FUZZY BINOMIAL DISTRIBUTION

Dr.Pranita Goswami, Int. J. Comp. Tech. Appl., Vol 2 (4), 813-815
ISSN:2229-6093
THE FUZZY SET BY FUZZY INTERVAL
Dr.Pranita Goswami
Associate Professor & Head Department of Statistics
Pragjyotish College
Guwahati, Assam, India
pranita_goswami@yahoo.com
ABSTRACT
Fuzzy set by Fuzzy interval is a
triangular fuzzy number lying between
the two specified limits. The limits to be
not greater than 2 and less than -2 by
fuzzy interval have been discussed in
this paper. Through fuzzy interval we
arrived at exactness which is a fuzzy
measure and fuzzy integral
.
KEY WORDS
Fuzzy variable, limits, Fuzzy
interval.
1. INTRODUCTION
Fuzzy Set is drawn over four quadrant
over the interval [0, 1], [-1, 0], [1, 2]
and [-2, 1] where the variables over
these intervals are fuzzy. Through the
fuzzy interval [0, 1] we get a straight
line and through the fuzzy interval [-1,
0] we get another straight line. If we
add these two fuzzy interval we get
fuzzy number from [-1, 1]. Now if we
add one fuzzy interval from [1, 2] we
get a straight line and over the interval
[-2,-1] we get again a straight line. If we
add all the four intervals we again get a
triangular fuzzy number lying between
the limits [-2, 2]. Works on fuzzy
statistics have started within the last few
years (see e.g. Watanabe and Imaizumi
(1993), Wagner (1959), Ishibuchi and
Tanaka (1990), Goswami and
Baruah(2007), (2008), Box and
Jenkins(1970)). We have found that not
much have been done on exactness
through fuzzy statistics. We put forward
one such example in this article.
2.Fuzzy Measure and Fuzzy
Integral
Let A be a Fuzzy set from [-2,2] is
called the core of the fuzzy set A when
its value is 1and is called support of A
i.e supp(A)=A for any crisp set A when
the set { x ∈U
/ A( x)
> 0}
.Thus Fuzzy
Set is a Fuzzy measure and Fuzzy
integral over the range [-2,2] which
satisfies
IJCTA | JULY-AUGUST 2011
Available online@www.ijcta.com
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Dr.Pranita Goswami, Int. J. Comp. Tech. Appl., Vol 2 (4), 813-815
ISSN:2229-6093
(1) boundness :i.e g(-2)=0 and g(x)=1
(2) monotonicity i.e A

Dr.Pranita Goswami, Int. J. Comp. Tech. Appl., Vol 2 (4), 813-815
ISSN:2229-6093
Pos
F
( A) Sup F( Y )
=
y∈A
...
(1)
( A) = 1−
Pos ( A) ...(2)
and NecF
F
In our example the α cuts which are
nested are
A
A
1
3
U sin
{ 0} , A2
= { −1,
0 1 },
{ −1.5
,1 ,1.5 }
g(1)
we find that Pos( A1
)
( A ) = Pos( A ) = 1
=
=
Pos
2
andPos
1/3, Pos
( A1
) = 2/3 , Pos( A2
)
( A ) = 0
U sin g(2)
we getNec(
A ) = 1/3,
Nec
( A ) = 2/3, Nec( A ) = 1
2
3
In this particular example by using
uniform density function i.e from
probability density function we have
obtained possibility distribution
function by using one probability
measure over the same interval .
1
-2 0
2
Fuzzy set and Possibility
distribution
3
3
1
=
=
0
-1
CONCLUSION
Fuzzy set is drawn over
constant density function i.e we have
obtained possibility distribution from
probability density function and the
function remains in equilibrium about a
constant mean level and converges
where it is stationary. Thus we conclude
that in this paper we arrive at exactness
through fuzzy interval when it is linear
which is Fuzzy Measure and Fuzzy
Integral .
REFERENCES:
[1].G.E.P.Box and G.M.Jenkins. Time
serier Analysis Holden day , San
Francisco(1985),77-78
[2].Goswami. P. and Baruah, H.K. The
Fuzzy ARIMA(1,1)Process, The journal
of Fuzzy Mathematics vol– 16.No.3,
2008 Los Angeles
[3].Goswami.P. and H.K.Baruah,
Fuzzy time series analysis,J.Fuzzy
Math ,Vol.15,Nos.3(2007),513-523
[4].Ishibuchi, H and Tanaka, H. several
formulations of interval regression
analysis, proceedings of Sino–Japan
Joint meeting on Fuzzy sets and
systems, B2–2, (1990).
[5].WagnerH.W.,Linear Programming
techniques for regression analysis. J.
Amer. Stats. Assoc., vol – 54 (1959)
275 – 287.
[6].Watanabe, N and Imaizumi, T. A
fuzzy statistical test of fuzzy hypethesis.
Fuzzy sets and systems 53 167–17
North Holland (1993).
[7].L.A.Zadeh,Fuzzy sets s a Basis for a
Theory of Possibility .Int. J. of Fuzzy
Sets and Systems ,Vol.1,(1978),3-8.
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