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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

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.

II.

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.

Keywords - Fuzzy, Fuzzy Cognitive Maps, Combined FCM, Gender role, women empowerment, violence against women. I.

FUNDAMENTALS OF COMBINED OVERLAP BLOCK FCM

B.

Definition

When the nodes of the FCM are fuzzy sets then they are called as fuzzy nodes.

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.

C.

Definition

A.

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.

FCMs with edge weights or causalities from the set {-1, 0, 1} are called simple FCMs. D.

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).

E. 67

Definition

Definition


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 Let C1, C2,… , Cn be the nodes of an FCM. Let A= (a1, a2,.. , Let P be the problem under investigation. Suppose let {C1, C2, an), where ai ( i  j ) {0,1}. A is called the instantaneous state ...,Cn} be n concepts associated with P (n very large) . Now vector and it denotes the on-off position of the node at an divide the number of concepts {C1, C2, ...,Cn} into classes S1,...,St where the classes are such that instant. ai = 0 if ai is off ai = 1 if ai is on, where i = 1, 2, , n. F.

(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.

Definition

Let C1, C2,…, Cn

be the nodes of and FCM.

C 1 C 2 , C 2 C 3 , C 3 C 4 , ..., C i C

j

Let

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.

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.

Definition

An FCM with cycles is said to have a feedback. H.

Definition 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

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 C 1 C 2 , C 2 C 3 , C 3 C 4 , ..., C n  1 C n 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 C i, for i =1, 2,…, n. The equilibrium state for this dynamical system is called the hidden pattern. J.

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}.

Definition

The directed graph and the relation matrix for the class S1 = {C1, C2, C3, C4,} given by the expert are as follows:

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.

C3

C4

Fig 1

s1

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.

C2

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.

C1

      

0

1

1

1

0

1

0

1

0

1

1

1

1   1  0   0 

The directed graph and the relation matrix for the class S 2 = {C3, C4, C5,C6} given by the expert are as follows:

Definition 68


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

C3

C3

C4

C4

C1

C5

C2

C5

C6

C6

Fig 2       

s2

C7

0

0

0

1

0

0

1

0

0

1

1

0

Fig 5

1   1  1   0 

c1 c1   c2  c3   c4  A  c5   c6  c7   c8  

The directed graph and the relation matrix for the class S 3 = {C5, C6, C7, C8} given by the expert is as follows: C5

C8

C6

c2

c3

c4

c5

c6

c7

0

2

1

1

0

0

1

2

0

1

1

0

0

1 0

0

1

0

0

0

1

1

1

2

0

0

1

0

0

0

1

0

0

2

1

0

0

1

1

0

0

1

1

1

0

0

0

1

0

1

1

0

0

1

1

0

c8 1   0  0   0  1   1  2    0 

The effect of X on the dynamical system A is given by:

C7

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:

C8

Fig 3

s3

      

0

1

1

0

0

1

0

1

0

1

1

0

1   1  1   0 

The directed graph and the relation matrix for the class S 4 ={ C7, C8, C1, C2} given by the expert are as follows: C7

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.

C8

C1

C2

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)

Fig 4

s4

      

0

1

1

0

0

1

1

1

0

1

0

1

1   1  1   0 

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 Sexselective preference for boy child is taken as the ON state and all other nodes are in the OFF state.

IV.

(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) 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

The combined directed graph and combined overlap block FCM of equal sizes is are follows: 69


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

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. REFERENCES [1] Axelrod, R. (1976), Structure of decision: The cognitive maps of political elites. Princeton, NJ: Princeton University Press. [2] Beal, C. [1994], Boys and Girls: The Development of Gender Roles. New York, NY: mcgraw- Hill. [3] Fafunwa, B.A. (1974), History of Education in Nigeria, London: Allen & Unwin, I974 Pp. 264. [4] Government of India. (2008), India Country Report: To prevent and combat trafficking and commercial sexual exploitation of children and women, World Congress III Against Sexual Exploitation of Children and Adolescents, Rio de Janeiro, Brazil, November 2008. [5] Kandasamy, V.W.B. and A.V. Devadoss. (2004), â&#x20AC;&#x153;Some New Fuzzy Techniquesâ&#x20AC;?, Jour. of inst. of Math. & Comp.Sci. (Math.ser.), Vol. 17, No.2, (2004 ), Pp.157- 160. [6] Klir G.J, and B. Yuan. (1997), Fuzzy sets and Fuzzy logic: Theory and Application, Prentice hall of India private limited, New Delhi. [7] Kosko, B.(1986), Fuzzy Cognitive Maps, International Journal of manmachine studies, January,1986, Pp.62-75. [8] UNICEF. (2012), Progress for Children: A report card on Adolescents, 3 United Nations Plaza, New York, NY 10017, USA.

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Analyzing the Role of a Family in Constructing Gender Roles Using Combined Overlap Block Fuzzy Cogni  

Family, as a social institution and as the fundamental unit of the society, plays a vital role in forming persons. We become full-fledged me...

Analyzing the Role of a Family in Constructing Gender Roles Using Combined Overlap Block Fuzzy Cogni  

Family, as a social institution and as the fundamental unit of the society, plays a vital role in forming persons. We become full-fledged me...

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