step 3: Let AiTr(M) = (a1, a2,…, an) will get a triangular vector.
Suppose A1Tr(M) = (1, 0,…, 0)it gives a triangular weight of
the attributes, we call it as Ai Tr(M)weight.
Step 4: Adding the corresponding node of the three experts
opinion, we call it as Ai Tr(M)sum.
Step 5: The threshold operation is denoted by( ) ie.,
A1Tr(M)Max(weight). That is by replacing ai by 1 if aiis the
maximum weight of the triangular node (ie.,ai=1), otherwise ai
by 0(ie., ai=0).
Step 6: Suppose A1Tr(M)→ A2 then consider A2Tr(M)weight is
nothing but addition of weightage of the ON attribute and A1
Tr(M)weight .
Step 7: Find A2 Tr(M)sum(ie., summing of the three experts
opinion of each attributes).
Step 8: The threshold operation is denoted by( ) ie.,
A2Tr(M)Max(weight). That is by replacing ai by 1 if ai is the
maximum weight of the triangular node (ie.,ai=1), otherwise ai
by 0 (ie., ai=0).
Step 9: If the A1Tr(M)Max(weight). =A2Tr(M)Max(weight). Then
dynamical system end otherwise repeat the same procedure.
Step 10: This procedure is repeated till we get a limit cycle or
a fixed point.
IV. CONCEPT OF THE PROBLEM
we have taken the following Twelve concepts {TrC1,
TrC2,…,TrC12} To analyze of the major reasons for divorce
happening in the society using linguistic questionnaire and the
expert’s opinion The following concepts are taken as the main
nodes of our problem.
TrC1-High Expectations
TrC2- Adultery (Illegal relationship)
TrC3- Incompatibility (Sexual dissatisfaction)
TrC4- Low Tolerance and Rigidity (Rough and Stiff Manner)
TrC5- Dowry and Harassment
TrC6- Lack of Commitment
TrC7- Lack of Physical Attraction/Boredom in Marriage
TrC8- Family Pressure
TrC9- Child rearing issues
TrC10- Lack of Communication
TrC11- Family Background
TrC12- Religious and Cultural Strains
Now we give the connection matrix related with the FCM.
TrC1 TrC2 TrC3 TrC4 TrC5 TrC6 TrC7 TrC8 TrC9 TrC10 TrC11 TrC12

4.
Integrated Intelligent Research(IIR) International Journal of Business Intelligent
Volume: 03 Issue: 01 June 2014,Pages No.4-9
ISSN: 2278-2400
7
( )
1
2
3
4
5
6
7
8
9
10
11
12
0
0
0
0
0
0
0
0
Tr
Tr
Tr
Tr
Tr
Tr
Tr
Tr
Tr
Tr
Tr
Tr
C VL M VL L VL L L H VL VH VL
C L VH H L VL M VL L VL L VL
C VL L VH H M L VL M VL L L
C L VL VH M VL L L L VL VL L
C L L VL VH M VL VH VL L L VL
C VL L VL VL L VH VH VL VL L VL
