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ELECTRE Decision Making Method

An introduction to ELECTRE Decision Making Method. This is an outranking method where options outranked each other such that the best option remains.Here both concordance and discordance index was used to find the outranking criteria.

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ELECTRE Decision Making Method

  1. 1. ELECTRE Dr. Mrinmoy Majumder Course Name : Intro to Multi Criteria Decision Making Methods Lecture No.10 out of 15 https://opticlasses.teachable.com Follow me on : RG : Mrinmoy Majumder Twitter : kuttu80 More such tutorials in http://www.baipatra.ws Publish your original research in http://www.energyinstyle.website
  2. 2. ELECTRE • ELECTRE is a family of multi-criteria decision analysis methods that originated under the French School of decision making in the mid- 1960s. • ELECTRE stands for: ELimination Et Choix Traduisant la REalité (ELimination and Choice Expressing REality). • The method was invented by Bernard Roy and his colleagues at SEMA consultancy company.
  3. 3. Example of ELECTRE Decision Goal : To buy a car Criteria : Cost and Speed Alternatives : Mercedes Benz(M), Jaguar(J), Toyota(T) Aggregation Methods to be used : ELECTRE
  4. 4. Step 1 : Development of the Alternative Indicator Matrix • First step of ELECTRE method is to create a Alternative-Indicator Matrix : Indicator Cost (in Lakh Rs.) Speed (in km/hr) Alternative Mercedes Benz 80 200 Jaguar 100 300 Toyota 120 250
  5. 5. Step 2 : Development of the Normalized Indicator Matrix or Normalized Decision Matrix Matrix from Step 1 Indicator Cost (in Lakh Rs.) Speed (in km/hr) Alternative Merced es Benz 80 200 Jaguar 100 300 Toyota 120 250 Square each value of the indicators and add column wise. Then find the square root of the summation. Divide each value of the Indicators with the square root. Indicator Cost (in Lakh Rs.) Speed (in km/hr) Alternative Mercedes Benz 6400 40000 Jaguar 10000 90000 Toyota 14400 62500 Column wise Sum 30800 192500 Square Root of the Sum 175.499 438.748
  6. 6. Step 2 : Contd. • The Normalized Decision Matrix Indicator Cost Speed Alternative Mercedes Benz 0.456 0.456 Jaguar 0.570 0.684 Toyota 0.684 0.570
  7. 7. Step 3 : Development of the Weighted Normalized Decision Matrix Indicator Cost (Weight of Indicator : 0.600) Speed (Weight of Indicator : 0.400) Alternative Mercedes Benz 0.456 0.456 Jaguar 0.570 0.684 Toyota 0.684 0.570 Multiply the weight of indicator of each column with each value of the alternatives for that indicator to find the weighted value of the indicators for the alternatives Indicator Cost (Weight of Indicator : 0.600) Speed (Weight of Indicator : 0.400) Alternative Mercedes Benz 0.274 0.182 Jaguar 0.342 0.274 Toyota 0.410 0.228
  8. 8. Step 4 : Development of the Concordance Matrix Each alternative is compared with the other alternative with respect to its normalized value for the indicators. If normalized value of M and J is compared with respect to Cost indicator then M < J, thus 0 is written. M is less than J for Speed indicator as well. Thus the value in the matrix will be 0.However when J is compared with M, J>M for both Cost and Speed Indicator. So the weight of both the indicator will be added and shown in that cell of the matrix. Mercedes Benz(M) Jaguar(J) Toyota(T) Mercedes Benz(M) 0 0 0 Jaguar(J) =0.6+0.4 0 =0+0.4 Toyota(T) =0.6+0.4 =0.6+0 0 Matrix from Step 3 Indicator Cost (Weight of Indicator : 0.600) Speed (Weight of Indicator : 0.400) Alternative Mercedes Benz(M) 0.274 0.182 Jaguar(J) 0.342 0.274 Toyota(T) 0.410 0.228
