Scibay Journal ofmathematics Vol. 2 (2) A study on benefits of globalization of business using fuzzy cognitive maps

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1 Scibay Journal ofmathematics Vol. 2 (2) A study on benefits of globalization of business using fuzzy cognitive maps N.Vijayaraghavan, S.Narasimhan and M.Baskar Mathematics Division, Department of Science and Humanities, KCG college of Technology, Chennai, India- 697 Abstract Globalization is the intensification of world-wide social relationships which link distant places in such a way that local happenings are shaped by events occurring many miles away and vice-versa. Well, the question: what exactly is globalization? is very easy to raise, but extremely difficult to answer. In this paper, however we propose to list and look at globalization impact on Business, and some benefits generated thereof. Fuzzy Cognitive Map (FCM) is a powerful method which analyses the data by directed graphs and connection matrices. Now we use this method to study globalization impact on the Business in India. Keywords:Globalization, Business, Benefits, Fuzzy Cognitive Map. Introduction In order to study the passenger transportation problem, matrix theory was developed by W.B.VasanthaKandhasamy and V.Indira. We use the same matrix theory to study this problem. This paper has four sections. In the first section, we discuss the methods of applications of FCM connection matrix. In section two, we discuss the globalization impact on Business in India and some Benefits generated thereof. The section three deals with the procedure, to find out the most common Benefit in globalization impact on Business in India by using FCM connection matrix. In final section, we discuss conclusions based on our research paper. Applications of FCM connection matrix: An FCM is a directed graph with concepts as nodes and causalities as edges. It represents causal relationship between concepts. When the nodes of the FCM are fuzzy sets then they are called as fuzzy nodes. FCMs with edge weights or causalities from the set {,, } are called simple FCMs. Let C, C 2,,C n be the nodes of an FCM. Suppose the directed graph is drawn using edge weight e ij {,, }. The matrix E is defined by E = (e ij) where e ij is the weight of the directed edge C ic j. E is called the adjacency matrix of the FCM, also known as the connection matrix of the FCM. Let C C 2, C 2C 3, C 3C 4,, C ic j 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. An FCM with cycles is said to have a feedback. If A = (a, a 2,, a n) where a i {, }, then A is called the instantaneous state vector and it denotes the on-off position of the node at an instant. a i = if a i is off and a i = if a i is on for i =, 2,, n.

2 Vijayaraghavan et al, Scibay Journal of Mathematics. Vol.2 (2)-5 If the FCM settles down with a state vector repeating in the form A A 2 A i A then this equilibrium is called a limit cycle. A = (a,, a n) is a vector which is passed into a dynamical system E. Then AE = (a',,a' n) after thresholding and updating the vector suppose we get (b,, b n) we denote that by (a', a' 2,, a' n) (b, b 2,, b n). Thus the symbol means the resultant vector has been thresholded and updated. The edges e ij take values in the fuzzy causal interval [, ]. e ij = indicates no causality, e ij> indicates causal increase i.e. C j increases as C i increases (or C j decreases as C i decreases). e ij< indicates causal decrease or negative causality i.e. C j decreases as C i increases (or C j increases as C i decreases). Simple FCMs have edge values in {,, }. Then if causality occurs, it occurs to a maximal positive or negative degree. Globalization impact on Business and some Benefits: The phenomenon of globalization, which refers to the rising trade and financial integration of the world economy, has gathered steam in recent decades. For instance, if consumers from different countries have a significant fraction of their investments in a particular stock market, then a decline in that stock market could induce a simultaneous decline in the demand for consumption and investment goods in these countries. Economic theory does not provide definitive guidance concerning the impact of increased trade and financial linkages on the degree of business cycle synchronization. International trade linkages generate both demand and supply-side spillovers across countries. For example, on the demand side, an investment or consumption boom in one country can generate increased demand for imports, boosting economies abroad. In theory, financial globalization can help developing countries to better manage output and consumption volatility. Indeed, a variety of theories imply that the volatility of consumption relative to that of output should decrease as the degree of financial integration increases; the essence of global financial diversification is that a country is able to shift some of its income risk to world markets. Since most developing countries are rather specialized in their output and factor endowment structures, they can, in theory, obtain even bigger gains than developed countries through international consumption risk sharing that is, by effectively selling off a stake in their domestic output in return for a stake in global output. Although it is difficult to find a simple relationship between financial globalization and growth or consumption volatility, there is some evidence of nonlinearities or threshold effects in the relationship. Financial globalization, in combination with good macroeconomic policies and good domestic governance, appears to be conducive to growth. Now we discuss this problem using FCM connection matrix method Description Of The Problem: The main aim of this paper is to list and look at globalization impact on the Business scenario, and some benefits generated thereof and then finding the most common benefit in globalization impact on Business by using FCM connection matrix. The eight paradoxes that are listed above are taken as nodes. i.e., C Business Expansion leads to economy of scale C 2 Access to resources C 3 Lowering price 2

