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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