Important Facts and Observations about Pairwise Comparisons (the special issue edition)

Issue title: Theory and Practice of Pairwise Comparisons

Guest editors: Ryszard Janicki and Konrad Kułakowski

Article type: Research Article

Authors: Koczkodaj, Waldemar W.^{a; *} | Mikhailov, Ludmil^b | Redlarski, Grzegorz^{c; †} | Soltys, Michael^d | Szybowski, Jacek^{e; ‡} | Tamazian, Gaik^{f; §} | Wajch, Eliza^g | Yuen, Kevin Kam Fung^h

Affiliations: [a] Laurentian University, 935 Ramsey Lake Road, Sudbury, Ontario P3E 2C6, Canada. [email protected] | [b] The University of Manchester, M13 9PL, United Kingdom. [email protected] | [c] Gdansk University of Technology, 80-297 Gdansk, Narutowicza st. 11/12, Poland. [email protected] | [d] California State University Channel Islands, One University Drive, Camarillo, CA 93012, USA, [email protected] | [e] AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland. [email protected] | [f] St. Petersburg State University, 198207 Srendiy Prospekt, d. 41, St. Petersburg, Russia. [email protected] | [g] Siedlce University of Natural Sciences and Humanities, 3 Maja 54, 08-110 Siedlice, Poland. [email protected] | [h] Xi’an Jiaotong-Liverpool University, Suzhou 215123, China. [email protected]

Correspondence: [*] Address for correspondence: Laurentian University, 935 Ramsey Lake Road, Sudbury, Ontario P3E 2C6, Canada

Note: [†] Supported in part by the European Union within the European Social Fund - Human Capital Operational Programme HC-OP

Note: [‡] Research supported by the Polish Ministry of Science and Higher Education

Note: [§] Supported, in part, by Russian Ministry of Science (Mega-grant no.11.G34.31.0068) and St.-Petersburg State University (grant no.1.37.165.2014)

Abstract: This study has been inspired by numerous requests for clarification from researchers who often confuse Saaty’s Analytic Hierarchy Process (AHP) with the pairwise comparisons (PC) method, taking AHP as the only representation of PC. This study should be regarded as an interpretation and clarification of past investigations of PC. In addition, this article is a reflection on general PC research at a higher level of abstraction: the philosophy of science. It delves into the foundations and implications of pairwise comparisons. Some results of this study are based on a recently published work by Koczkodaj and Szwarc. Finally, open problems have also been reported for future research.

Keywords: pairwise comparisons, inconsistency analysis, ratio scale, approximation

DOI: 10.3233/FI-2016-1336

Journal: Fundamenta Informaticae, vol. 144, no. 3-4, pp. 291-307, 2016