Simulation Experiments for Improving the Consistency Ratio of Reciprocal Matrices

Daji Ergu, Gang Kou, Yi Peng, Xinfeng Yang

Abstract


The consistency issue is one of the hot research topics in the analytic
hierarchy process (AHP) and analytic network process (ANP). To identify the most
inconsistent elements for improving the consistency ratio of a reciprocal pairwise
comparison matrix (PCM), a bias matrix can be induced to efficiently identify the
most inconsistent elements, which is only based on the original PCM. The goal of this
paper is to conduct simulation experiments by randomly generating millions numbers
of reciprocal matrices with different orders in order to validate the effectiveness of
the induced bias matrix model. The experimental results show that the consistency
ratios of most of the random inconsistent matrices can be improved by the induced
bias matrix model, few random inconsistent matrices with high orders failed the
consistency adjustment.


Keywords


Reciprocal random matrix, Consistency ratio, induced bias matrix, simulation experiment; analytic hierarchy process (AHP)/analytic network process (ANP)

Full Text:

PDF

References


Thurstone, L. (1927), A law of comparative judgment, Psychological review, 34(4): 273-273.
http://dx.doi.org/10.1037/h0070288

Saaty, T. L. 1986. Axiomatic Foundation of the Analytic Hierarchy Process, Management Science 32(7): 841-855.
http://dx.doi.org/10.1287/mnsc.32.7.841

Saaty, T. L. (1994), How to Make a Decision: The Analytic Hierarchy Process, Interfaces, 24: 19-43.
http://dx.doi.org/10.1287/inte.24.6.19

Siraj, S.; Mikhailov, L.; Keane, J. (2012), A heuristic method to rectify intransitive judgments in pairwise comparison matrices, European Journal of Operational Research, 216: 420-428.
http://dx.doi.org/10.1016/j.ejor.2011.07.034

Kou, G., Ergu,D., Shang,J. (2014). Enhancing Data Consistency in Decision Matrix: Adapting Hadamard Model to Mitigate Judgment Contradiction, European Journal of Operational Research, 236(1):261-271.
http://dx.doi.org/10.1016/j.ejor.2013.11.035

Saaty, T. L. (1980), The Analytical Hierarchy Process, New York: McGraw-Hill.

Saaty, T. L. (2003). Decision-making with the AHP: Why is the principal eigenvector necessary, European Journal of Operational Research, 145(1): 85-91.
http://dx.doi.org/10.1016/S0377-2217(02)00227-8

Ergu, D.; Kou, G.; Peng, Y.; Shi, Y. (2011). A Simple Method to Improve the Consistency Ratio of the Pair-wise Comparison Matrix in ANP, European Journal of Operational Research, 213(1): 246-259.
http://dx.doi.org/10.1016/j.ejor.2011.03.014

Harker, P. T. 1987. Derivatives of the Perron root of a positive reciprocal matrix: With applications to the analytic hierarchy process, Applied Mathematics and Computation, 22: 217-232.
http://dx.doi.org/10.1016/0096-3003(87)90043-9

Xu, Z., Wei, C. (1999),A consistency improving method in the analytic hierarchy process, European Journal of Operational Research, 116: 443-449.
http://dx.doi.org/10.1016/S0377-2217(98)00109-X

Cao, D., Leung, L. C., Law, J. S. (2008). Modifying inconsistent comparison matrix in analytic hierarchy process: A heuristic approach, Decision Support Systems, 44: 944-953.
http://dx.doi.org/10.1016/j.dss.2007.11.002

Choo, E., Wedley, W. (2004). A common framework for deriving preference values from pairwise comparison matrices, Computer and Operations Research, 31 (6): 893-908.
http://dx.doi.org/10.1016/S0305-0548(03)00042-X

Lin, C. (2007). A revised framework for deriving preference values from pairwise comparison matrices, European Journal of Operational Research, 176 (2): 1145-1150.
http://dx.doi.org/10.1016/j.ejor.2005.09.022

Kou,G, Lin,C. (2014). A cosine maximization method for the priority vector derivation in AHP, European Journal of Operational Research, 235:225-232.
http://dx.doi.org/10.1016/j.ejor.2013.10.019




DOI: https://doi.org/10.15837/ijccc.2014.4.1165



Copyright (c) 2017 Daji Ergu, Gang Kou, Yi Peng, Xinfeng Yang

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

CC-BY-NC  License for Website User

Articles published in IJCCC user license are protected by copyright.

Users can access, download, copy, translate the IJCCC articles for non-commercial purposes provided that users, but cannot redistribute, display or adapt:

  • Cite the article using an appropriate bibliographic citation: author(s), article title, journal, volume, issue, page numbers, year of publication, DOI, and the link to the definitive published version on IJCCC website;
  • Maintain the integrity of the IJCCC article;
  • Retain the copyright notices and links to these terms and conditions so it is clear to other users what can and what cannot be done with the  article;
  • Ensure that, for any content in the IJCCC article that is identified as belonging to a third party, any re-use complies with the copyright policies of that third party;
  • Any translations must prominently display the statement: "This is an unofficial translation of an article that appeared in IJCCC. Agora University  has not endorsed this translation."

This is a non commercial license where the use of published articles for commercial purposes is forbiden. 

Commercial purposes include: 

  • Copying or downloading IJCCC articles, or linking to such postings, for further redistribution, sale or licensing, for a fee;
  • Copying, downloading or posting by a site or service that incorporates advertising with such content;
  • The inclusion or incorporation of article content in other works or services (other than normal quotations with an appropriate citation) that is then available for sale or licensing, for a fee;
  • Use of IJCCC articles or article content (other than normal quotations with appropriate citation) by for-profit organizations for promotional purposes, whether for a fee or otherwise;
  • Use for the purposes of monetary reward by means of sale, resale, license, loan, transfer or other form of commercial exploitation;

    The licensor cannot revoke these freedoms as long as you follow the license terms.

[End of CC-BY-NC  License for Website User]


INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL (IJCCC), With Emphasis on the Integration of Three Technologies (C & C & C),  ISSN 1841-9836.

IJCCC was founded in 2006,  at Agora University, by  Ioan DZITAC (Editor-in-Chief),  Florin Gheorghe FILIP (Editor-in-Chief), and  Misu-Jan MANOLESCU (Managing Editor).

Ethics: This journal is a member of, and subscribes to the principles of, the Committee on Publication Ethics (COPE).

Ioan  DZITAC (Editor-in-Chief) at COPE European Seminar, Bruxelles, 2015:

IJCCC is covered/indexed/abstracted in Science Citation Index Expanded (since vol.1(S),  2006); JCR2018: IF=1.585..

IJCCC is indexed in Scopus from 2008 (CiteScore2018 = 1.56):

Nomination by Elsevier for Journal Excellence Award Romania 2015 (SNIP2014 = 1.029): Elsevier/ Scopus

IJCCC was nominated by Elsevier for Journal Excellence Award - "Scopus Awards Romania 2015" (SNIP2014 = 1.029).

IJCCC is in Top 3 of 157 Romanian journals indexed by Scopus (in all fields) and No.1 in Computer Science field by Elsevier/ Scopus.

 

 Impact Factor in JCR2018 (Clarivate Analytics/SCI Expanded/ISI Web of Science): IF=1.585 (Q3). Scopus: CiteScore2018=1.56 (Q2); Editors-in-Chief: Ioan DZITAC & Florin Gheorghe FILIP.