When collection of thing belongs to certain definition, it is known as Set. When these set shows a degree of membership, it is known as Fuzzy Set. Fuzzy Set theory was given by the Professor Lofti  Zadeh , University of California 1965. Copy the link given below and paste it in new browser window to get more information on Fuzzy Set:- http://www.transtutors.com/homework-help/statistics/fuzzy-set.aspx

1. 1
Fuzzy Set

2. 2
DEFINITIONS
A. Definitions
Sets
Classical Set Fuzzy Set

3. Fuzzy Set : Definition
It is the set containing elements that are partially are
gradually belong to the defined set. It represents transition.
For example, it includes all the colors between black and
white. It basically shows gradation

4. 4
Definitions: Fuzzy Sets

5. 5
Definitions: Fuzzy Sets

6. 6
The Geometry of Fuzzy Sets

7. 7
Fuzzy Number
A fuzzy number A possess the following properties:
1. Must be a normal fuzzy set,
2. The alpha levels should be closed for every ,
3. The support of A, , should be bounded.
)(αA ]1,0(∈α
)0( +A

8. 8
Fuzzy Equations
},where8.0)(|{
:istioninterpretaAnother
).(/)()(/)()(/)()(/)(ii)
(0,1])(/)()(/)(i)
:iffexistsequationfuzzytheosolution tThen the
)].(),([)(and)](),([)()],(),([)(Let
).()()(
:istioninterpretaOne
~~
*
~
BbAabaxx
abababab
abab
xxXbbBaaA
BXA
BXA
∈∈≥=
≤≤≤⇒≤
∈∀≤
===
=
=
µ
ααββββααβα
ααααα
ααααααααα
ααα

9. 9
Example : Fuzzy Equation
)()(
:that(ii)Verify
5
1232,
3
128)(
thatso
5
1232
3
128
:that(i)Verify
]1232,128[)(
]5,3[)(
3202for12/)32(
2012for8/)12(
32,12for0
)(
54for5
43for3
5,3for0
)(
βαβα
α
α
α
αα
α
α
α
α
ααα ααα
XX
X
B
A
xx
xx
xx
xB
xx
xx
xx
xA
⊆⇒≤
−
−
+
+=
−
−≤
+
+
−+=
−+=
≤<−
≤<−
>≤
=
≤<−
≤<−
>≤
=





























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