Tr M
C M VL L VL VL VL L VL L L VL
C VL L VL VL VH VL VH L VL VL L
C L
C
C
C
=
0
0
0
0
VL L VL L L M VH VH H VL
M L VL L VL VL VH L VL L L
VL H L VL L L VL VL L M VH
L VL VL L VL L L VL L H VH
é ù
ê ú
ê ú
ê ú
ê ú
ê ú
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ê ú
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ê ú
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ê ú
ê ú
ê ú
ê ú
ê ú
ê ú
ê ú
ê ú
ë û
TrC1 TrC2 TrC3 TrC4 TrC5 TrC6 TrC7 TrC8 TrC9 TrC10 TrC11 TrC12
( )
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
1
2
3
4
5
6
7
8
9
10
11
12
0 0,0,0.25 0.25,0.50,0.75 0,0,0.25 0,0.25,0.50 0,0,0.25 0,0.25,0.50 0,0.25,0.50 0.50,0.75,1 0,0,0.25 0.75,1,1 0,0,0.25
0,0.25,0.50 0 0.75,1,1 0.50,0.75,1 0,0.25,
Tr
Tr
Tr
Tr
Tr
Tr
Tr
Tr
Tr
Tr
Tr
Tr
C
C
C
C
C
C
Tr M
C
C
C
C
C
C
=
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( )
0.50 0,0,0.25 0.25,0.50,0.75 0,0,0.25 0,0.25,0.50 0,0,0.25 0,0.25,0.50 0,0,0.25
0,0,0.25 0,0.25,0.50 0 0.75,1,1 0.50,0.75,1 0.25,0.50,0.75 0,0.25,0.50 0,0,0.25 0.25,0.50,0.75 0,0,0.25 0,0.25,0.50 0,0.25,0.50
0,0.25,0.50 0
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
,0,0.25 0.75,1,1 0 0.25,0.50,0.75 0,0,0.25 0,0.25,0.50 0,0.25,0.50 0,0.25,0.50 0,0,0.25 0,0,0.25 0,0.25,0.50
0,0.25,0.50 0,0.25,0.50 0,0,0.25 0.75,1,1 0 0.25,0.50,0.75 0,0,0.25 0.75,1,1 0,0,0.25 0,0.25,0.50 0,0.25,0.50 0,0
( )
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
,0.25
0,0,0.25 0,0.25,0.50 0,0,0.25 0,0,0.25 0,0.25,0.50 0 0.75,1,1 0.75,1,1 0,0,0.25 0,0,0.25 0,0.25,0.50 0,0,0.25
0.25,0.50,0.75 0,0,0.25 0,0.25,0.50 0,0,0.25 0,0,0.25 0,0,0.25 0 0,0.25,0.50 0,0,0.25 0,0.25,0.50 0,0.25,0.
( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
50 0,0,0.25
0,0,0.25 0,0.25,0.50 0,0,0.25 0,0,0.25 0.75,1,1 0,0,0.25 0.75,1,1 0 0,0.25,0.50 0,0,0.25 0,0,0.25 0,0.25,0.50
0,0.25,0.50 0,0,0.25 0,0.25,0.50 0,0,0.25 0,0.25,0.50 0,0.25,0.50 0.25,0.50,0.75 0.75,1,1 0 0.75,1,1 0
( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( )
.50,0.75,1 0,0,0.25
0.25,0.50,0.75 0,0.25,0.50 0,0,0.25 0,0.25,0.50 0,0,0.25 0,0,0.25 0.75,1,1 0,0.25,0.50 0,0,0.25 0 0,0.25,0.50 0,0.25,0.50
0,0,0.25 0.50,0.75,1 0,0.25,0.50 0,0,0.25 0,0.25,0.50 0,0.25,0.50 0,0,0.25 0,0,
( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
0.25 0,0.25,0.50 0.25,0.50,0.75 0 0.75,1,1
