Family, as a social institution and as the fundamental unit of the society, plays a vital role in forming persons. We become full-fledged members of the society through the process of socialization which starts in the family. It provides the first foundational formation of personhood. Especially in traditional societies like India the role of the family assumes even greater importance. We learn to differentiate and to discriminate between man and woman from the role our parents play. In this paper we analyze the role of the family in constructing gender roles using Combined Overlap Block Fuzzy Cognitive Maps

1. Integrated Intelligent Research (IIR) International Journal of Data Mining Techniques and Applications
Volume: 02 Issue: 02 December 2013 Page No.67-70
ISSN: 2278-2419
67
Analyzing the Role of a Family in Constructing
Gender Roles Using Combined Overlap Block
Fuzzy Cognitive Maps
A.Victor Devadoss1
and K.Sudha2
1
Head & Associate Professor, Department of Mathematics, Loyola College, Chennai
2
Ph.D Research Scholar, Department of Mathematics, Loyola College, Chennai
Email: hanivictor@ymail.com,ashu.8788@gmail.com
Abstract - Family, as a social institution and as the
fundamental unit of the society, plays a vital role in forming
persons. We become full-fledged members of the society
through the process of socialization which starts in the family.
It provides the first foundational formation of personhood.
Especially in traditional societies like India the role of the
family assumes even greater importance. We learn to
differentiate and to discriminate between man and woman from
the role our parents play. In this paper we analyze the role of
the family in constructing gender roles using Combined
Overlap Block Fuzzy Cognitive Maps.
Keywords - Fuzzy, Fuzzy Cognitive Maps, Combined FCM,
Gender role, women empowerment, violence against women.
I. INTRODUCTION
Gender refers to the identification of the sexes usually
influenced by cultural factors like religion, politics social
factors and education. Fafunwa (1974), who analysed the role
of women in the African society, defines the traditional roles of
women to be mainly that of childbearing, housekeeping and the
sustenance of agricultural activities.
A. The Role of a Family
Family, as a social system and the fundamental unit of society,
plays vital role in building persons. In provides the first
foundational formation of personhood. It teaches what a person
is, what a boy is or what a girl is. As a social institution it is
also vulnerable to all kinds of social prejudices and
stereotypes, which it acquires from the society and teaches
them to the members of the society. Thus it plays a vital role in
constructing gender roles and gender relations. We first learn
to distinguish and discriminate men from women in family by
looking at the roles our parents play. As a Tamil poem says the
child learns to call her father when newspaper man comes and
call her mother when milkman comes without anyone to teach
her so. A recent survey, quoted in Unicef’s report, found
that 57 percent of adolescent Indian boys (15-19 years)
justified wife-beating by husbands as compared to 53 percent
female adolescents during 2002-2010. This clearly shows the
importance of the role played by social institutions like family
in defining and determining gender roles. In this paper we
analyze the role of the family in gender roles and gender
relations. For this we interviewed 25 families in Chennai. We
use Combined Overlap Block Fuzzy Cognitive Maps
(COBFCM).
II. FUNDAMENTALS OF COMBINED OVERLAP
BLOCK FCM
In this section we just recall that the fundamentals of Fuzzy
cognitive maps
A. Definition
An FCM is a directed graph with concepts like policies, events
etc. as nodes and causalities as edges. It represents causal
relationship between concepts.
B. Definition
When the nodes of the FCM are fuzzy sets then they are called
as fuzzy nodes.
C. Definition
FCMs with edge weights or causalities from the set {-1, 0, 1}
are called simple FCMs.
D. Definition
The edges eij take values in the fuzzy causal interval [–1, 1]. eij
= 0 indicates no causality, eij > 0 indicates causal increase Cj
increases as Ci increases (or Cj
decreases as Ci decreases). eij < 0 indicates causal decrease or
negative causality. Cj decreases as Ci increases (and or Cj
increases as Ci decreases). Simple FCMs have edge values in
{–1, 0, 1}. Then if causality occurs, it occurs to a maximal
positive or negative degree. Simple FCMs provide a quick first
approximation to an expert stand or printed causal knowledge.
If increase (or decrease) in one concept leads to increase (or
decrease) in another, then we give the value 1. If there exists
no relation between two concepts, the value 0 is given. If
increase (or decrease) in one concept decreases (or increases)
another, then we give the value –1. Thus FCMs are described
in this way. Consider the nodes or concepts C1
, , Cn of the FCM. Suppose the directed graph is drawn using
edge weight eij {0, 1, -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 the 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.
E. Definition

