Best matrix interval for consistent matrices approximating a given reciprocal matrix

• Type: Article in International Scientific Journal
• Date: 2025

Authors

Susana Borges Furtado (Author) FEP; Johnson, CR (Author) Other

Journal

Title: Annals of Operations Research

ISSN: 0254-5330

Publisher: Springer Nature

Indexing

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Other information

Authenticus ID: P-01A-BP6

DOI: 10.1007/s10479-025-06898-w

Abstract (EN): For each efficient vector w associated with an n-by-n reciprocal matrix A, we may form the matrix [ w(i)/w(j) ]. Our primary purpose is to give tight lower and upper bound matrices L-A and U-A such that L-A <= [w(i)/w(j) ] <= U-A (entry-wise). These matrices are calculated from the entries of A and we give insights into their special structure. We then use L-A and U-A to learn more about the cardinal ranking of alternatives associated with the pair-wise ratio comparisons in A. This includes (1) analysis of rank reversals; (2) a transparent characterization of the reciprocal matrices whose efficient vectors have a uniform order; and (3) a simple scheme to select a best order on the underlying alternatives. We discuss when two reciprocal matrices with the same set of efficient vectors are the same. We also mention new possible indices of inconsistency based upon L-A, U-A. They are compared to the classical measure (lambda(A)-n)/(n-1), in which lambda(A) is the Perron root of A.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 20