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Multi-Criteria Decision Making Method using
Intuitionistic fuzzy sets
Deepa Joshi
Ph.D Mathematics
G. B. Pant University o...
Intuitionistic Fuzzy sets
An intuitionistic fuzzy set(IFS) A on a universe X is
defined as an object of the following form...
Multi-Criteria Decision Making (MCDM)
Multi-Criteria Decision Making (MCDM) means
the process of determining the best feas...
Approaches For MCDM
ANP (Analytic network process)
AHP (The Analytical Hierarchy Process)
SIR (superiority and inferiority...
Score function definition
Let be an intuitionistic fuzzy value
for
The score function(S) of is given by
and
5
),( ijijijx
...
Score function
If is the hesitation degree of a decision maker
then the value of the Score function is given by
Where
= cr...
Example using Score function method
Objective
- To select best air-condition system
Criteria
- Economical, Function, Opera...
Applying Score function method to example
Step1- We provide intuitionistic values for each
criteria and construct the intu...
Applying Score function method to example
Step2-Using intuitionistic fuzzy arithmetic averaging
operator to aggregate all ...
Applying Score function method to example
Putting the values from decision matrix we get
=(0.310697, 0.00058)
=(0.2351, 0....
Applying Score function method to example
Step3-Using intuitionistic weighted arithmetic
averaging operator to aggregate a...
Applying Score function method to example
Putting the values from decision matrix in previous
formula we get
=(0.09321,0.0...
Applying Score function method to example
Step4-Using Score function formula
to get Score functions
& each alternative A, ...
Applying Score function method to example
= -0.36037
= -0.39441
=-0.47063
14
)( 1xS
)( 2xS
)( 3xS
Applying Score function method to example
Step5- Rank all the alternatives A, B,C and select the
best one in accordance wi...
REFERENCES
Atanassov K., “Intuitionistic fuzzy sets .Fuzzy Sets and System”,110(1986) 87-96
Atanassov K., “ More on intuit...
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Deepa seminar

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Deepa seminar

  1. 1. Multi-Criteria Decision Making Method using Intuitionistic fuzzy sets Deepa Joshi Ph.D Mathematics G. B. Pant University of Agriculture & Technology Pantnagar 1
  2. 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 1
  3. 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. 3
  4. 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) 4
  5. 5. Score function definition Let be an intuitionistic fuzzy value for The score function(S) of is given by and 5 ),( ijijijx 1ijij xij 2 13 )( ijij ijxS ]1,1[)(xij S
  6. 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 6 )().()()( ccccS jjjj ]1,1[)(cS j cj
  7. 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 7
  8. 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 8 )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. 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 9 x k ij )( )( 1 1 )()( cSxx j n j k ij k i n cj
  10. 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) 10 x )1( 1 x )2( 1 x )3( 1
  11. 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 11 x k i )( n k k ii xwx k1 )(
  12. 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) 12 x1 x2 x3
  13. 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. 14. Applying Score function method to example = -0.36037 = -0.39441 =-0.47063 14 )( 1xS )( 2xS )( 3xS
  15. 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. 15 )(&)(),( 321 xxx SSS )()()( 321 xxx SSS xxx 321
  16. 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 16

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