0,0.25,0.50 0,0,0.25 0,0,0.25 0,0.25,0.50 0,0,0.25 0,0.25,0.50 0,0.25,0.50 0,0,0.25 0,0.25,0.50 0.50,0.75,1 0.75,1,1 0
é ù
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Attribute TrC1 is ON:
A(1)
= (1 0 0 0 0 0 0 0 0 0 0 0)
A(1)
Tr(M)Weight = (0, (0,0,0.25), (0.25,0.50,0.75), (0,0,0.25),
(0,0.25,0.50), (0,0,0.25), (0,0.25,0.50), (0,0.25,0.50),
(0.50,0.75,1), (0,0,0.25), (0.75,1,1), (0,0,0.25))
A(1)
Tr(M)Average = (0, 0.0833, 0.5, 0.0833, 0.25, 0.0833, 0.25,
0.25, 0.75, 0.0833, 0.9167, 0.0833)
A(1)
Tr(M)Max(Weight)
 (0 0 0 0 0 0 0 0 0 0 1 0) =A1
(1)
A1
(1)
Tr(M)Average = (0.2292, 2.0626, 0.6875, 0.2292, 0.6875,
0.6875, 0.2292, 0.2292, 0.6875, 1.3751, 0, 2.5209)
A1
(1)
Tr(M)Max(Weight)
 (0 0 0 0 0 0 0 0 0 0 0 1) =A2
(1)
A2
(1)
Tr(M)Average = (1.8907, 0.6302, 0.6302, 1.8907, 0.6302,
1.8907, 1.8907, 0.6302, 1.8907, 5.6720, 6.9325, 0)
A2
(1)
Tr(M)Max(Weight)
 (0 0 0 0 0 0 0 0 0 0 1 0) =A2
(1)
=A1
(1)
Attribute TrC2 is ON:
A(2)
= (0 1 0 0 0 0 0 0 0 0 0 0)
A(2)
Tr(M)Weight = ((0,0.25,0.50), 0, (0.75,1,1), (0.50,0.75,1),
(0,0.25,0.50), (0,0,0.25), (0.25,0.50,0.75), (0,0,0.25),
(0,0.25,0.50), (0,0,0.25), (0,0.25,0.50), (0,0,0.25))
A(2)
Tr(M)Average = (0.25, 0, 0.9167, 0.75, 0.25, 0.0833, 0.5,
0.0833, 0.25, 0.0833, 0.25, 0.0833)
A(2)
Tr(M) Max(Weight)
 (0 0 1 0 0 0 0 0 0 0 0 0)= A1
(2)
A1
(2)
Tr(M)Average =(0.2292, 0.6875, 0, 2.5209, 2.0626, 1.3751,
0.6875, 0.2292, 1.3751, 0.2292, 0.6875, 0.6875)
A1
(2)
Tr(M) Max(Weight)
 (0 0 0 1 0 0 0 0 0 0 0 0)= A2
(2)
A2
(2)
Tr(M) Average =(1.8907, 0.6302, 6.9325, 0, 3.7814, 0.6302,
1.8907, 1.8907, 1.8907, 0.6302, 0.6302, 1.8907)
A2
(2)
Tr(M) Max(Weight)
 (0 0 1 0 0 0 0 0 0 0 0 0)= A3
(2)
= A1
(2)
Attribute P3 is ON:
A(3)
= (0 0 1 0 0 0 0 0 0 0 0 0 )
A(3)
Tr(M)weight = ((0,0,0.25), (0,0.25,0.50), 0, (0.75,1,1),
(0.50,0.75,1), (0.25,0.50,0.75), (0,0.25,0.50), (0,0,0.25),
(0.25,0.50,0.75), (0,0,0.25), (0,0.25,0.50), (0,0.25,0.50))
A(3)
Tr(M) Average = (0.0833, 0.25, 0, 0.9167, 0.75, 0.5, 0.25,
0.0833, 0.5, 0.0833, 0.25, 0.25)
A(3)
Tr(M) Max(Weight)
 (0 0 0 1 0 0 0 0 0 0 0 0)= A1
(3)
A1
(3)
Tr(M) Average = (0.6875, 0.2292, 2.5209, 0, 1.3751, 0.2292,
0.6875, 0.6875, 0.6875, 0.2292, 0.2292, 0.6875)
A1
(3)
Tr(M) Max(Weight)
 (0 0 1 0 0 0 0 0 0 0 0 0)= A2
(3)
A2
(3)
Tr(M)Average =(0.6302, 1.8907, 0, 6.9325, 5.6720, 3.7814,
1.8907, 0.6302, 3.7814, 0.6302, 1.8907, 1.8907)