2. Integrated Intelligent Research (IIR) International Journal of Data Mining Techniques and Applications
Volume: 02 Issue: 02 December 2013 Page No.67-70
ISSN: 2278-2419
68
Let C1, C2,… , Cn be the nodes of an FCM. Let A= (a1, a2,.. ,
an), where ai ( )i j {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 ai = 1 if ai is on, where i = 1, 2, , n.
F. 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 cyclic. An FCM is
said to be acyclic if it does not possess any directed cycle.
G. Definition
An FCM with cycles is said to have a feedback.
H. 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.
I. Definition
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 goes 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.
J. Definition
If the equilibrium state of a dynamical system is a unique state
vector, then it is called a fixed point. Consider an 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., the state vector remain as
(1, 0, 0,…, 1). This state vector (1, 0, …, 0, 1) is called the
fixed point.
K. 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 of the FCM.
L. Definition
Finite number of FCMs can be combined together to produce
the joint effect of all the FCMs. Let E1, E2, , Ep be adjacency
matrices of the FCMs with nodes C1, C2, , Cn, then the
combined FCM is got by adding all the adjacency matrices
E1,… , Ep. We denote the combined FCM adjacency matrix by
E = E1 + E2 + …+ Ep.
M. Definition
Let P be the problem under investigation. Suppose let {C1, C2,
...,Cn} be n concepts associated with P (n very large) . Now
divide the number of concepts {C1, C2, ...,Cn} into classes
S1,...,St where the classes are such that
(i) Si Si+1 Ø where (i = 1,2,...,t-1)
(ii) Si = { C1, C2, ...,Cn }
(iii) |Si| |Sj| if i j in general.
Now we obtain the FCM associated with each of the classes S1,
…, St. We determine the relational matrix associated with each
Si. Using these matrices we obtain a n × n matrix. This n × n
matrix is the matrix associated with the Combined Overlap
Block FCM (COBFCM) of blocks of same sizes.
III. ADAPTATION OF COBFCM TO THE
PROBLEM
Using the linguistic questionnaire and the experts opinion we
have taken the following eight concepts {C1, C2, ...,C8}. These
concepts are taken as the main nodes for our problem.
C1 – Sex-selective preferences for boy child
C2– Using ‘gender-sensitive statements’ in the family
C3 – Assigning ‘gender-specific’ works
C4 – Social status enjoyed by the family
C5 – Religious background
C6 – The role of siblings and relatives
C7 – Cultural values/stereotypes.
C8 – Educational status
Now we proceed on to apply the effect of combined overlap
block FCM of equal length. Let us consider the eight concepts
{C1, C2, ...,C8}. We divide these concepts into cyclic way of
classes, each having just four concepts in the following way:
S1, = {C1, C2, C3, C4,}, S2 ={C3, C4, C5,C6}, S3 = {C5,C6, C7
, C8, }, S4 ={ C7, C8, C1, C2}.
The directed graph and the relation matrix for the class S1 =
{C1, C2, C3, C4,} given by the expert are as follows:
C1
C3
C2
C4
Fig 1
1
0 1 1 1
1 0 1 1
0 1 0 0
1 1 1 0
s
 
 
 
 
 
 
The directed graph and the relation matrix for the class S2 =
{C3, C4, C5,C6} given by the expert are as follows:

3. Integrated Intelligent Research (IIR) International Journal of Data Mining Techniques and Applications
Volume: 02 Issue: 02 December 2013 Page No.67-70
ISSN: 2278-2419
69
C3
C5
C4
C6
Fig 2
2
0 0 0 1
1 0 0 1
1 0 0 1
1 1 0 0
s
 
 
 
 
 
 
The directed graph and the relation matrix for the class S3 =
{C5, C6, C7, C8} given by the expert is as follows:
C5
C7
C6
C8
Fig 3
3
0 1 1 1
0 0 1 1
0 1 0 1
1 1 0 0
s
 
 
 
 
 
