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The Effect of Globalization on Education using Fuzzy Associative Memories (FAMs) A. Victor Devadoss1, S. Christopher 2 PG and Research Department of Mathematics, Loyola College, Chennai-34,India 2 Department of Mathematics, School of Engineering and Technology Surya Group of Institutions,Vikiravandi, India Abstract Globalization has wide ranging potential to influence all sectors of development. Besides its impact on the pace and pattern of economic development, it also casts shadow on the system of education. It would, therefore, be pertinent to analyze its impact on the process and progress of education. The impact of globalization on education and the manner in which the system should respond to the needs of globalization would require to be studied basically Education is a favorite catchphrase of journalist and politicians. It has also become a key idea for business theory and a practice, and entered academic debates. But what people mean by “globalization” is often confused and confusing. In this research paper we examine some key themes in the theory and experiences of globalization in education using fuzzy relational equations. We have arrived at interesting conclusions.This paper has four sections. In section one we recall the notion of Fuzzy Associative Memories (FAM) and its properties. In section two we describe the problem. In Section three we adopt FAM to this problem and analyze the problem. Section four gives the conclusions based on our study. Keywords: Globalization, Education, Fuzzy Associative Memories (FAM), special fuzzy matrix. 1

1. Fuzzy Associative Memories (FAM) And Its Properties. In this section we give the essential definitions and results so as to make the paper a self contained one. The Unit hypercube In = [0, 1]n = [0, 1] ... [0, 1] product of [0, 1] taken n-times consists of the set of all vectors of length n and the coordinates are taken from the unit interval [0, 1]. In general fuzzy setsare maps from a universal set X to the unit interval [0,1]. i.e., : X [0, 1]. Throughout the paper by a fuzzy set we mean a point in the unit hypercube. Thus in this paper we do not take the usual fuzzy sets i.e., a map from a universal set X to the unit interval [0, 1]. Fuzzy system define mappings between cubes. Fuzzy system S maps fuzzy sets to fuzzy sets . Thus the fuzzy system S is a n

p

transformation. i.e., S : I where n and p are finite positive integers. The n-dimensional n

unit hypercube I consists of all the fuzzy

subsets of the domain space X = {x1, ... ,xn} ; p

x i R, i=1,...,n. Similarly I consists of all the fuzzy subsets of the range space Y = {y1,...,yp}; yi R, i=1,...,p. Hence X denotes n

p

a subset of R and Y denotes the subset of R . The function f maps n-vectors in X to pvectors in Y. The continuous function f maps small changes in input to small changes in output i.e., if the input patterns are close to one another then the output patterns are close to one another. The system maps similar inputs to similar outputs and so estimates continuous functions. Fuzzy Associative Memories (FAM) n

p

Fuzzy system S : I maps balls of fuzzy n

p

sets in I to balls of fuzzy sets in . These continuous fuzzy system behaves as an associative memory known as fuzzy associative memory. Let A and B be the fuzzy subsets of X and Y respectively where X = {x1, ... ,xn} and Y= {y1,...,yp}. A defines a point in the n-

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Indo-Bhutan International Conference On Gross National Happiness Pages: 178-182 n

dimensional unit hypercube I and B defines a p

point in the p-dimensional unit hypercube I . Equivalently A and B define the membership functions m and m respectively that map the A

B

elements x of X and y of Y to [0, 1]. The i

j

membership values will be known as fit values which indicate how much x belongs to i

or fits in the subset A and how much y

j

belongs to or fits in the subset B. Therefore we say that {x1, ... ,xn} is the fit vector that represents A and {y1,...,yp} is the fit vector that represents B . We describe this with the abstract functions mA : X [0, 1] mB: Y [0, 1]. Since in this paper the fuzzy sets A and B are points in unit hypercube, one can view A and B as natural vectors. Represent A and B by numerical fit vectors (if the fit values are given numerical values then the fit vector is known as numerical fit vector). A = {a1, ... ,an }and B = {b1, ... ,bp}, where ai = mA(xi) and bj = mB(yj).The fuzzy set association (Ai, Bi) is named as a “rule”. The antecedent term Ai in the fuzzy set association (Ai, Bi) is known as input associant and the consequent term Bi is known as output associant. The FAM system maps points Aj near Ai to points Bj near Bi. The closer Aj is to Ai, the closer the point (Aj, Bj) is to (Ai, Bi) in the n

p

product space I I . In this sense FAMs map n

p

balls in I to balls in I . That is only FAM can give results which are graded or it not only gives the solutions but the gradation of importance of each solution. 2. Description of the Problem. Globalization has wide ranging potential to influence all sectors of development. Besides its impact on the pace and pattern of economic development, it also casts shadow on the

