Thoughts and Happiness by iirpublications

Indo-Bhutan International Conference On Gross National Happiness Pages: 174-176

Vol 02, October 2013

Thoughts and Happiness A.Victor Devadoss1, A.Felix2, R.Vicram3 1 Head & Associate professor, Department of Mathematics, Loyola College, Chennai - 600 034 2 Ph.D. Research Scholar, Department of Mathematics, Loyola College, Chennai - 600 034 3 M.Phil. Research Scholar, Department of Mathematics, Loyola College, Chennai - 600 034 Abstract Our thoughts play a vital role in ones happiness. Mahatma Gandhi says “Happiness is when what you think, what you say, and what you do are in harmony”. Let us measure the happiness of a student after writing his exam with respect to his preparation and expectation by decision making. Keywords: Fuzzy sets, Satisfaction level, Degrees of satisfaction, Decision making. 1. Introduction The happiness of each and every person depends on how they take that situation. Let us see some of the situations. For example, if a person wants to buy a dress, he has a thought of buying a certain design, colour or at a particular price such as etc... In this case probably three situations happens  He will buy the dress what he wanted.  He may not get the particular dress so he may go to another shop.  He may compromise himself and will buy some dress. If we consider all the three situations, each category has certain happiness. First case will be happy of buying what he wanted and the second case will be happy that he is not compromised with anything but the third case thinks whether he must think before purchasing. In many situations our happiness is affected more. Let us discuss some of the situations such as expecting marks with regard to the preparation. If a person wants to expect something he should be with some preparation without preparing he is going to perform a task means it may lead him to sadness. 2. Basic Concepts 2.1 Fuzzy set: (Zadeh. L. A. Fuzzy Sets Information and Control) Let x  E then this fuzzy subset A of E is







the set of ordered pairs ( x /  A ( x ))  x  E 

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Where  A ( x ) is the grade of membership of x 

in A . Thus if  A ( x ) takes its value in a set



M, called membership set. One may say that x takes its value in M through the function

 A ( x) . 

x  M A ( x )

called

the



membership function. 2.2 Fuzzy set: A fuzzy set A is characterized by a membership function  A ( x ) which associates each element in U with a real value between [0, 1]. The fuzzy set is usually denoted by a set of pairs

A  ( x,  A ( x )) , x U ,  A ( x )  [0,1]. When U is finite set, i.e.  x1 , x2 ,...... xn  , the fuzzy set on U can be represented as follows, n

A   xi /  A ( xi ) . If there is a natural i 1

ordering of the elements in the universe U, one can simply use the vector

 A ( x1 ),....... A ( xn )

of the membership

degree to represent the fuzzy set A. all fuzzy sets on U is denoted by  U  . 2.3 Decision: Let Ci  x  , i  1, 2,...n , x  X 

the

membership function of constrains defining the decision space and Gi  x  , i  1, 2,...n , 

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Indo-Bhutan International Conference On Gross National Happiness Pages: 174-176

x X

be the membership function of objective functions or goals. A decision is defined by the membership function

 Di  x   i Ci  x    j Gi  x  , i  1, 2,...n . 



Where , i ,  j denote appropriate possibly content dependent aggregators(connectivites). 3. Preparing and Presenting Consider a situation in which one is going to write a test. He may prepare well or may not. But the thing is if he wants to be happy he must get good marks. Everyone expects some good thing to happen in all the situations. Even a full prepared person wants to get good marks and a not prepared person wants to get good marks. Let us assume the following: Let the preparation levels of a student be

Vol 02, October 2013

The expectation level of the student can be calculated as follows,

T  X i   1    t x   f x . Where t x and f x denotes the lower and upper preparation level of a student. Let us assume the student is expecting 90%. (i.e.) 0.90. The expectation is calculated as follows

T  EG   1  0.90 1   0.90 1 1 Similarly calculating we get,

T VG   0.971 T  G   0.771 T  NG   0.571 T  B   0.371 T  NB   0.172 T  EB   0

100% - 100% (Full marks)

The expectation of the student will be

80% - 99%

y1 , y2 , y3 , y4 , y5 , y6 , y7

60% - 79%

y1  1  1

40% - 59%

y2   0.971  0.9

20% - 39%

y3   0.771  0.7

1% - 19%

y4   0.571  0.5

y5   0.371  0.3 y6   0.172  0.1

Let us assume the students preparation level is

   0,1 . The happiness of the student is calculated as

D

obtained marks×expected limit  100% total marks

Let the obtained marks be 175 out of 200 and the preparation level be G, then 175  0.771 D  100% 200  67.4625% So the student gets 67% of happiness here.

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y7   0  0 4. Conclusion Our thoughts should be realistic, because if we are expecting more than what we have prepared we cannot get happiness. 5. References [1] Bowman, M., Debray, S. K., and Peterson, L. L. 1993. Reasoning about naming systems. [2] Ding, W. and Marchionini, G. 1997 A Study on Video Browsing Strategies.

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Indo-Bhutan International Conference On Gross National Happiness Pages: 174-176 Technical Report. University of Maryland at College Park. [3] Frรถhlich, B. and Plate, J. 2000. The cubic mouse: a new device for three-dimensional input. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems

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Vol 02, October 2013

Tavel, P. 2007 Modeling and Simulation Design. AK Peters Ltd. [5] Sannella, M. J. 1994 Constraint Satisfaction and Debugging for Interactive User Interfaces. Doctoral Thesis. UMI Order Number: UMI Order No. GAX95-09398., University of Washington. [4]

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