Analytic Hierarchy Process2

Analytic Hierarchy Process2 - The Analytic Héemrehy...

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Unformatted text preview: The Analytic Héemrehy Process (AB?) is a methodology for analytic decision making. It was ﬁrst introduced by Saaty in 1980 [16], and has been developed into one of the most powerful decision making tools ever since. Assume that there are n elements (alternatives, options} to be ranked. At some stage of the AHP, a matrix P is created, which is called the preference matrix, and whose elements are we; . . pg: w—j, 1,3 =1,...,n. Here numbers mi and w,- are used to compare the alternatives 3‘ and j. To compare two options, a 10-point scale is often used, in which mg, i = 1,. ..,n are assigned values from {0,1,2,. ..,9} as follows. Ifi = j, or a" and j are equal alternatives, then m,- = raj = 1. Otherwise, moderatly strongly very strongly extremely if i is preferable over 3'. E || ED'NI'UTW The numbers 2, 4, 6, 8 are used for levels of preference compromising between two of the speciﬁed above. In all of these cases, in,- is set equal to 1. For example, if element 3‘ is strongly preferable over element j, we have pij- = 5 and p3}- = 1/5. Zeroes are used when there is no enough information to compare two elements, in which case the diagonal element in each row is increased by the number of zeroes in that row. As soon as the preference matrix is constructed, one of the techniques used to rank the elements is the following eigenvalue method. Denote by w the eigenvector of P corresponding to its largest eigenvalue. Then element 1' is assigned the value of WU], and the elements are ranked accordingly to the nonincreasing order of the components of vector w. ...
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