 
The directed graph and the relation matrix for the class S4 ={
C7, C8, C1, C2} given by the expert are as follows:
C7
C1
C8
C2
Fig 4
4
0 1 1 1
0 0 1 1
1 1 0 1
1 0 1 0
s
 
 
 
 
 
 
Now using the matrix A of the Combined overlap block FCM
we determine the hidden pattern. Suppose the concept C1 is in
the ON state and all the nodes are in the OFF state. Let the
initial input vector be X = (1 0 0 0 0 0 0 0 ), where Sex-
selective preference for boy child is taken as the ON state and
all other nodes are in the OFF state.
The combined directed graph and combined overlap block
FCM of equal sizes is are follows:
C3
C1
C4
C2 C5 C6
C7 C8
Fig 5
1 2 3 4 5 6 7 8
c c c c c c c c
1
2
3
4
5
6
7
8
0 2 1 1 0 0 1 1
2 0 1 1 0 0 1 0
0 1 0 0 0 1 0 0
1 1 2 0 0 1 0 0
0 0 1 0 0 2 1 1
0 0 1 1 0 0 1 1
1 1 0 0 0 1 0 2
1 1 0 0 1 1 0 0
c
c
c
c
A
c
c
c
c
 
 
 
 
 
 

 
 
 
 
 
 
 
The effect of X on the dynamical system A is given by:
XA = ( 0 2 1 1 0 0 1 1)
↪ ( 1 1 1 1 0 0 1 1) = X1 (say)
X1 A = ( 5 6 4 2 1 4 2 3)
↪ ( 1 1 1 1 1 1 1 1) = X2 (say)
X2 A = ( 5 6 6 3 1 6 4 5 )
↪ ( 1 1 1 1 1 1 1 1) = X3 = X2Let us repeat the calculation
choosing another input vector X = (0 0 0 0 0 0 0 1), where
Educational status of the family is taken as the ON state and all
other nodes are in the OFF state. The effect of X on the
dynamical system A is given by:
XA = ( 1 1 0 0 1 1 0 0)
↪ ( 1 1 0 0 1 1 0 1) = X1 (say)
X1 A = ( 3 3 4 3 1 3 4 3)
↪ ( 1 1 1 1 1 1 1 1) = X2 (say)
X2 A = ( 5 6 6 3 1 6 4 5)
↪ ( 1 1 1 1 1 1 1 1 ) = X3 = X2(where ↪ denotes the
resultant vector after thresholding and updating ), X3 is the
hidden pattern, which is the fixed point.
Table 1
Input vector Limit point
( 1 0 0 0 0 0 0 0) ( 1 1 1 1 1 1 1 1)
( 0 1 0 0 0 0 0 0) ( 1 1 1 1 1 1 1 1)
( 0 0 1 0 0 0 0 0) ( 1 1 1 1 1 1 1 1)
( 0 0 0 1 0 0 0 0) ( 1 1 1 1 1 1 1 1)
(0 0 0 0 1 0 0 0) ( 1 1 1 1 1 1 1 1)
( 0 0 0 0 0 1 0 0) ( 1 1 1 1 1 1 1 1)
( 0 0 0 0 0 0 1 0) ( 1 1 1 1 1 1 1 1)
( 0 0 0 0 0 0 0 1) ( 1 1 1 1 1 1 1 1)
IV. CONCLUSION AND SUGGESTIONS
From the table above we can easily see that the family plays a
role in building gender roles in the society. For various input
vector we get the same limit point which means that all these
concepts do affect the gender roles. The terms of relationships
in a family are taken for granted and the rigidly defined gender
roles assigned within a family are hardly refuted. To bring

4. Integrated Intelligent Research (IIR) International Journal of Data Mining Techniques and Applications
Volume: 02 Issue: 02 December 2013 Page No.67-70
ISSN: 2278-2419
70
about a fundamental change in the society at large, one should
begin from family.Sex-selective preference for boy child by
the parents and the relatives is usually justified by the relative
difference in cost spent for the education and marriage of a girl
and a boy. Therefore the abolition of dowry system becomes
vital to bring about a change in the minds of the parents and
relatives.Parents should be trained or instructed over their use
of gender sensitive and assignment of gender-specific works
statements in the family. As educational status also plays a role
in building gender role, education of girl children should be
compulsorily promoted.
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