### Study on Impact of Media on Education Using Fuzzy Relational Maps

Josephine Suganya J
2014 International Journal of Computing Algorithm
In this paper we bring out the depth of impact of media upon the growth of education. Education moulds an individual to take firm decisions on issues. It makes to feel independent and leads to a more exposed world. Media is a very powerful tool to explore the world and have access to the world. Internet, Mobile phones, etc., helps for an easy access to any part of the world at our finger tips. Media may lead us to both constructive and destructive mechanism depending the way we deal with
more » ... we use FRM model to study and analyze the impact of media on education. Fuzzy Relational Maps (FRM),Media, Education. I. SECTION ONE: FUZZY RELATIONAL MAPS ( FRMS) The new notion called Fuzzy Relational Maps (FRMs) was introduced by Dr. W.B.Vasantha and Yasmin Sultana in the year 2000. In FRMs we divide the very casual associations into two disjoint units, like for example the relation between a teacher and a student or relation; between an employee and an employer or a relation; between the parent and the child in the case of school dropouts and so on. In these situations we see that we can bring out the casual relations existing between an employee and employer or parent and child and so on. Thus for us to define a FRM we need a domain space and a range space which are disjoint in the sense of concepts. We further assume no intermediate relations exist within the domain and the range space. The number of elements in the range space need not in general be equal to the number of elements in the domain space.In our discussion the elements of the domain space are taken from the real vector space of dimension n and that of the range space are real vectors from the vector space of dimension m (m in general need not be equal to n). We denote by R the set of nodes R 1 , ... , R m of the range space, where R i = {(x 1, x 2 , ..., x m ) / x j = 0 or 1} for i = 1, ... ,m. If x i = 1 it means that the node R i is in the ON state and if x i = 0 it means that the node R i is in the OFF state. Similarly D denotes the nodes D 1 ,...,D n of the domain space where D i = {(x 1, ..., x n ) / x j = 0 or 1} for i = 1, ..., n. If x i = 1, it means that the node D i is in the on state and if x i = 0 it means that the node D i is in the off state.A FRM is a directed graph or a map from D to R with concepts like policies or events etc. as nodes and causalities as edges. It represents casual relations between spaces D and R. Let D i and R j denote the two nodes of an FRM. The directed edge from D to R denotes the casuality of D on R , called relations. Every edge in the FRM is weighted with a number in the set {0, 1}.Let e i j be the weight of the edge D i R j ,e i j  {0.1}. The weight of the edge D i R j is positive if increase in D i implies increase in R j or decrease in D i implies decrease in R j . i.e. casuality of D i on R j is 1. If e i j = 0 then D i does not have any effect on R j . We do not discuss the cases when increase in D i implies decrease in R j or decrease in D i implies increase in R j .When the nodes of the FRM are fuzzy sets, then they are called fuzzy nodes, FRMs with edge weights {0, 1) are called simple FRMs.Let D 1 , ...,D n be the nodes of the domain space D of an FRM and R 1 , ..., R m be the nodes of the range space R of an FRM.Let the matrix E be defined as E = (e ij ) where e i j  {0, 1}; is the weight of the directed edge D i R j ( or R j D i ), E is called the relational matrix of the FRM.It is pertinent to mention here that unlike the FCMs, the FRMs can be a rectangular matrix; with rows corresponding to the domain space and columns corresponding to the range space. This is one of the marked difference between FRMs and FCMs. Let D 1 , ...,D n and R 1 ,...,R m be the nodes of an FRM. Let D i R j (or R j D i ) be the edges of an FRM, j = 1, ..., m, i = 1, ..., n. The edges form a directed cycle if it possesses a directed cycle. An FRM is said to be acycle if it does not posses any directed cycle.An FRM with cycles is said to have a feed back when there is a feed back in the FRM, i.e. when the casual relations flow through a cycle in a revolutionary manner the FRM is called a dynamical system.Let D i R j ( orR j D i ), 1  j  m, 1 i n. When R j ( or D i ) is switched on and if casuality flows through edges of the cycle and if it again causes R i (D j ), we say that the dynamical system goes round and round. This is true for any node R i (or D j ) for 1 im, ( or 1  j  n). The equilibrium state of this dynamical system is called the hidden pattern. If the equilibrium state of the dynamical system is a unique state vector, then it is called a fixed point. Consider an FRM with R 1 , ..., R m and D 1 , ..., D n as nodes. For example let us start the dynamical system by switching on R 1 or D 1 . Let us assume that the FRM settles down with R 1 and R m ( or D 1 and D n ) on i.e. the state vector remains as (10...01) in R [ or (10...01) in D], this state vector is called the fixed point.If the FRM settles down with a state vector repeating in the form A 1  A 2  ....  A i  A 1 or ( B 1  B 2  ...  B i  B 1 ) then this equilibrium is called a limit cycle. A. Methods of determination of hidden pattern. Let R 1 , ..., R m and D 1 , ..., D n be the nodes of a FRM with feed back. Let E be the n  m relational matrix. Let us find a hidden pattern when D 1 is switched on i.e. when an input is given as vector A 1 = (1000...0) in D the data should pass through the relational matrix E. This is done by multiplying A 1 with the relational matrix E. Let A 1 E = (r 1 , ... ,r m ) after thresholding and updating the resultant vector (say B) belongs to R. Now we pass on B into E T and obtain BE T . After thresholding and updating BE T we see the resultant vector say A 2 belongs to D.