Comparative Assessment of the Stability of AHP and FAHP Methods
Mathematical models describing physical, technical, economic, and other processes can be used to analyze these processes and predict their results, providing that these models are stable and their results are stable relative to the model parameters used. Small changes in the values of the model para...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2021-03-01
|
Series: | Symmetry |
Subjects: | |
Online Access: | https://www.mdpi.com/2073-8994/13/3/479 |
id |
doaj-fbc299c9e6e744828a15ec7926b358b2 |
---|---|
record_format |
Article |
spelling |
doaj-fbc299c9e6e744828a15ec7926b358b22021-03-16T00:03:11ZengMDPI AGSymmetry2073-89942021-03-011347947910.3390/sym13030479Comparative Assessment of the Stability of AHP and FAHP MethodsIrina Vinogradova-Zinkevič0Valentinas Podvezko1Edmundas Kazimeras Zavadskas2Department of Information Technologies, Vilnius Gediminas Technical University, Saulėtekio al. 11, 10223 Vilnius, LithuaniaDepartment of Mathematical Statistics, Vilnius Gediminas Technical University, Saulėtekio al. 11, 10223 Vilnius, LithuaniaLaboratory of Operational Research, Institute of Sustainable Construction, Vilnius Gediminas Technical University, Saulėtekio al. 11, 10223 Vilnius, LithuaniaMathematical models describing physical, technical, economic, and other processes can be used to analyze these processes and predict their results, providing that these models are stable and their results are stable relative to the model parameters used. Small changes in the values of the model parameters correspond to small changes in the results. Multicriteria decision-making models need to check the results’ stability against the models’ main components: the values of the criteria weights and the elements of the decision matrix. In this article, we study the stability of models associated with the calculation of criteria weights. For the analysis, the most commonly used models are taken—the Analytic Hierarchy Process (AHP) method and the fuzzy Analytic Hierarchy Process (FAHP) method, in which fuzzy numbers are used under conditions of data uncertainty. Both mathematically well-based methods verify the consistency of the expert evaluations. The method of statistical simulation (Monte Carlo) is the basis for studying the results’ stability. The study checks the experts’ provided evaluations’ consistency, calculates the criteria weights, and evaluates their relative errors after a slight change in the estimates of the pairwise comparisons of the criteria provided by the experts. The matrix of comparisons of the FAHP method is constructed based on the entire expert group’s assessments. It estimates the boundaries of variance in the fuzzy criteria weights. This paper estimates the stability of the criteria’ weights associated with the mathematical methods themselves and the experts’ estimates. The results are useful to study the stability of specific MCDM methods when ranking alternatives.https://www.mdpi.com/2073-8994/13/3/479Analytic Hierarchy Processfuzzy Analytic Hierarchy Processsymmetric and asymmetric fuzzy numbersuncertaintystability |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Irina Vinogradova-Zinkevič Valentinas Podvezko Edmundas Kazimeras Zavadskas |
spellingShingle |
Irina Vinogradova-Zinkevič Valentinas Podvezko Edmundas Kazimeras Zavadskas Comparative Assessment of the Stability of AHP and FAHP Methods Symmetry Analytic Hierarchy Process fuzzy Analytic Hierarchy Process symmetric and asymmetric fuzzy numbers uncertainty stability |
author_facet |
Irina Vinogradova-Zinkevič Valentinas Podvezko Edmundas Kazimeras Zavadskas |
author_sort |
Irina Vinogradova-Zinkevič |
title |
Comparative Assessment of the Stability of AHP and FAHP Methods |
title_short |
Comparative Assessment of the Stability of AHP and FAHP Methods |
title_full |
Comparative Assessment of the Stability of AHP and FAHP Methods |
title_fullStr |
Comparative Assessment of the Stability of AHP and FAHP Methods |
title_full_unstemmed |
Comparative Assessment of the Stability of AHP and FAHP Methods |
title_sort |
comparative assessment of the stability of ahp and fahp methods |
publisher |
MDPI AG |
series |
Symmetry |
issn |
2073-8994 |
publishDate |
2021-03-01 |
description |
Mathematical models describing physical, technical, economic, and other processes can be used to analyze these processes and predict their results, providing that these models are stable and their results are stable relative to the model parameters used. Small changes in the values of the model parameters correspond to small changes in the results. Multicriteria decision-making models need to check the results’ stability against the models’ main components: the values of the criteria weights and the elements of the decision matrix. In this article, we study the stability of models associated with the calculation of criteria weights. For the analysis, the most commonly used models are taken—the Analytic Hierarchy Process (AHP) method and the fuzzy Analytic Hierarchy Process (FAHP) method, in which fuzzy numbers are used under conditions of data uncertainty. Both mathematically well-based methods verify the consistency of the expert evaluations. The method of statistical simulation (Monte Carlo) is the basis for studying the results’ stability. The study checks the experts’ provided evaluations’ consistency, calculates the criteria weights, and evaluates their relative errors after a slight change in the estimates of the pairwise comparisons of the criteria provided by the experts. The matrix of comparisons of the FAHP method is constructed based on the entire expert group’s assessments. It estimates the boundaries of variance in the fuzzy criteria weights. This paper estimates the stability of the criteria’ weights associated with the mathematical methods themselves and the experts’ estimates. The results are useful to study the stability of specific MCDM methods when ranking alternatives. |
topic |
Analytic Hierarchy Process fuzzy Analytic Hierarchy Process symmetric and asymmetric fuzzy numbers uncertainty stability |
url |
https://www.mdpi.com/2073-8994/13/3/479 |
work_keys_str_mv |
AT irinavinogradovazinkevic comparativeassessmentofthestabilityofahpandfahpmethods AT valentinaspodvezko comparativeassessmentofthestabilityofahpandfahpmethods AT edmundaskazimeraszavadskas comparativeassessmentofthestabilityofahpandfahpmethods |
_version_ |
1724220376767004672 |