these ppts belongs to multi-criteria decision making using intuitionistic fuzzy

1. Multi-Criteria Decision Making Method using
Intuitionistic fuzzy sets
Deepa Joshi
Ph.D Mathematics
G. B. Pant University of Agriculture & Technology
Pantnagar
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2. Intuitionistic Fuzzy sets
An intuitionistic fuzzy set(IFS) A on a universe X is
defined as an object of the following form
A={(x, μA(x), νA(x))| x X}
where
0 ≤ μA(x) + νA(x) ≤ 1
is called intuitionistic fuzzy set (IFS) and functions
μA : X→ [0, 1] and νA : X → [0, 1] represent the
degree of membership and the degree of non-
membership respectively.
is called degree of hesitation.
2
xxx AAA
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3. Multi-Criteria Decision Making (MCDM)
Multi-Criteria Decision Making (MCDM) means
the process of determining the best feasible
solution according to the given criteria.
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4. Approaches For MCDM
ANP (Analytic network process)
AHP (The Analytical Hierarchy Process)
SIR (superiority and inferiority ranking method)
SMART (The Simple Multi Attribute Rating
Technique )
SCORE FUNCTION
TOPSIS (Technique for Order Preference by
Similarity to the Ideal Solution)
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5. Score function definition
Let be an intuitionistic fuzzy value
for
The score function(S) of is given by
and
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),( ijijijx
1ijij
xij
2
13
)(
ijij
ijxS
]1,1[)(xij
S

6. Score function
If is the hesitation degree of a decision maker
then the value of the Score function is given by
Where
= criteria , j=1,2……..n
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)().()()( ccccS jjjj
]1,1[)(cS j
cj

7. Example using Score function method
Objective
- To select best air-condition system
Criteria
- Economical, Function, Operative
with weight vector W=(0.3,0.3,0.4)
Alternatives
- A, B and C
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8. Applying Score function method to example
Step1- We provide intuitionistic values for each
criteria and construct the intutionistic group multi-
criteria decision matrix as follows
A
D = B
C
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)6.0,3.0()9.0,1.0()6.0,3.0(
)1.0,7.0()5.0,5.0()5.0,5.0(
)2.0,8.0()1.0,7.0()2.0,8.0(

9. Applying Score function method to example
Step2-Using intuitionistic fuzzy arithmetic averaging
operator to aggregate all over all the criteria.
,I, j, k=1,2,3
= criteria ,j=1,2,3
n = no. of criteria
S = score function
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x
k
ij
)(
)(
1
1
)()(
cSxx j
n
j
k
ij
k
i
n
cj

10. Applying Score function method to example
Putting the values from decision matrix we get
=(0.310697, 0.00058)
=(0.2351, 0.00142)
=(0.04914, 0.00062)
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x
)1(
1
x
)2(
1
x
)3(
1

11. Applying Score function method to example
Step3-Using intuitionistic weighted arithmetic
averaging operator to aggregate all
, I, j, k=1,2,3
Where W= weight of each criteria
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x
k
i
)(
n
k
k
ii xwx k1
)(

12. Applying Score function method to example
Putting the values from decision matrix in previous
formula we get
=(0.09321,0.000174)
=(0.07053, 0.000426)
=(0.01966, 0.000248)
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x1
x2
x3

13. Applying Score function method to example
Step4-Using Score function formula
to get Score functions
& each alternative A, B & C.
13
2
13
)(
v
x
ijij
ij
S
)(),( 21 xx SS
)( 3xS

14. Applying Score function method to example
= -0.36037
= -0.39441
=-0.47063
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)( 1xS
)( 2xS
)( 3xS

15. Applying Score function method to example
Step5- Rank all the alternatives A, B,C and select the
best one in accordance with the values of
Score function .
Now,
Therefore
Hence A > B > C A is best.
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)(&)(),( 321 xxx SSS
)()()( 321 xxx SSS
xxx 321

16. REFERENCES
Atanassov K., “Intuitionistic fuzzy sets .Fuzzy Sets and System”,110(1986) 87-96
Atanassov K., “ More on intuitionistic fuzzy Sets,Fuzzy Sets and Systems”,33(1989)
37-46
Bustine H. and Burillo P., “Vauge sets are intuitionistic fuzzy sets,Fuzzy sets and
systems”,79(1996) 403-405
Xu Z.S., “Intuitionistic preference relations and their applications in group decision
making.Information Sciences”,177(2007) 2263-2379
Zadeh L.A., “Fuzzy Sets.Information and control”,8(1965) 338-353
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