Further Discussions on Induced Bias Matrix Model for the Pair-Wise Comparison Matrix

Daji Ergu, Gang Kou (), János Fülöp and Yong Shi
Additional contact information
Daji Ergu: University of Electronic Science and Technology of China
Gang Kou: University of Electronic Science and Technology of China
János Fülöp: Hungarian Academy of Sciences
Yong Shi: University of Nebraska at Omaha

Journal of Optimization Theory and Applications, 2014, vol. 161, issue 3, No 18, 980-993

Abstract: Abstract The inconsistency issue of pairwise comparison matrices has been an important subject in the study of the analytical network process. Most inconsistent elements can efficiently be identified by inducing a bias matrix only based on the original matrix. This paper further discusses the induced bias matrix and integrates all related theorems and corollaries into the induced bias matrix model. The theorem of inconsistency identification is proved mathematically using the maximum eigenvalue method and the contradiction method. In addition, a fast inconsistency identification method for one pair of inconsistent elements is proposed and proved mathematically. Two examples are used to illustrate the proposed fast identification method. The results show that the proposed new method is easier and faster than the existing method for the special case with only one pair of inconsistent elements in the original comparison matrix.

Keywords: Analytic network process (ANP); The induced bias matrix model (IBMM); Inconsistency identification; Reciprocal pairwise comparison matrix (RPCM) (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-012-0223-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:161:y:2014:i:3:d:10.1007_s10957-012-0223-2

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-012-0223-2

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().