Bill Harris <[EMAIL PROTECTED]> writes: > I've attached the crude but documented file I've got right now. At > least it has the process documented. Feel free to make use of (or > improve) it, as you see fit.
Oops; I meant to inline it. Second try: ...................................................................... NB. A program to apply Saaty's method in an interactive fashion. NB. according to the link in http://actifeld.com/A%20Possible%20Method.doc NB. 2006-03-02 NB. John Randall developed the basic algorithm on the J Programming Forum NB. Raul Miller, Tarmo Veskioja, Devon McCormick, and Roger Hui contributed to the dialog NB. Bill Harris put a few other pieces on. NB. The steps: NB. Define the Client Preference Matrix as described on p. 6 of that article NB. Run (%+/)power on that matrix to find the principle eigenvector. NB. Run cr to calculate the Consistency Ratio; if it is much in excess of NB. 0.1, the judgments used to create the CPM are probably too random. NB. Create preference matrices for each of the alternatives on each of NB. the dimensions used in the CPM. Calculate the principal eigenvectors NB. and consistency ratio for each. NB. Create the Option Performance Matrix by assembling all the principal NB. eigenvectors for the preference matrices. NB. Multiply OPM time CVV to get the Value For Money vector. NB. Calculate principal eigenvectors of the matrix cpm by NB. (%+/) power cpm NB. Calculate the principal eigenvalue of the matrix cpm by NB. ev cpm NB. Calculate the consistency ratio of the matrix cpm by NB. cr cpm NB. The VFM shows in each position the relative preference the decision-maker NB. has shown for that alternative: OPM * CVV = VFM NB. If the Option Performance Matrix is NB. opm=: |:a,b,c,:d NB. where a, b, c, and d are the principal eigenvectors of each option matrix NB. then NB. (%/+)opm mp cpm NB. is the Value For Money (VFM) matrix, giving the relative NB. values of each alternative mp=:+/ . * normalize=:%(>./@:|) iterate=:normalize@:mp init=:[: ? # # 0: power=:13 : 'y.&iterate^:_ init y.' NB. If the array a is an n x n matrix, calculate n: n =: # NB. Calculate the principal eigenvalue NB. Postmultiply the current principal eigenvector by the matrix NB. Divide that vector (unnormalized) by the principal eigenvector NB. See p. 258 of Kincaid and Cheney's Numerical Analysis 3rd edition cureigenvec =: (%+/) @: power neweigenvec =: mp cureigenvec ev=: [: {. neweigenvec % cureigenvec NB. Calculate the consistency ratio cr =: (ev - n) % <: @: n NB. Test matrices from Geoff Coyle's paper referenced above: NB. peigen s/b 0.232,0.402,0.061,0.305, cr of 0.055 cpm=: >(1,(%3),5, 1);(3,1,5,1);((%5),(%5),1,(%5));(1,1,5,1) NB. peigen s/b 0.751,0.178,0.071 w/ cr of 0.072 exp=: >(1,5,9);((%5),1,3);((%9),(%3),1) NB. Expenses NB. peigen s/b 0.480,0.406,0.114 w/ cr of 0.026 und=: >(1,1,5);(1,1,3);((%5),(%3),1) NB. "Understandability NB. peigen s/b 0.077,0.231,0.692 w/ cr of 0 rod=: >(1,(%3),%9);(3,1,%3);9 3 1 NB. "Replication of detail", p. 7 NB. peigen s/b 0.066,0.615,0.319 w/ cr of 0 pod=: >(1,(%9),(%5));(9,1,2);(5,(%2),1) NB. Prediction of dynamics ...................................................................... -- Bill Harris http://facilitatedsystems.com/weblog/ Facilitated Systems Everett, WA 98208 USA http://facilitatedsystems.com/ phone: +1 425 337-5541 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
