Showing papers by "Thomas L. Saaty published in 2003"
TL;DR: It is shown that the principal eigenvector is a necessary representation of the priorities derived from a positive reciprocal pairwise comparison judgment matrix A=(aij) when A is a small perturbation of a consistent matrix.
1,184 citations
TL;DR: In this paper, it was shown that the number of elements in a set should be no more than seven plus or minus two, which is the upper limit on the capacity of the human mind to process information on simultaneously interacting elements with reliable accuracy and with validity.
522 citations
TL;DR: In this article, the authors used the analytic hierarchy process to estimate how much more benefits an alternative yields than the alternative with which it is compared, and put the final values in the idealized mode of the AHP and synthesizes the results for the criteria under benefits.
139 citations
01 Jan 2003
TL;DR: In this article, the fundamental scale of absolute numbers for representing judgments is introduced and the principal right eigenvector is shown to be the necessary vector of priorities derived from the possibly inconsistent matrix of comparisons of homogeneous elements.
Abstract: Highlights are given of the decision making theory the Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP) both of which deal with the measurement of tangible and intangible criteria in relative terms by using paired comparisons. The fundamental scale of absolute numbers for representing judgments is introduced and the principal right eigenvector is shown to be the necessary vector of priorities derived from the possibly inconsistent matrix of comparisons of homogeneous elements. A method of synthesis of priorities is proposed. Rank preservation and reversal are discussed. When independent, the alternatives can be rated one at a time with respect to the criteria using intensities. Negative priorities are also introduced. This paper will be followed soon by two other papers.
10 citations
TL;DR: In this paper, it is shown how priorities are derived as the principal right eigenvector of a pairwise comparison matrix and several examples are given to illustrate how the process works.
Abstract: Ranking is a process of prioritization. Priorities, as measurement rather than pure guessing, can be derived from paired comparison judgments that generalize on ratios of actual measurements. Paired comparisons involve the selection of the smaller of the two objects being compared as the unit and estimating how many multiples of that unit the larger object is with respect to an attribute they share. In this paper, it is shown how priorities are derived as the principal right eigenvector of a pairwise comparison matrix and several examples are given to illustrate how the process works.
9 citations
01 Aug 2003
9 citations