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Comparison of analytic hierarchy process and some new optimization procedures for ratio scaling

100%

Kazibudzki P.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2011

tom Vol. 10, nr 1

101-108

Deriving true priority vectors from intuitive pairwise comparison matrices constitutes a key part of the Analytic Hierarchy Process. The Eigenvalue Method, commonly applied in the Analytic Hierarchy Process, is the most popular concept in the process of ratio scaling. It is known that the Eigenvalue Method captures transitivity in matrices that are not consistent in a unique way. However, there are other methods such as statistical estimation techniques and methods based on constrained optimisation models that are equally interesting. This article compares two novel methods for priority vectors deriving, which combine the eigenvalue concept with a constrained optimisation based approach. Evidence is provided that contrary to the logarithmic least squares method, they coincide with the Eigenvalue Method in capturing the ratio scale rank order inherent in inconsistent pairwise comparison judgments.

New optimization based method for estimating priority weights

100%

Grzybowski A. Z.

Journal of Applied Mathematics and Computational Mechanics

2013

tom Vol. 12, nr 1

33--44

The estimation of priority vectors from pairwise comparison matrices is a core of the Analytic Hierarchy Process. Perhaps the most popular approach for deriving the priority weights is the right eigenvalue method (EM). Despite its popularity, various shortcomings of the EM have been described in literature. In this paper a new method for deriving priority vectors is proposed. This method makes use of the idea underlying the EM but in difference to the latter, the new one is optimization based. Important features of this new technique are studied via computer simulations and illustrated by some numerical examples.

Satisfaction of the condition of order preservation: A simulation study

100%

MAZUREK J. , KUŁAKOWSKI K.

Operations Research and Decisions

2020

tom 30

nr 2

77-89

We examine the satisfaction of the condition of order preservation (COP) concerning different levels of inconsistency for randomly generated multiplicative pairwise comparison matrices (MPCMs) of the order from 3 to 9, where a priority vector is derived both by the eigenvalue (eigenvector) method (EV) and the geometric mean (GM) method. Our results suggest that the GM method and the EV method preserve the COP almost identically, both for the less inconsistent matrices (with Saaty’s con-sistency index below 0.10), and the more inconsistent matrices (Saaty’s consistency index equal to or greater than 0.10). Further, we find that the frequency of the COP violations grows (almost linearly) with the increasing inconsistency of MPCMs measured by Koczkodaj’s inconsistency index and Saaty’s consistency index, respectively, and we provide graphs to illustrate these relationships

Satisfaction of the condition of order preservation : a simulation study

88%

Mazurek J. , Kułakowski K.

Operations Research and Decisions

2020

tom Vol. 30, No. 2

77--89

We examine the satisfaction of the condition of order preservation (COP) concerning different levels of inconsistency for randomly generated multiplicative pairwise comparison matrices (MPCMs) of the order from 3 to 9, where a priority vector is derived both by the eigenvalue (eigenvector) method (EV) and the geometric mean (GM) method. Our results suggest that the GM method and the EV method preserve the COP almost identically, both for the less inconsistent matrices (with Saaty’s consistency index below 0.10), and the more inconsistent matrices (Saaty’s consistency index equal to or greater than 0.10). Further, we find that the frequency of the COP violations grows (almost linearly) with the increasing inconsistency of MPCMs measured by Koczkodaj’s inconsistency index and Saaty’s consistency index, respectively, and we provide graphs to illustrate these relationships.

The properties of low pas first order LTV filters

63%

Walczak J. , Piwowar A.

Poznan University of Technology Academic Journals. Electrical Engineering

2011

tom No. 66

137--144

In this paper analysis of impulsive response and stability conditions of first order linear parametric filters has been carried out. The parameters of these filters have been described by some non-periodic functions. The affiliation of models of LTV (linear time-varying) filters to class of frozen systems (system with slowly varying coefficients) has been shown. In this article the BIBO (bounded input bounded output) stability of LTV filters for strictly positive parametric function has been proved using the generalized eigenvalue method.