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Thomas L Saaty - One of the best experts on this subject based on the ideXlab platform.

  • THE ANALYTIC HIERARCHY PROCESS WITHOUT THE THEORY OF OSKAR PERRON
    International Journal of the Analytic Hierarchy Process, 2014
    Co-Authors: Thomas L Saaty
    Abstract:

    It is known and has been mathematically proven that the Principal Eigenvector is necessary for deriving priorities from judgments in the Analytic Hierarchy Process (AHP). According to the work of Oskar Perron, the Principal Eigenvector can be obtained as the limiting power of a positive matrix. In this paper we show that the Principal Eigenvector does not need the theory of Perron for its existence based on the fact that the Principal eigenvalue and corresponding Principal Eigenvector are transparently obtained for a consistent matrix. By perturbation theory the result is obtained for a near consistent matrix. http://dx.doi.org/10.13033/ijahp.v5i2.191

  • Why is the Principal Eigenvector Necessary
    International Series in Operations Research & Management Science, 2012
    Co-Authors: Thomas L Saaty, Luis G. Vargas
    Abstract:

    In the field of decision-making, the concept of priority is quintessential and how priorities are derived influences the choices one makes. Priorities should be unique and not one of many possibilities, they must also capture the dominance of the order expressed in the judgments of the pairwise comparison matrix.

  • decision making with the ahp why is the Principal Eigenvector necessary
    European Journal of Operational Research, 2003
    Co-Authors: Thomas L Saaty
    Abstract:

    In this paper 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. When providing numerical judgments, an individual attempts to estimate sequentially an underlying ratio scale and its equivalent consistent matrix of ratios. Near consistent matrices are essential because when dealing with intangibles, human judgment is of necessity inconsistent, and if with new information one is able to improve inconsistency to near consistency, then that could improve the validity of the priorities of a decision. In addition, judgment is much more sensitive and responsive to large rather than to small perturbations, and hence once near consistency is attained, it becomes uncertain which coefficients should be perturbed by small amounts to transform a near consistent matrix to a consistent one. If such perturbations were forced, they could be arbitrary and thus distort the validity of the derived priority vector in representing the underlying decision.

  • Decision Aiding Decision-making with the AHP: Why is the Principal Eigenvector necessary
    2003
    Co-Authors: Thomas L Saaty
    Abstract:

    In this paper it is shown that the Principal Eigenvector is a necessary representation of the priorities derived from a positive reciprocal pairwise comparison judgment matrix A ¼ð aijÞ when A is a small perturbation of a consistent matrix. When providing numerical judgments, an individual attempts to estimate sequentially an underlying ratio scale and its equivalent consistent matrix of ratios. Near consistent matrices are essential because when dealing with intangibles, human judgment is of necessity inconsistent, and if with new information one is able to improve inconsistency to near consistency, then that could improve the validity of the priorities of a decision. In addition, judgment is much more sensitive and responsive to large rather than to small perturbations, and hence once near consistency is attained, it becomes uncertain which coefficients should be perturbed by small amounts to transform a near consistent matrix to a consistent one. If such perturbations were forced, they could be arbitrary and thus distort the validity of the derived priority vector in representing the underlying decision. 2002 Elsevier Science B.V. All rights reserved.

  • PRIORITY AS DOMINANCE IN DERIVED MEASUREMENT: INVARIANCE OF THE Principal Eigenvector
    International Journal of Information Technology & Decision Making, 2003
    Co-Authors: Thomas L Saaty, Mujgan Ozdemir
    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.