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system of education. It would, therefore, be pertinent to analyze its impact on the process and progress of education. The impact of globalization on education and the manner in which the system should respond to the needs of globalization would require to be studied basically under two broad heads: 1. The needed reforms within the educational system like content, equity and excellence etc. 2. The fall out of globalization, this will entail determining strategies relating to the impending internationalization of education. It also needs to be stressed that education should help to engender a new “ humanism that contains an essential ethical component and sets considerable store by knowledge of, and respect for culture and spiritual values of different civilizations, as a much needed counter weight to globalization that would otherwise be seen only in economical or technological terms. The sense of shared values as a common destiny is in fact the basis on which any scheme of international cooperation must be founded “ The merits of internationalization of education are: 1. Education will improve if it is internationalized and healthy competition takes place; 2. It will provide global opportunities and promote international good will; 3. It will encourage exchange of scholars. This can be done by involvement of reputed scholars in the respective countries in curriculum designing and transaction of knowledge. Notwithstanding of the merits of internationalization of education, it will be harmful for our country to allow an unregulated entry of foreign institutions in India. Quite a few of these institutions are dubious quality – some of them not even been recognized in their own countries.

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It appears, as though the phenomenon of globalization will mean many different things for education. Most certainly, in the near future, “ it will mean a more competitive and deregulated educational system modeled after free market but with more pressure on it to assure that the next generation of workers are prepared for some amorphous ‘job market of 21st century ‘. It will also mean …” that educational system will increasingly provides the sites of struggle over the meaning and power of national identity and a national culture. And finally, schools will no doubt also be the various counter- hegemonic movements and pedagogies”. (Wells, et.al, 1998) We have made a sample survey of around 50 people living in Chennai. They were interviewed using a linguistic questionnaire. The Fuzzy concepts, i.e. attributes are first given in the form of matrix relational equations and then solved. In this paper we use this method to study the effect of Globalization in Education. The following attributes are taken as the main point for study. The dimensions of Globalizations are world systems, Global culture, Global Society, and Global capitalism. The attributes of impact of globalization on world education are Globalization of labour markets; market forces in education, Cross–cultural and transnational trends in education provision; knowledge as global construct, Global organizations and agenda in education, emerging global and regional structures in education and Students, educational professionals and knowledge workers in a globalizing world.

finite. On the suggestion of the experts and the Stake holders of education the following attributes are taken. C 1 - Globalization of labour markets; market forces in education. C 2 - Cross–cultural and trans-national trends in education provision; knowledge as global Construct. C 3 - Global organizations and agenda in education. C 4 - Emerging global and regional structures in education C5 Students, educational professionals and knowledge workers in a globalizing world. G 1 - World systems G 2 - Global culture G 3 - Global Society G 4 – Global capitalism Here we analyze this problem only on the aspect of Globalizations and impact of globalization on world education. The related fuzzy matrix M formulated using the experts opinion is as follows:

3. Adaptation of FAM to the Problem. Let us consider ther e are n attributes say x 1 , ... ,x n wher e n is finit e

i.e. Globalization of labour markets; market forces in education., Global organizations and agenda in education, and Students, educational professionals and knowledge workers in a globalising world. are taken as on state of the fit vector. We comput e the r ecalled component by taking the

associated with the impact of globalization on world education and let y 1 , ... ,y p be the attributes associated with the dimensions of Globalizations , wher e p is

C1 G1 G2 M = G3 G4

C2 .8 0 .5 0

.8 .9 T M = .6 .8 . 4

0 0 .2 .7 .9

C3 .9 0 .6 0

.6 .2 .6 0

.5 .6 .6 .9 .6

C4

C5

.8 .7 .9 9

0 0 0 .9 .4

.4 .9 .6 6

Consider a fit vector B=(1 0 1 0 1)

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Indo-Bhutan International Conference On Gross National Happiness Pages: 178-182 fuzzy inner product of fit vector B with j

th

column of M for each column.

