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

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Presentation transcript:

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

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.

Given Pairwise comparison..

Calculate EigenVector by Edrisi.

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.

Step-1 LandfuzzTownfuzzWaterfuzzRoadfuzzSlopefuzzdevelopfuzz Landfuzz Townfuzz Waterfuzz Roadfuzz Slopefuzz developfuzz

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.

LandfuzzTownfuzzWaterfuzzRoadfuzzSlopefuzzdevelopfuzz Landfuzz Townfuzz Waterfuzz Roadfuzz Slopefuzz developfuzz

Step-4 Calculate the sum of each column. LandfuzzTownfuzzWaterfuzzRoadfuzzSlopefuzzdevelopfuzz Landfuzz Townfuzz Waterfuzz Roadfuzz Slopefuzz developfuzz

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/ etc … LandfuzzTownfuzzWaterfuzzRoadfuzzSlopefuzzdevelopfuzz Landfuzz Townfuzz Waterfuzz Roadfuzz Slopefuzz developfuzz

Step-6 Landfuz zTownfuzzWaterfuzzRoadfuzzSlopefuzzdevelopfuzz Landfuzz Townfuzz Waterfuzz Roadfuzz Slopefuzz developfuzz Sum the weights in each row. (R1, R2, R3 …) Add the results … Sum = (R1 + R2 + R3 + R4 + R5 + R6).

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

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; u.ac.jp/~thc0456/EAHP/EAHP_manu.html u.ac.jp/~thc0456/EAHP/EAHP_manu.html