1) The document discusses how a student's level of preparation for an exam can impact their expectations and subsequent happiness with the results. It uses fuzzy set theory to model the student's preparation level, expectations, and happiness level as grades between 0-1. 2) It defines the student's preparation level across categories from fully prepared (EG) to not prepared (EB). The student's expectation is calculated based on their preparation level and their desired result (e.g. a student hoping for 90% who prepared at a G level would have an expectation of 0.771). 3) The student's happiness is then calculated as the ratio of their obtained marks to expected limit based on their preparation level. For example

1. Integrated Intelligent Research(IIR) International Journal of Business Intelligent
Volume: 04 Issue: 01 June 2015,Pages No.39- 40
ISSN: 2278-2400
39
Thoughts and Happiness
A.Victor Devadoss1
, A.Felix2
, R.Vicram3
1
Head & Associate professor, Department of Mathematics, Loyola College, Chennai
2
Ph.D. Research Scholar, Department of Mathematics, Loyola College, Chennai
3
M.Phil. Research Scholar, Department of Mathematics, Loyola College, Chennai
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.
I. 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.
1. Basic Concepts
1.1 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 
( / ( ))
A
x x x E
   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
 . ( )
A x
x M


 is called the
membership function.
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  
( , ( )) , , ( ) [0,1].
A A
A x x x U x
 
   When U is
finite set, i.e. 
1 2
, ,...... n
x x x , the fuzzy set on U can be
represented as follows,
1
/ ( )
n
i A i
i
A x x


  . If there is a
natural ordering of the elements in the universe U, one can
simply use the vector  
1
( ),....... ( )
A A n
x x
  of the
membership degree to represent the fuzzy set A. all fuzzy sets
on U is denoted by  
U
 .
1.2 Decision:
Let  , 1,2,...
i
C x i n
  , x X
 be the membership function
of constrains defining the decision space and
 , 1,2,...
i
G x i n
  , x X
 be the membership function of
objective functions or goals.A decision is defined by the
membership function
     , 1,2,...
i i i
D i C j G
x x x i n
  
    . Where
, ,
i j
   denote appropriate possibly content dependent
aggregators(connectivites).
II. 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
EG 100% - 100% (Full marks)
VG 80% - 99%
G 60% - 79%

2. Integrated Intelligent Research(IIR) International Journal of Business Intelligent
Volume: 04 Issue: 01 June 2015,Pages No.39- 40
ISSN: 2278-2400
40
NG 40% - 59%
B 20% - 39%
VB 1% - 19%
EB 0%
Let us assume the students preparation level is  
0,1
  .
The expectation level of the student can be calculated as
follows,    
1
i x x
T X t f
 
   . Where x
t and x
f
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
       
1 0.90 1 0.90 1
1
T EG   

Similarly calculating we get,
 
 
 
 
 
 
0.971
0.771
0.571
0.371
0.172
0
T VG
T G
T NG
T B
T NB
T EB






The expectation of the student will be
1 2 3 4 5 6 7
, , , , , ,
y y y y y y y
 
 
 
 
 
 
 
1
2
3
4
5
6
7
1 1
0.971 0.9
0.771 0.7
0.571 0.5
0.371 0.3
0.172 0.1
0 0
y
y
y
y
y
y
y
 
 
 
 
 
 
 
The happiness of the student is calculated as
obtained marks×expected limit
100%
total marks
D  
Let the obtained marks be 175 out of 200 and the preparation
level be G, then
175 0.771
100%
200
67.4625%
D

 

So the student gets 67% of happiness here.
III. CONCLUSION
Our thoughts should be realistic, because if we are expecting
more than what we have prepared we cannot get happiness.
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SIGCHI Conference on Human Factors in Computing Systems
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Peters Ltd.
[5] Sannella, M. J. 1994 Constraint Satisfaction and Debugging
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