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professionals and knowledge workers in a globalizing world.

T

B o M = A = (.8 .9 .6 .4) Accor ding to the fit vector A, we see that the Global cultur e is cr eated which has the maximum value 0.9. Secondly the fit vector reads world systems being created with second maximum valu e 0.8. The Global Society is for med is the thir d graded value. Taking the resultant A as the fit vector now we calculate A o M. i.e., A o M = (.8 .8 .6 .8 .9). Since 0.9 is the largest value it implies that ther e priority is given to Students, educational professionals and knowledge workers in a globalising world. Thus accor ding to this expert, the first place is given to C 5 . The next largest value is 0.8 given to the attributes C 1 ,C 2 and C 4 wher e Globalization of labour markets; market forces in education., Cross–cultural and trans-national trends in education provision; knowledge as global Construct and Emerging global and regional structures in education are next preferred Now suppose we consider the fit vector B 1 = (1 0 0 0 1) Consider

B1

o

T

M ,

as

befor e

we

compute by r ecalling fit vector as T

B 1 o M = (.8. 9. 6 .4) = A 1 . Thus from this resultant fit vector we see that the on state of C 3 does not influence the model the resultant fit vector is the same. Suppose we take A 1 = (1 0 1 1) which implies that world systems, Global Society, and Global capitalism are in the on state we get A 2 o M = (0 0 .2 .9 .9). The r esultant vector means that the highest grade is being given to protect emerging global and regional structures in education and Students, educational

4. Conclusions and Suggestions. The following conclusions are not only derived from the three experts described in this paper but all the fifty opinions of stake holders of education are used and some of the stake holders of education whom we have interviewed are also ingrained in this analysis. 01. Globalization has impacted upon the nature of the agencies those ‘school’ children, young people and adults. 02.The question we are facing now is , to what extended is the educational endeavor affected by the processes of globalization that are threatening the autonomy of national educational systems and the sovereignty of the nation-state as the ultimate rule in democratic societies ? 03. How is globalization changing the fundamental conditions of an educational system premised on fitting into a community, a community characterized by proximity and familiarity?. 04. Competition, however, can bring out the best and worst in us. 05. At the first glances it would seem that national government still has considerable freedom to intervene in the education systems. It has significantly increased the scale of central direction and intervention through the use of national curriculum requirements, special initiatives (involving direct fund) and other institutional means, However, as soon as we examine the nature of this expansion of intervention we can see that the overriding concern is with economic growth and international competitiveness – and that the efforts of politicians have been deeply flawed and their record dismal. References [1]George J. Klir and Bo Yuan, [1977]. “Fuzzy sets and fuzzy logic theory and Applications”. Prentice – Hall of India Private Limited, New Delhi.

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Indo-Bhutan International Conference On Gross National Happiness Pages: 178-182 [2]Kellner,D.(1997) ‘Globalization and the postmodern turn’, UCLA [3]Cogburn, D.L. (1998) ‘Globalization, knowledge,education and training in the global world’, Conference paper for the InfoEhics98,UNESCO [4]Giddens, A. (1990) Consequences of Modernity, Cambridge: Polity. [5]Sen,A. (2002) ‘How to judge globalization’, The American Prospect online,

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http://www.p stake holders of education rospect.org/print/V13/1/sen-.htm [6]Kosko, Bart (1992). Neural Networks and Fuzzy Systems, Prentice – Hall, Englewood Cliffs, New Jersey. [7]Kosko, Bart (1986), Fuzzy Cognitive Maps, International Journal of Man – Machine Studies, 34, 65– 75. [8]Starr M.K (1978) Operations Management, Prentice Hall Inc., USA.

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