3 Vijayaraghavan et al, Scibay Journal of Mathematics. Vol.2 (2)-5 C 4 Economic growth C 5 Technology transfer C 6 Job creator C 7 Joint venture C 8 Strategic alliance C 9 Globalization impact on Business in India The directed graph is drawn by taking these paradoxes C, C 2,, C 9 as nodes depicted inside the circles and the causalities among these nodes are denoted by the edges which is shown in the Figure C C 3 C 2 2 C 9 C 4 C 5 C 6 C 7 C 8 Figure: Directed graph. 3

4 Vijayaraghavan et al, Scibay Journal of Mathematics. Vol.2 (2)-5 The corresponding FCM connection matrix is represented by E E = Consider the first node C =. We hold C on the temporal associative memories recall process. Threshold signal functions synchronously update each concept after each pass, through the connection matrix E. We start with the Business Expansion leads to economy of scale A = ( ). The arrow indicates the threshold operation. Now A = ( ) A E = ( ) ( ) = A 2 A 2E = ( 2 ) ( ) = A 3 A 3E = ( 3 ) ( ) = A 4 A 4E = ( 2 5 ) ( ) = A 5 A 5E = ( 2 7 ) ( ) = A 6 A 6E = ( ) ( ) = A 7 = A 6 Since ( ) is a limit cycle, we see that Business Expansion leads to economy of scale influences all other Benefits. Conclusion: Here we give the conclusions based on the work which is discussed above. From the discussed fuzzy matrix, when we switch on the Business Expansion leads to economy of scale node, it automatically influences all other nodes to switch on. Therefore Business Expansion leads to economy of scale is the most common Benefit in globalization impact on the Business in India. Globalisation helps in bringing whole world as one village. Every consumer has free and frequent reach to the products of foreign countries. In a global world there is free flow or movement of improved technology. Globalization leads to high investment levels and therefore increased wealth. Wealth is generated through economic gains of globalization. It will possibly help decrease the rate of poverty and unemployment in several countries. Workers in developing countries now have moreoccupational choices than ever before. Production workers in developing 4

5 Vijayaraghavan et al, Scibay Journal of Mathematics. Vol.2 (2)-5 countries are notonly able to compete, they have a strong advantage over their counterparts in the industrialized world. This translates into increased opportunity References. R.E. Bellman, L.A. Zadeh, Decision Making in Fuzzy Environment, Management Science 7, 997,pp G.J. Klir,B.Yuan, Fuzzy sets and Fuzzy logic, Prentice Hall, New Jersey, B. Kosko, Neural Networks and Fuzzy Systems, Prentice Hall, Englewood Cliffs, New Jersey, B. Kosko, Fuzzy Cognitive Maps, InternationalJournal of Man-Machine Studies, 34, 986, pp W.B. VasanthaKandasamy,V. Indira, Applications of Fuzzy Cognitive Maps to determine the Maximum Utility of Route, Journal of FuzzyMaths. publ. by the International Fuzzy Mathematical Institute, 8,2, pp W.B. VasanthaKandasamy, S. Antony Raj, A.Victor Devadoss, Some new fuzzy techniques, Journalof Math & Comp. Sci. (Math.ser.), 7 (2), 24,pp W.B.VasanthaKandasamy,FlorentinSmarandache,Ilanthenral,Elementary Fuzzy Matrix Theory and Fuzzy Models for Social Scientists,Printed in UnitedStates of America, W.B. VasanthaKandasamy,FlorentinSmarandache and Ilanthenral,Special FuzzyMatrices For Social Scientist, Printed inunited States of America, M. Ayhan Kose Eswar E. Prasad and IZA Bonn Marco E. Terrones, How Does Globalization Affect the Synchronization of Business Cycles?, 23 annual meetings of the American Economic Association in Washington, DC.. Guy Neave, Globalisation: Threat, Opportunity or Both, Report presented to the IAU Administrative Board Meeting at its Mexico City meeting in November 2). 5