A2
(3)
Tr(M) Max(Weight)
 (0 0 0 1 0 0 0 0 0 0 0 0 )= A2
(3)
= A1
(3)
Attribute P4 is ON:
A(4)
= (0 0 0 1 0 0 0 0 0 0 0 0)
A(4)
Tr(M)weight = ((0,0.25,0.50), (0,0,0.25), (0.75,1,1), 0,
(0.25,0.50,0.75), (0,0,0.25), (0,0.25,0.50), (0,0.25,0.50),
(0,0.25,0.50), (0,0,0.25), (0,0,0.25), (0,0.25,0.50))
A(4)
Tr(M)Average = (0.25, 0.0833, 0.9167, 0, 0.5, 0.0833, 0.25,
0.25, 0.25, 0.0833, 0.0833, 0.25)
A(4)
Tr(M Max(Weight)
 (0 0 1 0 0 0 0 0 0 0 0 0) = A1
(4)
A1
(4)
Tr(M)Average = (0.2292, 0.6875, 0, 2.5209, 2.0626, 1.3751,
0.6875, 0.2292, 1.3751, 0.2292, 0.6875, 0.6875)
A1
(4)
Tr(M) Max(Weight)
 (0 0 0 1 0 0 0 0 0 0 0 0) = A2
(4)
A2
(4)
Tr(M)Average = (01.8907, 0.6302, 6.9325, 0, 3.7814, 0.6302,
1.8907, 1.8907, 1.8907, 0.6302, 0.6302, 1.8907)
A2
(4)
Tr(M) Max(Weight)
 (0 0 0 1 0 0 0 0 0 0 0 0) = A3
(4)
= A2
(4)
Attribute P5 is ON:
A(5)
= (0 0 0 0 1 0 0 0 0 0 0 0)
A(5)
Tr(M)Weight = ((0,0.25,0.50), (0,0.25,0.50), (0,0,0.25),
(0.75,1,1), 0, (0.25,0.50,0.75), (0,0,0.25), (0.75,1,1), (0,0,0.25),
(0,0.25,0.50), (0,0.25,0.50), (0,0,0.25))

5.
Integrated Intelligent Research(IIR) International Journal of Business Intelligent
Volume: 03 Issue: 01 June 2014,Pages No.4-9
ISSN: 2278-2400
8
A(5)
Tr(M)Average = (0.25, 0.25, 0.0833, 0.9167, 0, 0.5, 0.0833,
0.9167, 0.0833, 0.25, 0.25, 0.0833)
A(5)
Tr(M) Max(Weight)
 (0 0 0 1 0 0 0 1 0 0 0 0) = A1
(5)
A1
(5)
Tr(M)Average = (0.9167, 0.9167, 2.7501, 0.2292, 3.8960,
0.4584, 3.2085, 0.6875, 1.3751, 0.4584, 0.4584, 1.3751)
A1
(5)
Tr(M) Max(Weight)
 (0 0 0 0 1 0 0 0 0 0 0 0) = A2
(5)
A2
(5)
Tr(M)Average = (2.9220, 2.9220, 0.9740, 10.7140, 0.0000,
5.8440, 0.9740, 10.7140, 0.9740, 2.9220, 2.9220, 0.9740)
A2
(5)
Tr(M) Max(Weight)
 (0 0 0 1 0 0 0 1 0 0 0 0) = A3
(5)
= A1
(5)
Do the process for the remaining attributes
Table: 1 Weightage of the attributes
Attributes TrC1 TrC2 TrC3 TrC4 TrC5 TrC6 TrC7 TrC8 TrC19 TrC10 TrC11 TrC12
(1 0 0 0 0 0 0 0 0 0
0 0)
1.890
7
0.630
2
0.630
2
1.890
7
0.630
2
1.890
7
1.890
7
0.630
2
1.890
7
5.672
0
6.932
5
0.000
0
(0 1 0 0 0 0 0 0 0 0
0 0)
1.890
7
0.630
2
6.932
5
0.000
0
3.781
4
0.630
2
1.890
7
1.890
7
1.890
7
0.630
2
0.630
2
1.890
7
(0 0 1 0 0 0 0 0 0 0
0 0)
0.630
2
1.890
7
0.000
0
6.932
5
5.672
0
3.781
4
1.890
7
0.630
2
3.781
4
0.630
2
1.890
7
1.890
7
(0 0 0 1 0 0 0 0 0 0
0 0)
1.890
7
0.630
2