  9. 9. Step 5 : Concordance Matrix Mercedes Benz Jaguar Toyota Mercedes Benz 0 0 0 Jaguar 1 0 0.4 Toyota 1 0.6 0 Column wise Sum = 0+1+1 = 2 = 0+0+0.6 = 0.6 =0+0.4+0 = 0.4 Total : =2 + 0.6 + 0.4 = 3 Total/Number of Values in the Matrix = 3/4 = 0.75 Matrix from Step 4 Mercedes Benz Jaguar Toyota Mercedes Benz 0 0 0 Jaguar =0.6+0.4 0 =0+0.4 Toyota 0.6+0.4 =0.6+0 0 1 2 3 4 Only the cell which depicts the comparison between J with M,T with M,T with J and J with T has real values. As a result number of values in the matrix is 4
  10. 10. Step 5 : Contd. Concordance Set : If C bar (see last row of matrix 4) is less than the value in the cell of the matrix then the value will be replaced by 1 otherwise if R is greater than the real value in the cell then 0 is used instead of the existing value. Mercedes Benz Jaguar Toyota Mercedes Benz 0 0 0 Jaguar 1 0 0 Toyota 1 0 0 Matrix 4 Mercedes Benz Jaguar Toyota Mercedes Benz 0 0 0 Jaguar 1 0 0.4 Toyota 1 0.6 0 Column wise Sum 2 0.6 0.4 Total : =2 + 0.6 + 0.4 = 3 Total / (Number of cells in the Matrix where a real number exist) = C bar = 3/4 = 0.75
  11. 11. Step 6 : Development of the Discordance Matrix Matrix from Step 3 Indicator Cost (Weight of Indicator : 0.600) Speed (Weight of Indicator : 0.400) Alternative Mercedes Benz(M) 0.274 0.182 Jaguar(J) 0.342 0.274 Toyota(T) 0.410 0.228 The normalized value of each alternative for each indicator is deducted from the values of other alternatives for the same indicator Cost Speed M-J = 0.274 - 0.342 = 0.182 - 0.274 M-T = 0.274 - 0.410 = 0.182 - 0.228 J-M = 0.342 - 0.274 = 0.274 - 0.182 J-T = 0.342 - 0.410 = 0.274 - 0.228 T-M = 0.410 – 0.274 = 0.228 - 0.182 T-J = 0.410 – 0.342 = 0.228 - 0.274
  12. 12. Column : 1 The normalized value of each alternative for each indicator is deducted from the values of other alternatives for the same indicator Column : 2 Cost Column : 3 Speed Column : 4 Find the maximum value in the row (A) Column : 5 Find the maximum negative value or if there is no negative, then use the maximum value of the row(B) Column : 6 (B)÷(A) M-J -0.068 -0.091 0.091 0.091 1 M-T -0.137 -0.046 0.137 0.137 1 J-M 0.068 0.091 0.091 0.091 1 J-T -0.068 0.046 0.068 0.068 1 T-M 0.137 0.046 0.137 0.137 1 T-J 0.068 -0.046 0.068 0.046 0.667 Rough Set Matrix
  13. 13. Discordance Set : If D bar (see last row of matrix 5) is less than the value in the cell of the matrix then the value will be replaced by 1 otherwise if R is greater than the real value in the cell then 0 is used instead of the existing value. Mercedes Benz Jaguar Toyota Mercedes Benz 0 1 1 Jaguar 1 0 1 Toyota 1 0 0 Matrix 5 : Matrix from Step 4 can be rewritten by using the values from Column 6 of Rough Set Matrix Mercedes Benz(M) Jaguar(J) Toyota(T) Mercedes Benz(M) 0 1 1 Jaguar(J) 1 0 1 Toyota(T) 1 0.667 0 Column wise Sum 2 1.667 2 Total : =2 + 1.667 + 2 = 5.667 Total / (Number of cells in the Matrix where a real number exist) = D bar = 5.667/6 = 0.945
  14. 14. Concordance Set (C) Mercedes Benz Jaguar Toyota Mercedes Benz 0 0 0 Jaguar 1 0 0 Toyota 1 0 0 C (AND or × ) D Mercedes Benz Jaguar Toyota Mercedes Benz 0 0 0 Jaguar 1 0 0 Toyota 1 0 0 Discordance Set(D) Mercedes Benz Jaguar Toyota Mercedes Benz 0 1 1 Jaguar 1 0 1 Toyota 1 0 0 0 0AND or × = 0 1 1AND or × = 1 AND or × EXAMPLE It Implies that : J > M and T> M Or J and T > M 0 1AND or × = 0
  15. 15. Thank you

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