1 / 13

MCE: Eigen Values Calculations from Pair Wise Comparisons.

MCE: Eigen Values Calculations from Pair Wise Comparisons. Addition to Exercise 2-8. Pair Wise Comparison.

york
Download Presentation

MCE: Eigen Values Calculations from Pair Wise Comparisons.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MCE: Eigen Values Calculations from Pair Wise Comparisons. Addition to Exercise 2-8

  2. Pair Wise Comparison. • The analytic hierarchy process (AHP) is a multi-criteria decision making method that employs a procedure of multiple comparisons to rank order alternative solutions to a multi-objective decision problem.

  3. Given Pairwise comparison..

  4. Calculate EigenVector by Edrisi.

  5. The Calculation of eigenvector from the pairwise comparison values requires a lot of work in terms of matrix algebra. • The method presented here is an approximation that suits to a good degree of accuracy in terms of eigenvalues.

  6. Step-1

  7. Step-2 • Complete the upper diagonal values of the pair wise matrix. • If ‘A’ is 5 time of ‘B’ means ‘B’ is 1/5 times of ‘A’. • In the next diagram shaded values shows these values.

  8. Step-4 • Calculate the sum of each column.

  9. Step-5 • Divide the values in each cell by its column’s sum. • Eg: Col-1: 1/16, 3/16 ….. Col-2: 0.333/15.33, 1/15.333 etc …

  10. Step-6 • Sum the weights in each row. (R1, R2, R3 …) • Add the results … Sum = (R1 + R2 + R3 + R4 + R5 + R6).

  11. Step-7 • Get the ratio of each of the individual row’s sum to the resulting sum. • Eg. 0.379/6 = 0.063 etc .. • The Weights we get are the approximated weights as in the values obtained through Idrisi.

  12. References: • The method for conversion taken from the lecture notes: • mat.gsia.cmu.edu/classes/mstc/multiple/node4.html • For the exact values calculation refer to the attached paper • The Analysis of the Principal Eigenvector of Pairwise Comparison Matrices; András Farkas • Excel file with the auto-calculation is also attached. • A very good software for auto conversion from pairwise values is; • http://www.isc.senshu-u.ac.jp/~thc0456/EAHP/EAHP_manu.html

More Related