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Estimating Weight

Estimating Weight . Mirza Muhammad Waqar Contact: mirza.waqar@ist.edu.pk +92-21-34650765-79 EXT:2257. RG712. Course: Special Topics in Remote Sensing & GIS. Estimating Weights.

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Estimating Weight

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  1. Estimating Weight Mirza Muhammad Waqar Contact: mirza.waqar@ist.edu.pk +92-21-34650765-79 EXT:2257 RG712 Course: Special Topics in Remote Sensing & GIS

  2. Estimating Weights • A weight can be defined as a value assigned to an evaluation criterion that indicates its importance relative to other criteria under consideration. • The larger the weight, the more important is the criterion in the overall utility. • Assigning weights of importance to evaluation criteria accounts for: • Changes in the range of variation for each evaluation criterion • The different degrees of importance being attached to these ranges of variation.

  3. Ranking Method • The simplest method for assessing the importance of weights is to arrange them in rank order in the order of the decision maker’s preference. • Straight ranking 1 most important ,2,3…n least important • Inverse ranking 1: least important, 2,3…n most important • Once the ranking established for a set of criteria, generate numerical weights from rank‐order information

  4. Ranking Method P = 0 results in equal weights to all the criteria P = 1 results in rank sum weight

  5. Site Selection using Ranking Method

  6. Rating Method • The rating methods require the decision maker to estimate weights on the basis of a predetermined scale. • i.e. 0 to 100 • 0 indicted that the criterion can be ignored • 100 means only one criterion need to be considered.

  7. Point Allocation Method • 50 points to the cost of establishing the plant. (W: 0.5) • 30 points to accessibility to the transportation. (W: 0.3) • 20 points to the availability of water. (W: 0.2) • Sum= 0 (ignore) location Sum=100 Select with confidence

  8. Ratio Estimation Procedure • It starts by assigning an arbitrary weight to the most important criterion, as identified by one of the ranking methods. • A score of 100 is assigned to the most important criterion. • Proportionately smaller wrights are then given to criteria lower in the order. • The procedure is continued until a score is assigned to the least important criterion which shall then be taken as an anchor point for calculating the ratios. • Score of each criterion is divided by the score of the least important criterion Wj/W* where Wj is the score for the jthcriterion and W* is lowest score.

  9. Site Selection using Rating Method

  10. Pair‐wise Comparison Methods • Developed by Saatay (1980) in the context of AHP (Analytic Hierarchy Process) • This method involves pair‐wise comparisons to create a ratio matrix. • It takes pair‐wise comparisons as input and produces the relative weights as output. • Development of the pair‐wise comparison matrix • Computation of the criterion weights • Estimation of the consistency ratio

  11. Scale for Pair‐wise Comparison

  12. Example: Site Suitability Analysis • Parameters: • Price • Slope • View • Price is moderately to strongly preferred over slope • Price is very strongly preferred over view • Slope is strongly preferred over view

  13. Step1: Development of Pairwise Comparison Matrix

  14. Step2: Computation of the Criterion Weights • This step involves following operations: • Sum the values in each column of the pair-wise comparison matrix. • Divide each element in the matrix by its column total • Compute the average of elements in each row of the normalized matrix.

  15. Step2: Computation of the Criterion Weights

  16. Step3: Estimation of the Consistency Ratio • This step involves following operations: • Determine the weighted sum vector by multiplying the criterion weights with the values of the original pairwise comparison matrix and finally sum these values over rows. • Determine the consistency vector by dividing the weighted sum vector by the criterion weights.

  17. Step3: Estimation of the Consistency Ratio

  18. Step3: Estimation of the Consistency ratio • Computation of Lambda λ : λ = (3.250+3.119+3.014) / 3 = 3.128 • λ should always be greater than or equal to the number of criterion to be considered. • λ = n (if the pair wise comparison matrix is a consistent matrix)

  19. Step3: Estimation of the Consistency ratio • Computation of CI (Consistency Index) : • CI= (λ‐n) / (n-1) = (3.128‐3) / (3-1) = 0.064 • Computation of CR (Consistency Ratio) : • CR= CI / RI = 0.064 / 0.58 = 0.110 • Where RI is the random index provided by Saaty and it depends on the number of criterion (n).

  20. Random Inconsistency Index RI • If CR<0.10 the ratio indicates a reasonable level of consistency. • If CR>0.10 the ratio indicates an inconsistent judgment and the relative criterion pair wise comparison matrix needs reconsideration and the whole process must be repeated.

  21. Questions & Discussion

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