6.932
5
0.000
0
3.781
4
0.630
2
1.890
7
1.890
7
1.890
7
0.630
2
0.630
2
1.890
7
(0 0 0 0 1 0 0 0 0 0
0 0)
2.922
0
2.922
0
0.974
0
10.71
40
0.000
0
5.844
0
0.974
0
10.71
40
0.974
0
2.922
0
2.922
0
0.974
0
(0 0 0 0 0 1 0 0 0 0
0 0)
1.885
2
1.885
2
5.655
5
0.471
3
8.011
9
0.942
6
6.598
0
1.413
9
2.827
7
0.942
6
0.942
6
2.827
7
(0 0 0 0 0 0 1 0 0 0
0 0)
2.836
0
0.945
3
0.945
3
2.836
0
0.945
3
2.836
0
2.836
0
0.945
3
2.836
0
8.507
9
10.39
86
0.000
0
(0 0 0 0 0 0 0 1 0 0
0 0)
0.401
1
1.203
2
0.401
1
0.401
1
4.411
6
0.401
1
4.411
6
0.000
0
1.203
2
0.401
1
0.401
1
1.203
2
(0 0 0 0 0 0 0 0 1 0
0 0)
2.836
0
1.260
5
1.260
5
3.781
4
0.315
1
2.205
8
0.315
1
4.411
6
0.630
2
1.890
7
1.890
7
0.630
2
(0 0 0 0 0 0 0 0 0 1
0 0)
1.885
2
1.885
2
5.655
5
0.471
3
8.011
9
0.942
6
6.598
0
1.413
9
2.827
7
0.942
6
0.942
6
2.827
7
(0 0 0 0 0 0 0 0 0 0
1 0)
0.401
1
1.203
2
0.401
1
0.401
1
4.411
6
0.401
1
4.411
6
0.000
0
1.203
2
0.401
1
0.401
1
1.203
2
(0 0 0 0 0 0 0 0 0 0
0 1)
0.630
2
1.890
7
0.000
0
6.932
5
5.672
0
3.781
4
1.890
7
0.630
2
3.781
4
0.630
2
1.890
7
1.890
7
Total Weight
20.09
89
16.97
64
29.78
80
34.83
16
45.64
43
24.28
68
35.59
76
24.57
07
25.73
67
24.20
08
29.87
28
17.22
87
Total Average
Weight
1.674
9
1.414
7
2.482
3
2.902
6
3.803
7
2.023
9
2.966
5
2.047
6
2.144
7
2.016
7
2.489
4
1.435
7
V. CONCLUSION
Using A new fuzzy model Triangular Fuzzy Cognitive Maps
(TrFCM) gives the ranking for the causes of suicide thought in
domestic violence are 3.8037- Dowry and Harassment, 2.9665-
Lack of Physical Attraction/Boredom in Marriage, 2.9026-
Low Tolerance and Rigidity (Rough and Stiff Manner),
2.4894- Family Background, 2.4823- Incompatibility (Sexual
dissatisfaction), 2.1447- Child rearing issues, 2.0476- Family
Pressure, 2.0239- Lack of Commitment , 2.0167- Lack of
Communication, 1.6749-High Expectations, 1.4357- Religious
and Cultural Strains, 1.4147- Adultery (Illegal relationship) in
this research we found that, every marriage couple is not
having the child rearing issues, it’s happening 1 out of 100 or o
1 out of 200 divorce case. When we use Fuzzy Cognitive Maps
(FCM) the above causes are ON stage. But this new model
gives the ranking of the causes of the problem. This is the
beauty of this Triangular Fuzzy Cognitive Maps (TrFCM).
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